7933:
6787:
7928:{\displaystyle \mathbf {U^{u}} ={\begin{bmatrix}{-{\sqrt {\mathbf {x^{2}+y^{2}} }} \over {\sqrt {\mathbf {2(x^{2}+y^{2}+x^{2}y^{2})} }}}&{\mathbf {x(y^{2}-i{\sqrt {\mathbf {x^{2}+y^{2}+x^{2}y^{2}} }})} \over {{\sqrt {2}}{\sqrt {\mathbf {x^{2}+y^{2}} }}{\sqrt {\mathbf {x^{2}+y^{2}+x^{2}y^{2}} }}}}&{\mathbf {y(x^{2}+i{\sqrt {\mathbf {x^{2}+y^{2}+x^{2}y^{2}} }})} \over {{\sqrt {2}}{\sqrt {\mathbf {x^{2}+y^{2}} }}{\sqrt {\mathbf {x^{2}+y^{2}+x^{2}y^{2}} }}}}\\{-{\sqrt {\mathbf {x^{2}+y^{2}} }} \over {\sqrt {\mathbf {2(x^{2}+y^{2}+x^{2}y^{2})} }}}&{\mathbf {x(y^{2}+i{\sqrt {\mathbf {x^{2}+y^{2}+x^{2}y^{2}} }})} \over {{\sqrt {2}}{\sqrt {\mathbf {x^{2}+y^{2}} {\sqrt {\mathbf {x^{2}+y^{2}+x^{2}y^{2}} }}}}}}&{\mathbf {y(x^{2}-i{\sqrt {\mathbf {x^{2}+y^{2}+x^{2}y^{2}} )}} \over {{\sqrt {\bf {2}}}{\sqrt {\bf {x^{2}+y^{2}}}}{\sqrt {\bf {x^{2}+y^{2}+x^{2}y^{2}}}}}} }\\{\mathbf {xy} \over {\sqrt {\mathbf {x^{2}+y^{2}+x^{2}y^{2}} }}}&{\mathbf {y \over {\sqrt {\mathbf {x^{2}+y^{2}+x^{2}y^{2}} }}} }&{\mathbf {x \over {\sqrt {\mathbf {x^{2}+y^{2}+x^{2}y^{2}} }}} }\end{bmatrix}}.}
14541:
4014:
10159:
9283:
932:
14796:
924:
10563:
9687:
8682:
8379:
12286:
12485:< 0 would undergo an opposite CP violation, so the CP-symmetry would be preserved as a whole. The anomalous excess of matter over antimatter after the Big Bang in the orthochronous (or positive) sector, becomes an excess of antimatter before the Big Bang (antichronous or negative sector) as both charge conjugation, parity and arrow of time are reversed due to CPT reflections of all phenomena occurring over the initial singularity:
44:
3732:
2767:
14808:
6053:
11322:
6228:
12168:
8386:
8086:
2422:
4009:{\displaystyle \mathbf {M^{2}} ={\begin{bmatrix}\mathbf {A_{1}} &\mathbf {B_{1}} +i\mathbf {C_{1}} &\mathbf {B_{2}} +i\mathbf {C_{2}} \\\mathbf {B_{1}} -i\mathbf {C_{1}} &\mathbf {A_{2}} &\mathbf {B_{3}} +i\mathbf {C_{3}} \\\mathbf {B_{2}} -i\mathbf {C_{2}} &\mathbf {B_{3}} -i\mathbf {C_{3}} &\mathbf {A_{3}} \end{bmatrix}},}
10924:
5865:
3674:
9693:
8817:
11940:
6057:
668:
The combination of CPT is thought to constitute an exact symmetry of all types of fundamental interactions. Because of the long-held CPT symmetry theorem, provided that it is valid, a violation of the CP-symmetry is equivalent to a violation of the T-symmetry. In this theorem, regarded as one of the
10165:
9289:
8677:{\displaystyle V=V{\begin{bmatrix}2\\3\\1\end{bmatrix}}{\begin{bmatrix}2&3&1\end{bmatrix}}=V^{*}=V^{*}{\begin{bmatrix}1\\3\\2\end{bmatrix}}{\begin{bmatrix}1&3&2\end{bmatrix}}={\begin{bmatrix}r&p&s^{*}\\p^{\prime *}&q&p^{\prime }\\s&p^{*}&r^{*}\end{bmatrix}},}
8374:{\displaystyle V=V{\begin{bmatrix}1\\3\\2\end{bmatrix}}{\begin{bmatrix}2&3&1\end{bmatrix}}=V^{*}=V^{*}{\begin{bmatrix}2\\3\\1\end{bmatrix}}{\begin{bmatrix}1&3&2\end{bmatrix}}={\begin{bmatrix}s&p^{*}&r^{*}\\p^{\prime *}&q&p^{\prime }\\r&p&s^{*}\end{bmatrix}}}
11527:
895:
or parity symmetry, but also their combination. The discovery shocked particle physics and opened the door to questions still at the core of particle physics and of cosmology today. The lack of an exact CP-symmetry, but also the fact that it is so close to a symmetry, introduced a great puzzle.
11862:
Since the discovery of CP violation in 1964, physicists have believed that in theory, within the framework of the
Standard Model, it is sufficient to search for appropriate Yukawa couplings (equivalent to a mass matrix) in order to generate a complex phase in the CKM matrix, thus automatically
2206:
578:
symmetry). CP-symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle (C-symmetry) while its spatial coordinates are inverted ("mirror" or P-symmetry). The discovery of CP violation in 1964 in the decays of neutral
2762:{\displaystyle {\begin{alignedat}{3}M&=|M_{1}|\ e^{i\theta _{1}}\ e^{i\phi _{1}}&&+|M_{2}|\ e^{i\theta _{2}}\ e^{i\phi _{2}}\\{\bar {M}}&=|M_{1}|\ e^{i\theta _{1}}\ e^{-i\phi _{1}}&&+|M_{2}|\ e^{i\theta _{2}}\ e^{-i\phi _{2}}\ .\end{alignedat}}}
6346:
6048:{\displaystyle \mathbf {M^{2}} ={\begin{bmatrix}\mathbf {A} +\mathbf {B(xy-{x \over y})} &\mathbf {yB} &\mathbf {xB} \\\mathbf {yB} &\mathbf {A+B({y \over x}-{x \over y})} &\mathbf {B} \\\mathbf {xB} &\mathbf {B} &\mathbf {A} \end{bmatrix}}}
2977:
832:
Oehme then wrote a paper with Lee and Yang in which they discussed the interplay of non-invariance under P, C and T. The same result was also independently obtained by Ioffe, Okun and Rudik. Both groups also discussed possible CP violations in neutral kaon decays.
6692:
6560:
10930:
3383:
10154:{\displaystyle s={{(x^{2}+y^{2})(x'^{2}+y'^{2})+(xx'+yy')(xyx'y'-{\sqrt {x^{2}+y^{2}+x^{2}y^{2}}}{\sqrt {x'^{2}+y'^{2}+x'^{2}y'^{2}}})} \over {2{\sqrt {x^{2}+y^{2}}}{\sqrt {x'^{2}+y'^{2}}}{\sqrt {x^{2}+y^{2}+x^{2}y^{2}}}{\sqrt {x'^{2}+y'^{2}+x'^{2}y'^{2}}}}}}
9278:{\displaystyle r={{(x^{2}+y^{2})(x'^{2}+y'^{2})+(xx'+yy')(xyx'y'+{\sqrt {x^{2}+y^{2}+x^{2}y^{2}}}{\sqrt {x'^{2}+y'^{2}+x'^{2}y'^{2}}})} \over {2{\sqrt {x^{2}+y^{2}}}{\sqrt {x'^{2}+y'^{2}}}{\sqrt {x^{2}+y^{2}+x^{2}y^{2}}}{\sqrt {x'^{2}+y'^{2}+x'^{2}y'^{2}}}}}}
3067:
794:
5727:
1416:
12404:
sector, has been observed experimentally and can only account for a small portion of the CP violation required to explain the matter-antimatter asymmetry. The strong interaction should also violate CP, in principle, but the failure to observe the
10569:
5589:
matrix patterns given above are the most general ones. The perfect way to solve the CPV problem in the standard model is to diagonalize such matrices analytically and to achieve a U matrix which applies to both. Unfortunately, even though the
6223:{\displaystyle +i{\begin{bmatrix}0&\mathbf {C \over y} &-\mathbf {C \over x} \\-\mathbf {C \over y} &0&\mathbf {C} \\i\mathbf {C \over x} &-\mathbf {C} &0\end{bmatrix}}\equiv \mathbf {M_{R}^{2}} +i\mathbf {M_{I}^{2}} ,}
5495:
5324:
5153:
4982:
4811:
4640:
3678:
This M matrix contains 9 elements and 18 parameters, 9 from the real coefficients and 9 from the imaginary coefficients. Obviously, a 3x3 matrix with 18 parameters is too difficult to diagonalize analytically. However, a naturally
Hermitian
12172:
For a nonzero choice of the θ angle and the chiral phase of the quark mass θ′ one expects the CP-symmetry to be violated. One usually assumes that the chiral quark mass phase can be converted to a contribution to the total effective
12393:, and so on. This would have resulted in a sea of radiation in the universe with no matter. Since this is not the case, after the Big Bang, physical laws must have acted differently for matter and antimatter, i.e. violating CP-symmetry.
665:, which corresponds to reversal of motion. Invariance under time reversal implies that whenever a motion is allowed by the laws of physics, the reversed motion is also an allowed one and occurs at the same rate forwards and backwards.
4469:
4328:
4187:
10558:{\displaystyle +i{{(xy'-x'y)(x'y'{\sqrt {x^{2}+y^{2}+x^{2}y^{2}}}-xy{\sqrt {x'^{2}+y'^{2}+x'^{2}y'^{2}}})} \over {2{\sqrt {x^{2}+y^{2}}}{\sqrt {x'^{2}+y'^{2}}}{\sqrt {x^{2}+y^{2}+x^{2}y^{2}}}{\sqrt {x'^{2}+y'^{2}+x'^{2}y'^{2}}}}},}
9682:{\displaystyle +i{{(xy'-x'y)(x'y'{\sqrt {x^{2}+y^{2}+x^{2}y^{2}}}+xy{\sqrt {x'^{2}+y'^{2}+x'^{2}y'^{2}}})} \over {2{\sqrt {x^{2}+y^{2}}}{\sqrt {x'^{2}+y'^{2}}}{\sqrt {x^{2}+y^{2}+x^{2}y^{2}}}{\sqrt {x'^{2}+y'^{2}+x'^{2}y'^{2}}}}},}
12163:{\displaystyle {\mathcal {L}}=-{\frac {1}{4}}F_{\mu \nu }F^{\mu \nu }-{\frac {n_{f}g^{2}\theta }{32\pi ^{2}}}F_{\mu \nu }{\tilde {F}}^{\mu \nu }+{\bar {\psi }}\left(i\gamma ^{\mu }D_{\mu }-me^{i\theta '\gamma _{5}}\right)\psi }
8078:. As mentioned earlier, there are no inherent constraints that dictate the assignment of eigenvalues to specific quark flavors. Consequently, all 36 potential permutations of eigenvalues are listed in the provided reference
8015:
6778:
2057:
1517:
12465:
would be required to explain additional sources of CP violation. Adding new particles and/or interactions to the
Standard Model generally introduces new sources of CP violation since CP is not a symmetry of nature.
722:
revealed that while parity conservation had been verified in decays by the strong or electromagnetic interactions, it was untested in the weak interaction. They proposed several possible direct experimental tests.
12366:. Explanations which do not involve CP violation are less plausible, since they rely on the assumption that the matter–antimatter imbalance was present at the beginning, or on other admittedly exotic assumptions.
11810:
2776:
12204:
angle, but it remains to be explained why this angle is extremely small instead of being of order one; the particular value of the θ angle that must be very close to zero (in this case) is an example of a
12445:
could have two additional CP violating
Majorana phases, leading to a fourth source of CP violation within the Standard Model. The experimental evidence for Majorana neutrinos would be the observation of
12655:
11916:
fields, the gluons couple to vector currents. Experiments do not indicate any CP violation in the QCD sector. For example, a generic CP violation in the strongly interacting sector would create the
2336:
2297:
1777:
8021:
After obtaining a general U matrix pattern, it can also be applied to down-type quarks by introducing primed parameters. To construct the CKM matrix, the U matrix for up-type quarks, denoted as
2062:
11863:
breaking CP symmetry. However, the specific matrix pattern has remained elusive. The above derivation provides the first evidence for this idea and offers some explicit examples to support it.
887:
decay that CP-symmetry could be broken. (cf. also Ref. ). This work won them the 1980 Nobel Prize. This discovery showed that weak interactions violate not only the charge-conjugation symmetry
6235:
1285:
11317:{\displaystyle p^{\prime }={{+i(xy'-x'y){\sqrt {x'^{2}+y'^{2}+x'^{2}y'^{2}}}} \over {{\sqrt {2}}{\sqrt {x^{2}+y^{2}+x^{2}y^{2}}}{\sqrt {x'^{2}+y'^{2}}}{\sqrt {x'^{2}+y'^{2}+x'^{2}y'^{2}}}}},}
6566:
3669:{\displaystyle M={\begin{bmatrix}A_{1}+iD_{1}&B_{1}+iC_{1}&B_{2}+iC_{2}\\B_{4}+iC_{4}&A_{2}+iD_{2}&B_{3}+iC_{3}\\B_{5}+iC_{5}&B_{6}+iC_{6}&A_{3}+iD_{6}\end{bmatrix}}.}
2415:
1267:
mixing. A necessary condition for the appearance of the complex phase is the presence of at least three generations of fermions. If fewer generations are present, the complex phase parameter
12409:
in experiments suggests that any CP violation in the strong sector is also too small to account for the necessary CP violation in the early universe. The third source of CP violation is the
12202:
2374:
6436:
6396:
3141:
3104:
11682:
11606:
3725:
12458:. This could become the preferred explanation in the Standard Model for the matter-antimatter asymmetry of the universe if CP violation is experimentally confirmed in the lepton sector.
2987:
11328:
5624:
1903:
14167:
13824:
11858:
5826:
5763:
3214:
3176:
1724:
10919:{\displaystyle p={{+i(xy'-x'y){\sqrt {x^{2}+y^{2}+x^{2}y^{2}}}} \over {{\sqrt {2}}{\sqrt {x^{2}+y^{2}}}{\sqrt {x^{2}+y^{2}+x^{2}y^{2}}}{\sqrt {x'^{2}+y'^{2}+x'^{2}y'^{2}}}}},}
6429:
5858:
5792:
5617:
5587:
5555:
5526:
4045:
2048:
1562:
3372:
1942:
1692:
8719:
1977:
1838:
1654:
738:, and demonstrated conclusively that weak interactions violate the P-symmetry or, as the analogy goes, some reactions did not occur as often as their mirror image. However,
2254:
8810:
5330:
5159:
4988:
4817:
4646:
4475:
1444:
13703:
Kelly, Kevin J.; Machado, Pedro A.N.; Parke, Stephen J.; Perez-Gonzalez, Yuber F.; Funchal, Renata
Zukanovich (2021). "Neutrino mass ordering in light of recent data".
12425:, may be able to find evidence of CP violation over a small fraction of possible values of the CP violating Dirac phase while the proposed next-generation experiments,
8783:
8739:
821:
who observed parity non-conservation in pion and muon decay and found that C is also violated. Charge violation was more explicitly shown in experiments done by
801:
and A. P. Rudik showed that the parity violation meant that charge conjugation invariance must also be violated in weak decays. Charge violation was confirmed in the
8076:
2006:
1619:
8046:
3332:
3305:
3275:
3248:
1803:
1590:
1566:
The reason why such a complex phase causes CP violation is not immediately obvious, but can be seen as follows. Consider any given particles (or sets of particles)
1231:
beams. The results were not yet precise enough to determine the size of the CP violation, relative to that seen in quarks. In addition, another similar experiment,
1098:
911:
is replaced with the other's antiquark) and vice versa, but such transformation does not occur with exactly the same probability in both directions; this is called
706:
symmetry was that the equations of particle physics are invariant under mirror inversion. This led to the prediction that the mirror image of a reaction (such as a
12433:, will be sensitive enough to definitively observe CP violation over a relatively large fraction of possible values of the Dirac phase. Further into the future, a
4334:
4193:
4052:
12369:
The Big Bang should have produced equal amounts of matter and antimatter if CP-symmetry was preserved; as such, there should have been total cancellation of both—
650:
seem to be invariant under the combined CP transformation operation, further experiments showed that this symmetry is slightly violated during certain types of
13613:
Abe, K.; Akutsu, R.; et al. (T2K Collaboration) (16 April 2020). "Constraint on the matter-antimatter symmetry-violating phase in neutrino oscillations".
1040:" experiments, there was a logical possibility that all CP violation was confined to kaon physics. However, this raised the question of why CP violation did
14134:(A compilation of reprints of numerous important papers on the topic, including papers by T.D. Lee, Cronin, Fitch, Kobayashi and Maskawa, and many others.)
12905:
Culligan, G.; Frank, S. G. F.; Holt, J. R. (1959). "Longitudinal polarization of the electrons from the decay of unpolarized
Positive and Negative Muons".
1276:
714:) occurs at the same rate as the original reaction. However, in 1956 a careful critical review of the existing experimental data by theoretical physicists
689:, respectively. Already in 1970 Klaus Schubert observed T violation independent of assuming CPT symmetry by using the Bell–Steinberger unitarity relation.
14426:
533:
470:
12442:
12410:
7940:
859:
was assumed to be equivalent to the mirror image of the original process and so the combined CP-symmetry would be conserved in the weak interaction.
12806:
13758:
Denton, Peter B.; Gehrlein, Julia; Pestes, Rebekah (2021). "CP-Violating
Neutrino Non-Standard Interactions in Long-Baseline-Accelerator Data".
6698:
1449:
14570:
2981:
Thus, we see that a complex phase gives rise to processes that proceed at different rates for particles and antiparticles, and CP is violated.
12447:
14678:
12358:
as might be expected. It can be demonstrated that, to create an imbalance in matter and antimatter from an initial condition of balance, the
2427:
337:
237:
12943:
1063:
using 0.6 fb of Run 1 data. However, the same measurement using the full 3.0 fb Run 1 sample was consistent with CP-symmetry.
14854:
13198:
Fanti, V.; et al. (NA48 Collaboration) (1999). "A new measurement of direct CP violation in two pion decays of the neutral kaon".
12461:
If CP violation in the lepton sector is experimentally determined to be too small to account for matter-antimatter asymmetry, some new
11688:
14812:
12864:"Observations of the Failure of Conservation of Parity and Charge Conjugation in Meson Decays: The Magnetic Moment of the Free Muon"
14555:
12559:
12397:
2201:{\displaystyle {\begin{aligned}M&=|M|\ e^{i\theta }\ e^{+i\phi }\\{\bar {M}}&=|M|\ e^{i\theta }\ e^{-i\phi }\end{aligned}}}
14280:
14419:
3378:
For a standard model with three fermion generations, the most general non-Hermitian pattern of its mass matrices can be given by
526:
13025:
1274:
A popular rephasing invariant whose vanishing signals absence of CP violation and occurs in most CP violating amplitudes is the
5528:
matrix with 9 parameters, it has the same effect as diagonalizing an M matrix with 18 parameters. Therefore, diagonalizing the
257:
14256:
12362:
must be satisfied, one of which is the existence of CP violation during the extreme conditions of the first seconds after the
14673:
14155:
14126:
14100:
14077:
14054:
14031:
332:
2302:
2263:
14319:
12274:
11887:
1729:
997:
CP violation). The observation was somewhat controversial, and final proof for it came in 1999 from the KTeV experiment at
187:
6341:{\displaystyle \mathbf {A\equiv A_{3}} ,\mathbf {B\equiv B_{3}} ,\mathbf {C\equiv C_{3}} ,\mathbf {x\equiv B_{2}/B_{3}} ,}
2972:{\displaystyle |M|^{2}-|{\bar {M}}|^{2}=-4\ |M_{1}|\ |M_{2}|\ \sin(\theta _{1}-\theta _{2})\ \sin(\phi _{1}-\phi _{2})\ .}
862:
In 1962, a group of experimentalists at Dubna, on Okun's insistence, unsuccessfully searched for CP-violating kaon decay.
14756:
12907:
12825:
Friedman, J. I.; Telegdi, V. L. (1957). "Nuclear
Emulsion Evidence for Parity Nonconservation in the Decay Chain π→μ→e".
6687:{\displaystyle \mathbf {m_{2}^{2}} =\mathbf {A-B{x \over y}+C{{\sqrt {\mathbf {x^{2}+y^{2}+x^{2}y^{2}} }} \over {xy}}} ,}
475:
192:
13380:
14412:
13998:
11897:. As there is no known reason for it to be conserved in QCD specifically, this is a "fine tuning" problem known as the
6555:{\displaystyle \mathbf {m_{1}^{2}} =\mathbf {A-B{x \over y}-C{\sqrt {\mathbf {x^{2}+y^{2}+x^{2}y^{2}} \over {xy}}}} ,}
855:: C for charge conjugation and P for parity. In other words, a process in which all particles are exchanged with their
519:
2379:
1107:
reported some indications of CP violation in leptons for the first time. In this experiment, beams of muon neutrinos (
14580:
12493:< 0 from contracting matter having an excess of antiquarks, that they pass "one through the other" at the instant
12462:
12333:
12210:
12176:
2341:
35:
14279:
An elementary discussion of parity violation and CP violation is given in chapter 15 of this student level textbook
12315:
6351:
3109:
3072:
14761:
14092:
11612:
11536:
3682:
3062:{\displaystyle \ \mathrm {V} _{\mathsf {CKM}}=\mathrm {U} _{\mathsf {u}}\ \mathrm {U} _{\mathsf {d}}^{\dagger }\ ,}
480:
222:
11522:{\displaystyle q={{xx'+yy'+xyx'y'} \over {{\sqrt {x^{2}+y^{2}+x^{2}y^{2}}}{\sqrt {x'^{2}+y'^{2}+x'^{2}y'^{2}}}}},}
12579:
13677:
12477:
of events on each side of what he called the "initial singularity". Because of this, phenomena with an opposite
5722:{\displaystyle \mathbf {M_{R}^{2}} }\cdot \mathbf {M_{I}^{2+}} -\mathbf {M_{I}^{2}} \cdot \mathbf {M_{R}^{2+}=0}
14721:
13476:
Aaij, R.; et al. (LHCb
Collaboration) (30 May 2013). "First Observation of CP Violation in the Decays of B
13423:
12454:
experiment. CP violation in the lepton sector generates a matter-antimatter asymmetry through a process called
12406:
12311:
427:
13930:
I. Bars; C. Deliduman; O. Andreev (1998). "Gauged
Duality, Conformal Symmetry, and Spacetime with Two Times".
1847:
14834:
14612:
14560:
12307:
114:
13544:
5619:
matrix has only 9 parameters, it is still too complicated to be diagonalized directly. Thus, an assumption
14771:
14118:
12574:
490:
147:
11817:
5797:
5734:
3181:
1411:{\displaystyle \ J=c_{12}\ c_{13}^{2}\ c_{23}\ s_{12}\ s_{13}\ s_{23}\ \sin \delta \ \approx \ 0.00003\ ,}
3146:
647:
17:
13253:
Aubert, B; et al. (2001). "Measurement of CP-Violating Asymmetries in B Decays to CP Eigenstates".
1697:
14844:
14069:
12616:
Schwarzschild, Bertram (1999). "Two Experiments Observe Explicit Violation of Time-Reversal Symmetry".
985:
Despite many searches, no other manifestation of CP violation was discovered until the 1990s, when the
12396:
The Standard Model contains at least three sources of CP violation. The first of these, involving the
6405:
5834:
5768:
5593:
5563:
5531:
5502:
4021:
2011:
1522:
14849:
14726:
14208:
12989:
11932:
3337:
1908:
1659:
442:
267:
252:
232:
12534:
8689:
1947:
1808:
1624:
639:
14731:
14312:
13139:
Alavi-Harati, A.; et al. (KTeV Collaboration) (1999). "Observation of Direct CP Violation in K
12973:
12451:
12437:
could be sensitive to nearly all possible values of the CP violating Dirac phase. If neutrinos are
12296:
12229:
5490:{\displaystyle \mathbf {C_{3}} =C_{4}B_{5}-B_{4}C_{5}+D_{2}B_{6}-A_{2}C_{6}+A_{3}C_{3}-B_{3}D_{3}.}
5319:{\displaystyle \mathbf {C_{2}} =D_{1}B_{5}-A_{1}C_{5}+B_{6}C_{1}-B_{1}C_{6}+A_{3}C_{2}-B_{2}D_{3},}
5148:{\displaystyle \mathbf {C_{1}} =D_{1}B_{4}-A_{1}C_{4}+A_{2}C_{1}-B_{1}D_{2}+B_{3}C_{2}-B_{2}C_{3},}
4977:{\displaystyle \mathbf {B_{3}} =B_{4}B_{5}+C_{4}C_{5}+B_{6}A_{2}+C_{6}D_{2}+A_{3}B_{3}+D_{3}C_{3},}
4806:{\displaystyle \mathbf {B_{2}} =A_{1}B_{5}+D_{1}C_{5}+B_{1}B_{6}+C_{1}C_{6}+B_{2}A_{3}+C_{2}D_{3},}
4635:{\displaystyle \mathbf {B_{1}} =A_{1}B_{4}+D_{1}C_{4}+B_{1}A_{2}+C_{1}D_{2}+B_{2}B_{3}+C_{2}C_{3},}
635:
452:
302:
8048:, can be multiplied with the conjugate transpose of the U matrix for down-type quarks, denoted as
2213:
14800:
14645:
14513:
14503:
14023:
13760:
13552:
13482:
13318:
13255:
13145:
13091:
12300:
12217:
8788:
1151:. By the time they got to the detector, a significantly higher proportion of electron neutrinos (
826:
182:
1423:
673:, charge conjugation, parity, and time reversal are applied together. Direct observation of the
14518:
14491:
12455:
12259:
11917:
11894:
631:
584:
432:
422:
367:
357:
142:
94:
13316:
Abe K; et al. (2001). "Observation of Large CP Violation in the Neutral B Meson System".
8747:
8724:
14766:
14640:
14607:
13024:
Anikina, M. Kh.; Neagu, D. V.; Okonov, E. O.; Petrov, N. I.; Rozanova, A. M.; Rusakov, V. A.
12206:
4464:{\displaystyle \mathbf {A_{3}} =A_{3}^{2}+D_{3}^{2}+B_{5}^{2}+C_{5}^{2}+B_{6}^{2}+C_{6}^{2},}
4323:{\displaystyle \mathbf {A_{2}} =A_{2}^{2}+D_{2}^{2}+B_{3}^{2}+C_{3}^{2}+B_{4}^{2}+C_{4}^{2},}
4182:{\displaystyle \mathbf {A_{1}} =A_{1}^{2}+D_{1}^{2}+B_{1}^{2}+C_{1}^{2}+B_{2}^{2}+C_{2}^{2},}
1235:
sees no evidence of CP violation in neutrino oscillations and is in slight tension with T2K.
810:
485:
447:
262:
242:
177:
52:
49:
12216:
There are several proposed solutions to solve the strong CP problem. The most well-known is
8051:
1982:
1595:
14716:
14655:
14650:
14624:
14471:
14227:
14186:
14147:
14108:(A collection of essays introducing the subject, with an emphasis on experimental results.)
13951:
13902:
13843:
13779:
13724:
13634:
13571:
13501:
13442:
13337:
13274:
13219:
13164:
13100:
12998:
12957:
12916:
12877:
12836:
12766:
12723:
12674:
12627:
8024:
3310:
3283:
3253:
3226:
1782:
1569:
1148:
1076:
670:
412:
307:
172:
167:
162:
124:
1044:
extend to the strong force, and furthermore, why this was not predicted by the unextended
657:
Only a weaker version of the symmetry could be preserved by physical phenomena, which was
8:
14683:
14383:
14305:
13127:
13042:
12359:
11909:
5831:
Such an assumption could further reduce the parameter number from 9 to 5 and the reduced
993:
suggested evidence for CP violation in the decay process of the very same neutral kaons (
852:
626:
Until the 1950s, parity conservation was believed to be one of the fundamental geometric
14231:
14190:
13955:
13906:
13847:
13783:
13728:
13638:
13575:
13505:
13446:
13341:
13278:
13223:
13168:
13104:
13002:
12961:
12920:
12881:
12840:
12770:
12727:
12678:
12631:
1028:) in Japan, observed direct CP violation in a different system, namely in decays of the
14839:
14711:
14481:
14393:
14243:
14217:
14176:
14139:
13967:
13941:
13892:
13859:
13833:
13803:
13769:
13740:
13714:
13658:
13624:
13595:
13561:
13525:
13491:
13458:
13432:
13401:
13361:
13327:
13298:
13264:
13235:
13209:
13180:
13154:
12690:
12664:
11905:
747:
643:
599:
342:
272:
212:
13231:
14597:
14151:
14122:
14096:
14073:
14050:
14027:
13994:
13932:
13863:
13807:
13795:
13744:
13705:
13662:
13650:
13587:
13517:
13462:
13353:
13290:
13200:
13184:
13010:
12928:
12798:
12694:
12469:
Sakharov proposed a way to restore CP-symmetry using T-symmetry, extending spacetime
11925:
11898:
11872:
806:
759:
711:
707:
678:
627:
417:
197:
79:
14247:
13599:
13529:
13302:
13239:
4018:
and it has the same unitary transformation matrix U with M. Besides, parameters in
14776:
14523:
14508:
14449:
14342:
14264:
14235:
14194:
13971:
13959:
13910:
13851:
13791:
13787:
13732:
13685:
13642:
13615:
13583:
13579:
13513:
13509:
13450:
13365:
13345:
13282:
13227:
13172:
13108:
13006:
12965:
12924:
12885:
12844:
12774:
12731:
12682:
12635:
12438:
12434:
12426:
12241:
1021:
1013:
818:
743:
739:
703:
615:
575:
571:
567:
547:
495:
407:
362:
13421:
LHCb Collaboration (2014). "Measurement of CP asymmetry in D→KK and D→ππ decays".
13349:
14698:
14565:
14165:
Bigi, I. (1998). "CP Violation – An Essential Mystery in Nature's Grand Design".
14046:
13051:
12948:
12868:
12827:
12757:
12714:
12569:
12564:
12554:
12221:
1067:
1002:
986:
936:
822:
735:
380:
297:
202:
14292:
13822:
Lin, C.L. (2021). "Exploring the Origin of CP Violation in the Standard Model".
13736:
13454:
13400:
Carbone, A. (2012). "A search for time-integrated CP violation in D→hh decays".
13286:
12505:< 0 are assumed in this hypothesis to be CPT reflections of the phenomena at
8010:{\displaystyle (\mathbf {m_{1}^{2}} ,\mathbf {m_{2}^{2}} ,\mathbf {m_{3}^{2}} )}
3143:
are unitary transformation matrices which diagonalize the fermion mass matrices
1268:
899:
The kind of CP violation discovered in 1964 was linked to the fact that neutral
677:
violation without any assumption of CPT theorem was done in 1998 by two groups,
14736:
14435:
14239:
13963:
13113:
13077:
12686:
12418:
12228:. A newer, more radical approach not requiring the axion is a theory involving
1248:
1244:
1104:
1045:
814:
790:
719:
104:
99:
65:
14198:
13646:
13176:
12944:"Remarks on Possible Noninvariance under Time Reversal and Charge Conjugation"
12596:
14828:
14706:
14665:
13990:
13385:
12890:
12863:
12848:
12779:
12752:
12653:
Schubert, K.R. (2015). "T violation and CPT tests in neutral-meson systems".
12618:
12489:
We can visualize that neutral spinless maximons (or photons) are produced at
12478:
12255:
802:
771:
715:
392:
325:
227:
207:
12969:
12751:
Wu, C. S.; Ambler, E.; Hayward, R. W.; Hoppes, D. D.; Hudson, R. P. (1957).
12736:
12709:
14688:
14528:
14486:
14476:
14370:
13855:
13799:
13689:
13654:
13591:
13521:
13357:
13294:
12549:
12501:> 0, realizing total CPT symmetry of the universe. All the phenomena at
12245:
11928:·m while the experimental upper bound is roughly one trillionth that size.
3374:, or the CKM matrix will be an identity matrix, which is also purely real.
3219:
Thus, there are two necessary conditions for getting a complex CKM matrix:
904:
876:
856:
783:
658:
588:
402:
387:
352:
312:
12497:= 0 when the density is infinite, and decay with an excess of quarks when
6773:{\displaystyle \mathbf {m_{3}^{2}} =\mathbf {A+B{{(x^{2}+1)y} \over x}} ,}
1512:{\displaystyle \ J_{\max }={\tfrac {1}{6}}{\sqrt {3\ }}\ \approx \ 0.1\ .}
14602:
14496:
14464:
14459:
14297:
13026:"An experimental investigation of some consequences of CP-invariance in K
12592:
12390:
12347:
11931:
This is a problem because at the end, there are natural terms in the QCD
1260:
437:
282:
277:
152:
109:
89:
84:
56:
13915:
13878:
14347:
14337:
14222:
14181:
13946:
13332:
13269:
13214:
13159:
12544:
12539:
12374:
12355:
12251:
1252:
931:
836:
727:
674:
651:
642:
in 1956, CP-symmetry was proposed to restore order. However, while the
607:
563:
247:
14388:
12987:
Landau, L. (1957). "On the conservation laws for weak interactions".
12639:
12529:
12378:
1037:
880:
731:
592:
397:
292:
59:
produced by colliding protons decaying into hadron jets and electrons
27:
Violation of charge-parity symmetry in particle physics and cosmology
13076:
Christenson, J. H.; Cronin, J. W.; Fitch, V. L.; Turlay, R. (1964).
12417:
sector. The current long-baseline neutrino oscillation experiments,
12285:
11908:; unlike the electroweak theory in which the gauge fields couple to
1905:
If a phase term is introduced from (e.g.) the CKM matrix, denote it
14781:
14360:
13897:
13883:
13838:
13774:
13719:
13629:
13566:
12386:
12382:
12363:
12263:
11876:
2256:
thus so far nothing is different. However, consider that there are
1844:
complex number. We can separate the magnitude and phase by writing
1264:
1073:
In March 2019, LHCb announced discovery of CP violation in charmed
998:
923:
798:
770:
remains unbroken. This rather subtle point about the structure of
686:
611:
500:
347:
287:
217:
157:
13496:
13437:
13406:
12669:
43:
14454:
14404:
14040:
12370:
11921:
11913:
11893:
There is no experimentally known violation of the CP-symmetry in
11805:{\displaystyle |V_{us}|=|V_{ts}|=|V_{cd}|=|V_{cb}|\sim 0.122023,}
1052:
1033:
1029:
1012:
Starting in 2001, a new generation of experiments, including the
12422:
7937:
However, the eigenvalues' order does not necessarily have to be
13702:
12414:
12351:
12271:
Why does the universe have so much more matter than antimatter?
742:
symmetry still appears to be valid for all reactions involving
603:
13676:
Himmel, Alex; et al. (NOvA Collaboration) (2 July 2020).
4047:
are correlated to those in M directly in the ways shown below
1100:
decays with a deviation from zero of 5.3 standard deviations.
13929:
12799:"The Problem of Parity Non-conservation in Weak Interactions"
12401:
12225:
1256:
908:
661:. Besides C and P, there is a third operation, time reversal
13075:
14260:
12430:
1840:
respectively. Before CP violation, these terms must be the
1232:
1060:
1056:
1017:
1006:
990:
961:
941:
900:
884:
682:
580:
505:
6782:
and the U matrix for up-type quarks can then be given by
11884:
Why is the strong nuclear interaction force CP-invariant?
2210:
Physically measurable reaction rates are proportional to
1025:
12753:"Experimental Test of Parity Conservation in Beta Decay"
12232:
first proposed in 1998 by Bars, Deliduman, and Andreev.
939:
providing the leading contributions to the amplitude of
778:
violation, and it was proposed that charge conjugation,
2984:
From the theoretical end, the CKM matrix is defined as
1048:, despite the model's accuracy for "normal" phenomena.
762:
system can be restored if another approximate symmetry
12861:
12710:"Question of Parity Conservation in Weak Interactions"
12354:, rather than consisting of equal parts of matter and
12180:
11904:
QCD does not violate the CP-symmetry as easily as the
8575:
8543:
8510:
8446:
8413:
8275:
8243:
8210:
8146:
8113:
6811:
6072:
5889:
3756:
3398:
2331:{\displaystyle \ a{\overset {2}{\longrightarrow }}b\ }
2292:{\displaystyle \ a{\overset {1}{\longrightarrow }}b\ }
1470:
1024:
at the High Energy Accelerator Research Organisation (
12862:
Garwin, R. L.; Lederman, L. M.; Weinrich, M. (1957).
12750:
12179:
11943:
11820:
11691:
11615:
11539:
11331:
10933:
10572:
10168:
9696:
9292:
8820:
8791:
8750:
8727:
8692:
8389:
8089:
8054:
8027:
7943:
6790:
6701:
6569:
6439:
6408:
6354:
6238:
6060:
5868:
5837:
5800:
5771:
5737:
5628:
5596:
5566:
5534:
5505:
5333:
5162:
4991:
4820:
4649:
4478:
4337:
4196:
4055:
4024:
3735:
3685:
3386:
3340:
3313:
3286:
3256:
3229:
3184:
3149:
3112:
3075:
2990:
2779:
2425:
2382:
2344:
2305:
2266:
2216:
2060:
2014:
1985:
1950:
1911:
1850:
1811:
1785:
1772:{\displaystyle \ {\bar {a}}\rightarrow {\bar {b}}\ ,}
1732:
1700:
1662:
1627:
1598:
1572:
1525:
1452:
1426:
1288:
1238:
1079:
1051:
In 2011, a hint of CP violation in decays of neutral
13757:
13023:
2338:
or equivalently, two unrelated intermediate states:
1066:
In 2013 LHCb announced discovery of CP violation in
847:
as the true symmetry between matter and antimatter.
598:It plays an important role both in the attempts of
14138:
14089:CP Violation in Particle, Nuclear and Astrophysics
13879:"BAU Production in the SN-Breaking Standard Model"
13678:"New Oscillation Results from the NOvA Experiment"
13543:R. Aaij; et al. (LHCb Collaboration) (2019).
13420:
12196:
12162:
11852:
11804:
11676:
11600:
11521:
11316:
10918:
10557:
10153:
9681:
9277:
8804:
8777:
8733:
8713:
8676:
8373:
8081:Among these 36 potential CKM matrices, 4 of them
8070:
8040:
8009:
7927:
6772:
6686:
6554:
6423:
6390:
6340:
6222:
6047:
5852:
5820:
5786:
5757:
5721:
5611:
5581:
5549:
5520:
5489:
5318:
5147:
4976:
4805:
4634:
4463:
4322:
4181:
4039:
4008:
3719:
3668:
3366:
3326:
3299:
3277:is complex, or the CKM matrix will be purely real.
3269:
3242:
3208:
3170:
3135:
3098:
3061:
2971:
2761:
2409:
2368:
2330:
2291:
2248:
2200:
2042:
2000:
1971:
1936:
1897:
1832:
1797:
1771:
1718:
1686:
1648:
1613:
1584:
1556:
1511:
1438:
1410:
1092:
14206:Mark Trodden (1999). "Electroweak Baryogenesis".
12904:
7619:
7550:
7445:
7374:
7358:
7309:
7167:
7096:
6992:
6921:
6905:
6856:
6754:
6735:
6000:
5974:
5926:
5904:
793:in a letter to Chen-Ning Yang and shortly after,
734:nuclei was carried out in 1956 by a group led by
14826:
12797:Ioffe, B. L.; Okun, L. B.; Rudik, A. P. (1957).
5557:matrix is certainly the most reasonable choice.
2410:{\displaystyle \ a\rightarrow 2\rightarrow b\ .}
1461:
14254:
14063:
12824:
12807:Journal of Experimental and Theoretical Physics
12197:{\displaystyle \scriptstyle {\tilde {\theta }}}
2369:{\displaystyle \ a\rightarrow 1\rightarrow b\ }
1036:decays have now been discovered. Before these "
786:, was the suitable symmetry to restore order.
14571:Mathematical formulation of the Standard Model
14112:
14041:G. C. Branco; L. Lavoura; J. P. Silva (1999).
12796:
12235:
6391:{\displaystyle \mathbf {y\equiv B_{1}/B_{3}} }
3136:{\displaystyle \ \mathrm {U} _{\mathsf {d}}\ }
3099:{\displaystyle \ \mathrm {U} _{\mathsf {u}}\ }
1032:. A large number of CP violation processes in
14420:
14313:
14086:
13978:
13545:"Observation of CP Violation in Charm Decays"
12615:
11677:{\displaystyle |V_{ub}|=|V_{td}|\sim 0.0075,}
11601:{\displaystyle |V_{ud}|=|V_{tb}|\sim 0.9925,}
8017:; they can also be any permutation of them.
5731:was employed to simplify the pattern, where
3720:{\displaystyle \mathbf {M^{2}} =M\cdot M^{+}}
766:can be found such that the combined symmetry
527:
14205:
13138:
12941:
6431:analytically, the eigenvalues are given by
891:between particles and antiparticles and the
774:was realized shortly after the discovery of
14017:
12942:Lee, T. D.; Oehme, R.; Yang, C. N. (1957).
12314:. Unsourced material may be challenged and
12265:
11878:
1726:and the corresponding antiparticle process
1016:at the Stanford Linear Accelerator Center (
883:and coworkers provided clear evidence from
14427:
14413:
14327:
14320:
14306:
1271:into redefinitions of the fermion fields.
534:
520:
42:
14221:
14180:
13945:
13914:
13896:
13837:
13773:
13718:
13628:
13612:
13565:
13495:
13436:
13405:
13331:
13268:
13213:
13158:
13112:
12889:
12778:
12735:
12668:
12334:Learn how and when to remove this message
1519:For leptons, only an upper limit exists:
13984:
13078:"Evidence for the 2π Decay of the K
12656:Progress in Particle and Nuclear Physics
12652:
12535:Parity (physics) § Parity violation
11935:that are able to break the CP-symmetry.
1898:{\displaystyle \ M=|M|\ e^{i\theta }\ .}
1243:"Direct" CP violation is allowed in the
930:
922:
870:
13542:
13399:
13378:
12792:
12790:
12707:
12209:in physics, and is typically solved by
8741:is one of the Wolfenstein parameters.
782:, which transforms a particle into its
14:
14827:
13675:
13252:
13069:
12986:
12411:Pontecorvo–Maki–Nakagawa–Sakata matrix
11531:The best fit of the CKM elements are
8686:fit experimental data to the order of
3194:
3159:
3124:
3087:
3042:
3025:
3008:
3005:
3002:
918:
865:
258:de Sitter invariant special relativity
238:N = 4 supersymmetric Yang–Mills theory
14408:
14301:
13315:
13197:
12585:
12407:electric dipole moment of the neutron
11924:which would be comparable to 10
14807:
14164:
14144:Introduction to Elementary Particles
14020:Discrete symmetries and CP violation
13475:
13191:
12787:
12595:has a song in its soundtrack titled
12473:the Big Bang. He described complete
12312:adding citations to reliable sources
12279:
11866:
11853:{\displaystyle |V_{cs}|\sim 0.9845.}
5821:{\displaystyle \mathbf {M_{I}^{2}} }
5758:{\displaystyle \mathbf {M_{R}^{2}} }
3209:{\displaystyle \ M_{\mathsf {d}}\ ,}
1189:beams, than electron antineutrinos (
188:6D (2,0) superconformal field theory
13985:Sakharov, A. D. (7 December 1982).
13876:
13821:
13121:
12908:Proceedings of the Physical Society
12275:(more unsolved problems in physics)
11888:(more unsolved problems in physics)
8744:The full expressions of parameters
3171:{\displaystyle \ M_{\mathsf {u}}\ }
935:The two box diagrams above are the
193:Noncommutative quantum field theory
55:particle detector data depicting a
24:
14434:
14010:
13381:"Where did all the antimatter go?"
11946:
10939:
8797:
8627:
8607:
8334:
8314:
3118:
3081:
3036:
3019:
2996:
1719:{\displaystyle \ a\rightarrow b\ }
1239:CP violation in the Standard Model
1147:) were alternately produced by an
560:charge conjugation parity symmetry
25:
14866:
14855:Physics beyond the Standard Model
14286:
12463:physics beyond the Standard Model
12211:physics beyond the Standard Model
8721:or better, at tree level, where
5499:That means if we diagonalize an
1979:contains the conjugate matrix to
14806:
14795:
14794:
14539:
14365:
12708:Lee, T. D.; Yang, C. N. (1956).
12560:Cabibbo–Kobayashi–Maskawa matrix
12450:. The best limits come from the
12398:Cabibbo–Kobayashi–Maskawa matrix
12284:
7998:
7993:
7989:
7978:
7973:
7969:
7958:
7953:
7949:
7903:
7899:
7893:
7889:
7885:
7880:
7876:
7872:
7867:
7863:
7856:
7840:
7836:
7830:
7826:
7822:
7817:
7813:
7809:
7804:
7800:
7793:
7778:
7774:
7768:
7764:
7760:
7755:
7751:
7747:
7742:
7738:
7730:
7727:
7708:
7704:
7698:
7694:
7690:
7685:
7681:
7677:
7672:
7668:
7656:
7652:
7648:
7643:
7639:
7629:
7613:
7609:
7603:
7599:
7595:
7590:
7586:
7582:
7577:
7573:
7566:
7563:
7558:
7554:
7547:
7528:
7524:
7518:
7514:
7510:
7505:
7501:
7497:
7492:
7488:
7478:
7474:
7470:
7465:
7461:
7437:
7433:
7427:
7423:
7419:
7414:
7410:
7406:
7401:
7397:
7390:
7387:
7382:
7378:
7371:
7353:
7349:
7343:
7339:
7335:
7330:
7326:
7322:
7317:
7313:
7306:
7294:
7290:
7286:
7281:
7277:
7252:
7248:
7242:
7238:
7234:
7229:
7225:
7221:
7216:
7212:
7200:
7196:
7192:
7187:
7183:
7159:
7155:
7149:
7145:
7141:
7136:
7132:
7128:
7123:
7119:
7112:
7109:
7104:
7100:
7093:
7077:
7073:
7067:
7063:
7059:
7054:
7050:
7046:
7041:
7037:
7025:
7021:
7017:
7012:
7008:
6984:
6980:
6974:
6970:
6966:
6961:
6957:
6953:
6948:
6944:
6937:
6934:
6929:
6925:
6918:
6900:
6896:
6890:
6886:
6882:
6877:
6873:
6869:
6864:
6860:
6853:
6841:
6837:
6833:
6828:
6824:
6797:
6793:
6761:
6757:
6751:
6748:
6743:
6739:
6729:
6726:
6723:
6713:
6708:
6704:
6674:
6671:
6662:
6658:
6652:
6648:
6644:
6639:
6635:
6631:
6626:
6622:
6613:
6610:
6605:
6602:
6597:
6594:
6591:
6581:
6576:
6572:
6541:
6538:
6531:
6527:
6521:
6517:
6513:
6508:
6504:
6500:
6495:
6491:
6483:
6480:
6475:
6472:
6467:
6464:
6461:
6451:
6446:
6442:
6424:{\displaystyle \mathbf {M^{2}} }
6415:
6411:
6382:
6378:
6373:
6367:
6363:
6356:
6329:
6325:
6320:
6314:
6310:
6303:
6293:
6289:
6282:
6272:
6268:
6261:
6251:
6247:
6240:
6211:
6206:
6202:
6188:
6183:
6179:
6157:
6146:
6143:
6130:
6117:
6114:
6100:
6097:
6085:
6082:
6033:
6026:
6019:
6016:
6007:
5995:
5992:
5987:
5982:
5979:
5971:
5968:
5965:
5958:
5955:
5946:
5943:
5936:
5933:
5921:
5918:
5913:
5910:
5907:
5901:
5893:
5875:
5871:
5853:{\displaystyle \mathbf {M^{2}} }
5844:
5840:
5812:
5807:
5803:
5787:{\displaystyle \mathbf {M^{2}} }
5778:
5774:
5749:
5744:
5740:
5716:
5713:
5708:
5705:
5700:
5696:
5685:
5680:
5676:
5665:
5662:
5657:
5653:
5640:
5635:
5631:
5612:{\displaystyle \mathbf {M^{2}} }
5603:
5599:
5582:{\displaystyle \mathbf {M^{2}} }
5573:
5569:
5550:{\displaystyle \mathbf {M^{2}} }
5541:
5537:
5521:{\displaystyle \mathbf {M^{2}} }
5512:
5508:
5340:
5336:
5169:
5165:
4998:
4994:
4827:
4823:
4656:
4652:
4485:
4481:
4344:
4340:
4203:
4199:
4062:
4058:
4040:{\displaystyle \mathbf {M^{2}} }
4031:
4027:
3989:
3985:
3975:
3971:
3957:
3953:
3943:
3939:
3925:
3921:
3909:
3905:
3891:
3887:
3877:
3873:
3863:
3859:
3845:
3841:
3829:
3825:
3811:
3807:
3797:
3793:
3779:
3775:
3765:
3761:
3742:
3738:
3692:
3688:
2771:Some further calculation gives:
2043:{\displaystyle \ e^{-i\phi }\ .}
1557:{\displaystyle \ |J|<0.03\ .}
805:and in experiments performed by
223:Mathematical universe hypothesis
13923:
13870:
13814:
13751:
13696:
13669:
13606:
13536:
13469:
13414:
13393:
13372:
13309:
13246:
13132:
13017:
12980:
12580:Electron electric dipole moment
3367:{\displaystyle U_{u}\neq U_{d}}
1937:{\displaystyle \ e^{i\phi }\ .}
1687:{\displaystyle \ {\bar {b}}\ .}
14722:Causal dynamical triangulation
14257:"What is direct CP-violation?"
14168:Surveys of High Energy Physics
13825:Letters in High Energy Physics
13792:10.1103/PhysRevLett.126.051801
13584:10.1103/PhysRevLett.122.211803
13514:10.1103/PhysRevLett.110.221601
13424:Journal of High Energy Physics
13379:Rodgers, Peter (August 2001).
12935:
12898:
12855:
12818:
12744:
12701:
12646:
12609:
12448:neutrinoless double-beta decay
12187:
12084:
12060:
11912:currents constructed from the
11840:
11822:
11789:
11771:
11763:
11745:
11737:
11719:
11711:
11693:
11661:
11643:
11635:
11617:
11585:
11567:
11559:
11541:
11069:
11041:
11032:
11029:
11012:
10988:
10971:
10950:
10701:
10673:
10664:
10661:
10644:
10620:
10603:
10582:
10357:
10209:
10206:
10178:
9956:
9808:
9805:
9777:
9771:
9735:
9732:
9706:
9481:
9333:
9330:
9302:
9080:
8932:
8929:
8901:
8895:
8859:
8856:
8830:
8714:{\displaystyle \lambda ^{1/2}}
8489:
8483:
8399:
8393:
8183:
8176:
8099:
8093:
8004:
7944:
2960:
2934:
2922:
2896:
2883:
2868:
2860:
2845:
2822:
2814:
2804:
2790:
2781:
2696:
2681:
2619:
2604:
2590:
2530:
2515:
2456:
2441:
2395:
2389:
2357:
2351:
2314:
2275:
2230:
2221:
2155:
2147:
2133:
2084:
2076:
1972:{\displaystyle \ {\bar {M}}\ }
1960:
1869:
1861:
1833:{\displaystyle \ {\bar {M}}\ }
1821:
1757:
1748:
1742:
1707:
1672:
1649:{\displaystyle \ {\bar {a}}\ }
1637:
1538:
1530:
753:
428:Causal dynamical triangulation
13:
1:
14561:Spontaneous symmetry breaking
13350:10.1103/PhysRevLett.87.091802
13232:10.1016/S0370-2693(99)01030-8
12603:
3280:If both of them are complex,
697:
115:Cosmological constant problem
13011:10.1016/0029-5582(57)90061-5
12575:Neutral particle oscillation
12350:universe is made chiefly of
2249:{\displaystyle \ |M|^{2}\ ,}
2008:so it picks up a phase term
1779:and denote their amplitudes
927:Kaon oscillation box diagram
681:and KTeV collaborations, at
602:to explain the dominance of
587:in 1980 for its discoverers
148:Cosmic censorship hypothesis
7:
14087:Michael Beyer, ed. (2002).
13737:10.1103/PhysRevD.103.013004
13287:10.1103/PhysRevLett.86.2515
13128:The Fitch-Cronin Experiment
12523:
12373:should have cancelled with
12266:Unsolved problem in physics
12236:Matter–antimatter imbalance
11879:Unsolved problem in physics
8805:{\displaystyle p^{\prime }}
1694:Now consider the processes
1446:times the maximum value of
758:Overall, the symmetry of a
648:electromagnetic interaction
621:
10:
14871:
14240:10.1103/RevModPhys.71.1463
14070:Cambridge University Press
14064:I. Bigi; A. Sanda (1999).
13987:Collected Scientific Works
13964:10.1103/PhysRevD.58.066004
13114:10.1103/PhysRevLett.13.138
13050:(1): 93–96. Archived from
12929:10.1088/0370-1328/73/2/303
12687:10.1016/j.ppnp.2014.12.001
12516:Collected Scientific Works
12249:
12239:
11870:
1439:{\displaystyle \ 0.0003\ }
1126:) and muon antineutrinos (
692:
638:). After the discovery of
14790:
14749:
14727:Canonical quantum gravity
14697:
14664:
14633:
14590:
14579:
14548:
14537:
14442:
14379:
14356:
14333:
14209:Reviews of Modern Physics
14199:10.1080/01422419808228861
13647:10.1038/s41586-020-2177-0
13177:10.1103/PhysRevLett.83.22
3334:must be different, i.e.,
2052:Now the formula becomes:
1170:) were detected from the
903:can transform into their
443:Canonical quantum gravity
268:Black hole thermodynamics
253:Doubly special relativity
36:Beyond the Standard Model
14732:Superfluid vacuum theory
14119:North–Holland Publishing
12891:10.1103/PhysRev.105.1415
12849:10.1103/PhysRev.106.1290
12780:10.1103/PhysRev.105.1413
8778:{\displaystyle p,q,r,s,}
8734:{\displaystyle \lambda }
1621:and their antiparticles
726:The first test based on
636:conservation of momentum
453:Superfluid vacuum theory
303:Gauge gravitation theory
14514:Quantum electrodynamics
14504:Electroweak interaction
14113:L. Wolfenstein (1989).
14024:Oxford University Press
13761:Physical Review Letters
13553:Physical Review Letters
13483:Physical Review Letters
13455:10.1007/JHEP07(2014)041
13319:Physical Review Letters
13256:Physical Review Letters
13146:Physical Review Letters
13143:→ππ Decays".
13092:Physical Review Letters
12970:10.1103/PhysRev.106.340
12737:10.1103/PhysRev.104.254
5860:matrix can be given by
5828:is the imaginary part.
827:University of Liverpool
14492:Quantum chromodynamics
14328:C, P, and T symmetries
13856:10.31526/LHEP.2021.221
13690:10.5281/zenodo.3959581
12521:
12260:Lorentz transformation
12198:
12164:
11918:electric dipole moment
11895:quantum chromodynamics
11854:
11806:
11678:
11602:
11523:
11318:
10920:
10559:
10155:
9683:
9279:
8806:
8779:
8735:
8715:
8678:
8375:
8072:
8071:{\displaystyle U^{d+}}
8042:
8011:
7929:
6774:
6688:
6556:
6425:
6392:
6342:
6224:
6049:
5854:
5822:
5788:
5759:
5723:
5613:
5583:
5551:
5522:
5491:
5320:
5149:
4978:
4807:
4636:
4465:
4324:
4183:
4041:
4010:
3721:
3670:
3368:
3328:
3301:
3271:
3244:
3210:
3172:
3137:
3100:
3063:
2973:
2763:
2411:
2370:
2332:
2293:
2250:
2202:
2044:
2002:
2001:{\displaystyle \ M\ ,}
1973:
1938:
1899:
1834:
1799:
1773:
1720:
1688:
1650:
1615:
1614:{\displaystyle \ b\ ,}
1586:
1558:
1513:
1440:
1412:
1094:
982:
928:
851:is the product of two
675:time reversal symmetry
632:conservation of energy
614:, and in the study of
585:Nobel Prize in Physics
562:): the combination of
433:Causal fermion systems
423:Loop quantum cosmology
368:Large extra dimensions
358:Supersymmetry breaking
263:Causal fermion systems
14608:Cosmological constant
14255:Davide Castelvecchi.
14148:John Wiley & Sons
12487:
12199:
12165:
11855:
11807:
11679:
11603:
11524:
11319:
10921:
10560:
10156:
9684:
9280:
8807:
8780:
8736:
8716:
8679:
8376:
8073:
8043:
8041:{\displaystyle U^{u}}
8012:
7930:
6775:
6689:
6557:
6426:
6393:
6343:
6225:
6050:
5855:
5823:
5789:
5765:is the real part of
5760:
5724:
5614:
5584:
5552:
5523:
5492:
5321:
5150:
4979:
4808:
4637:
4466:
4325:
4184:
4042:
4011:
3722:
3671:
3369:
3329:
3327:{\displaystyle U_{d}}
3302:
3300:{\displaystyle U_{u}}
3272:
3270:{\displaystyle U_{d}}
3245:
3243:{\displaystyle U_{u}}
3211:
3173:
3138:
3101:
3064:
2974:
2764:
2412:
2371:
2333:
2294:
2251:
2203:
2045:
2003:
1974:
1939:
1900:
1835:
1800:
1798:{\displaystyle \ M\ }
1774:
1721:
1689:
1651:
1616:
1587:
1585:{\displaystyle \ a\ }
1559:
1514:
1441:
1420:for quarks, which is
1413:
1251:phase appears in the
1095:
1093:{\displaystyle D^{0}}
934:
926:
871:Indirect CP violation
618:in particle physics.
448:Semiclassical gravity
243:Twistor string theory
233:Randall–Sundrum model
50:Large Hadron Collider
14835:Quantum field theory
14717:Loop quantum gravity
14656:Theory of everything
14651:Grand Unified Theory
14625:Neutrino oscillation
14472:Quantum field theory
14293:Cern Courier article
14018:Sozzi, M.S. (2008).
12514:Andrei Sakharov, in
12308:improve this section
12177:
11941:
11818:
11689:
11613:
11537:
11329:
10931:
10570:
10166:
9694:
9290:
8818:
8789:
8748:
8725:
8690:
8387:
8087:
8052:
8025:
7941:
6788:
6699:
6567:
6437:
6406:
6352:
6236:
6058:
5866:
5835:
5798:
5769:
5735:
5625:
5594:
5564:
5532:
5503:
5331:
5160:
4989:
4818:
4647:
4476:
4335:
4194:
4053:
4022:
3733:
3683:
3384:
3338:
3311:
3284:
3254:
3227:
3182:
3147:
3110:
3073:
2988:
2777:
2423:
2380:
2342:
2303:
2264:
2258:two different routes
2214:
2058:
2012:
1983:
1948:
1909:
1848:
1809:
1783:
1730:
1698:
1660:
1625:
1596:
1570:
1523:
1450:
1424:
1286:
1077:
1055:was reported by the
843:, often called just
671:quantum field theory
669:basic principles of
413:Loop quantum gravity
308:Gauge theory gravity
173:Grand Unified Theory
168:Unified field theory
163:Theory of everything
125:Neutrino oscillation
14684:Split supersymmetry
14646:Kaluza–Klein theory
14519:Fermi's interaction
14232:1999RvMP...71.1463T
14191:1998SHEP...12..269B
13956:1998PhRvD..58f6004B
13916:10.3390/sym15051051
13907:2023Symm...15.1051L
13848:2021LHEP....4..221L
13784:2021PhRvL.126e1801D
13729:2021PhRvD.103a3004K
13639:2020Natur.580..339T
13576:2019PhRvL.122u1803A
13506:2013PhRvL.110v1601A
13447:2014JHEP...07..041A
13342:2001PhRvL..87i1802A
13279:2001PhRvL..86.2515A
13224:1999PhLB..465..335F
13169:1999PhRvL..83...22A
13105:1964PhRvL..13..138C
13043:Soviet Physics JETP
13003:1957NucPh...3..127L
12962:1957PhRv..106..340L
12921:1959PPS....73..169C
12882:1957PhRv..105.1415G
12841:1957PhRv..106.1290F
12771:1957PhRv..105.1413W
12728:1956PhRv..104..254L
12679:2015PrPNP..81....1S
12632:1999PhT....52b..19S
12360:Sakharov conditions
12230:two time dimensions
12218:Peccei–Quinn theory
12207:fine-tuning problem
8002:
7982:
7962:
6717:
6585:
6455:
6215:
6192:
5816:
5753:
5712:
5689:
5669:
5644:
4457:
4439:
4421:
4403:
4385:
4367:
4316:
4298:
4280:
4262:
4244:
4226:
4175:
4157:
4139:
4121:
4103:
4085:
3052:
1325:
919:Direct CP violation
866:Experimental status
748:strong interactions
183:Kaluza–Klein theory
14712:Superstring theory
14482:Strong interaction
14394:Symmetry (physics)
14140:David J. Griffiths
13877:Lin, C.L. (2023).
13057:on 27 January 2021
12586:In popular culture
12194:
12193:
12160:
11906:electroweak theory
11850:
11802:
11674:
11598:
11519:
11314:
10916:
10555:
10151:
9679:
9275:
8802:
8775:
8731:
8711:
8674:
8665:
8561:
8532:
8464:
8435:
8371:
8365:
8261:
8232:
8164:
8135:
8068:
8038:
8007:
7988:
7968:
7948:
7925:
7916:
6770:
6703:
6684:
6571:
6552:
6441:
6421:
6388:
6338:
6220:
6201:
6178:
6168:
6045:
6039:
5850:
5818:
5802:
5784:
5755:
5739:
5695:
5675:
5652:
5646:
5630:
5609:
5579:
5547:
5518:
5487:
5316:
5145:
4974:
4803:
4632:
4461:
4443:
4425:
4407:
4389:
4371:
4353:
4320:
4302:
4284:
4266:
4248:
4230:
4212:
4179:
4161:
4143:
4125:
4107:
4089:
4071:
4037:
4006:
3997:
3717:
3666:
3657:
3364:
3324:
3297:
3267:
3240:
3206:
3168:
3133:
3096:
3059:
3034:
2969:
2759:
2757:
2407:
2366:
2328:
2289:
2246:
2198:
2196:
2040:
1998:
1969:
1934:
1895:
1830:
1795:
1769:
1716:
1684:
1646:
1611:
1582:
1554:
1509:
1479:
1436:
1408:
1311:
1277:Jarlskog invariant
1090:
983:
929:
760:quantum mechanical
644:strong interaction
568:charge conjugation
554:is a violation of
343:Superstring theory
273:Unparticle physics
213:Superstring theory
143:Brans–Dicke theory
14845:Conservation laws
14822:
14821:
14745:
14744:
14620:Strong CP problem
14598:Hierarchy problem
14402:
14401:
14157:978-0-471-60386-3
14128:978-0-444-88081-9
14102:978-3-540-43705-5
14079:978-0-521-44349-4
14056:978-0-19-850399-6
14033:978-0-19-929666-8
13933:Physical Review D
13706:Physical Review D
13623:(7803): 339–344.
13201:Physics Letters B
12976:on 5 August 2012.
12439:Majorana fermions
12344:
12343:
12336:
12190:
12087:
12063:
12038:
11965:
11899:strong CP problem
11873:Strong CP problem
11867:Strong CP problem
11514:
11511:
11441:
11309:
11306:
11236:
11199:
11149:
11140:
10911:
10908:
10838:
10788:
10761:
10752:
10550:
10547:
10477:
10427:
10390:
10355:
10276:
10149:
10146:
10076:
10026:
9989:
9954:
9884:
9674:
9671:
9601:
9551:
9514:
9479:
9400:
9273:
9270:
9200:
9150:
9113:
9078:
9008:
7911:
7909:
7848:
7846:
7786:
7784:
7717:
7714:
7662:
7633:
7622:
7539:
7536:
7534:
7455:
7443:
7364:
7362:
7300:
7261:
7258:
7206:
7177:
7165:
7086:
7083:
7031:
7002:
6990:
6911:
6909:
6847:
6764:
6678:
6668:
6608:
6546:
6545:
6478:
6149:
6120:
6103:
6088:
5998:
5985:
5924:
3202:
3187:
3167:
3152:
3132:
3115:
3095:
3078:
3055:
3033:
2993:
2965:
2927:
2889:
2866:
2843:
2817:
2751:
2725:
2702:
2648:
2625:
2593:
2559:
2536:
2485:
2462:
2403:
2385:
2365:
2347:
2327:
2320:
2308:
2288:
2281:
2269:
2242:
2219:
2177:
2161:
2136:
2106:
2090:
2036:
2017:
1994:
1988:
1968:
1963:
1953:
1930:
1914:
1891:
1875:
1853:
1829:
1824:
1814:
1794:
1788:
1765:
1760:
1745:
1735:
1715:
1703:
1680:
1675:
1665:
1645:
1640:
1630:
1607:
1601:
1581:
1575:
1550:
1528:
1505:
1499:
1493:
1489:
1488:
1478:
1455:
1435:
1429:
1404:
1398:
1392:
1380:
1367:
1354:
1341:
1328:
1310:
1291:
1105:T2K Collaboration
839:proposed in 1957
807:Valentine Telegdi
712:radioactive decay
708:chemical reaction
628:conservation laws
616:weak interactions
544:
543:
418:Quantum cosmology
198:Quantum cosmology
120:Strong CP problem
80:Hierarchy problem
16:(Redirected from
14862:
14850:Particle physics
14810:
14809:
14798:
14797:
14588:
14587:
14543:
14542:
14524:Weak hypercharge
14509:Weak interaction
14450:Particle physics
14429:
14422:
14415:
14406:
14405:
14322:
14315:
14308:
14299:
14298:
14276:
14274:
14272:
14263:. Archived from
14251:
14225:
14216:(5): 1463–1500.
14202:
14184:
14175:(1–4): 269–336.
14161:
14132:
14106:
14083:
14060:
14037:
14005:
14004:
13982:
13976:
13975:
13949:
13927:
13921:
13920:
13918:
13900:
13874:
13868:
13867:
13841:
13818:
13812:
13811:
13777:
13755:
13749:
13748:
13722:
13700:
13694:
13693:
13673:
13667:
13666:
13632:
13610:
13604:
13603:
13569:
13549:
13540:
13534:
13533:
13499:
13473:
13467:
13466:
13440:
13418:
13412:
13411:
13409:
13397:
13391:
13390:
13376:
13370:
13369:
13335:
13313:
13307:
13306:
13272:
13250:
13244:
13243:
13217:
13208:(1–4): 335–348.
13195:
13189:
13188:
13162:
13136:
13130:
13125:
13119:
13118:
13116:
13086:
13085:
13073:
13067:
13066:
13064:
13062:
13056:
13039:
13034:
13033:
13021:
13015:
13014:
12984:
12978:
12977:
12972:. Archived from
12939:
12933:
12932:
12902:
12896:
12895:
12893:
12876:(4): 1415–1417.
12859:
12853:
12852:
12835:(6): 1290–1293.
12822:
12816:
12815:
12803:
12794:
12785:
12784:
12782:
12765:(4): 1413–1415.
12748:
12742:
12741:
12739:
12705:
12699:
12698:
12672:
12650:
12644:
12643:
12640:10.1063/1.882519
12613:
12519:
12435:neutrino factory
12427:Hyper-Kamiokande
12339:
12332:
12328:
12325:
12319:
12288:
12280:
12267:
12242:Baryon asymmetry
12222:scalar particles
12220:, involving new
12203:
12201:
12200:
12195:
12192:
12191:
12183:
12169:
12167:
12166:
12161:
12156:
12152:
12151:
12150:
12149:
12148:
12139:
12117:
12116:
12107:
12106:
12089:
12088:
12080:
12074:
12073:
12065:
12064:
12056:
12052:
12051:
12039:
12037:
12036:
12035:
12022:
12018:
12017:
12008:
12007:
11997:
11992:
11991:
11979:
11978:
11966:
11958:
11950:
11949:
11880:
11859:
11857:
11856:
11851:
11843:
11838:
11837:
11825:
11811:
11809:
11808:
11803:
11792:
11787:
11786:
11774:
11766:
11761:
11760:
11748:
11740:
11735:
11734:
11722:
11714:
11709:
11708:
11696:
11683:
11681:
11680:
11675:
11664:
11659:
11658:
11646:
11638:
11633:
11632:
11620:
11607:
11605:
11604:
11599:
11588:
11583:
11582:
11570:
11562:
11557:
11556:
11544:
11528:
11526:
11525:
11520:
11515:
11513:
11512:
11510:
11509:
11508:
11495:
11494:
11493:
11477:
11476:
11475:
11459:
11458:
11457:
11444:
11442:
11440:
11439:
11430:
11429:
11417:
11416:
11404:
11403:
11394:
11391:
11390:
11382:
11365:
11351:
11339:
11323:
11321:
11320:
11315:
11310:
11308:
11307:
11305:
11304:
11303:
11290:
11289:
11288:
11272:
11271:
11270:
11254:
11253:
11252:
11239:
11237:
11235:
11234:
11233:
11217:
11216:
11215:
11202:
11200:
11198:
11197:
11188:
11187:
11175:
11174:
11162:
11161:
11152:
11150:
11145:
11142:
11141:
11139:
11138:
11137:
11124:
11123:
11122:
11106:
11105:
11104:
11088:
11087:
11086:
11073:
11065:
11054:
11022:
11011:
11010:
11009:
10981:
10970:
10969:
10968:
10948:
10943:
10942:
10925:
10923:
10922:
10917:
10912:
10910:
10909:
10907:
10906:
10905:
10892:
10891:
10890:
10874:
10873:
10872:
10856:
10855:
10854:
10841:
10839:
10837:
10836:
10827:
10826:
10814:
10813:
10801:
10800:
10791:
10789:
10787:
10786:
10774:
10773:
10764:
10762:
10757:
10754:
10753:
10751:
10750:
10741:
10740:
10728:
10727:
10715:
10714:
10705:
10697:
10686:
10660:
10643:
10642:
10633:
10619:
10602:
10601:
10592:
10580:
10564:
10562:
10561:
10556:
10551:
10549:
10548:
10546:
10545:
10544:
10531:
10530:
10529:
10513:
10512:
10511:
10495:
10494:
10493:
10480:
10478:
10476:
10475:
10466:
10465:
10453:
10452:
10440:
10439:
10430:
10428:
10426:
10425:
10424:
10408:
10407:
10406:
10393:
10391:
10389:
10388:
10376:
10375:
10366:
10360:
10356:
10354:
10353:
10352:
10339:
10338:
10337:
10321:
10320:
10319:
10303:
10302:
10301:
10288:
10277:
10275:
10274:
10265:
10264:
10252:
10251:
10239:
10238:
10229:
10227:
10219:
10202:
10191:
10176:
10160:
10158:
10157:
10152:
10150:
10148:
10147:
10145:
10144:
10143:
10130:
10129:
10128:
10112:
10111:
10110:
10094:
10093:
10092:
10079:
10077:
10075:
10074:
10065:
10064:
10052:
10051:
10039:
10038:
10029:
10027:
10025:
10024:
10023:
10007:
10006:
10005:
9992:
9990:
9988:
9987:
9975:
9974:
9965:
9959:
9955:
9953:
9952:
9951:
9938:
9937:
9936:
9920:
9919:
9918:
9902:
9901:
9900:
9887:
9885:
9883:
9882:
9873:
9872:
9860:
9859:
9847:
9846:
9837:
9832:
9824:
9804:
9790:
9770:
9769:
9768:
9752:
9751:
9750:
9731:
9730:
9718:
9717:
9704:
9688:
9686:
9685:
9680:
9675:
9673:
9672:
9670:
9669:
9668:
9655:
9654:
9653:
9637:
9636:
9635:
9619:
9618:
9617:
9604:
9602:
9600:
9599:
9590:
9589:
9577:
9576:
9564:
9563:
9554:
9552:
9550:
9549:
9548:
9532:
9531:
9530:
9517:
9515:
9513:
9512:
9500:
9499:
9490:
9484:
9480:
9478:
9477:
9476:
9463:
9462:
9461:
9445:
9444:
9443:
9427:
9426:
9425:
9412:
9401:
9399:
9398:
9389:
9388:
9376:
9375:
9363:
9362:
9353:
9351:
9343:
9326:
9315:
9300:
9284:
9282:
9281:
9276:
9274:
9272:
9271:
9269:
9268:
9267:
9254:
9253:
9252:
9236:
9235:
9234:
9218:
9217:
9216:
9203:
9201:
9199:
9198:
9189:
9188:
9176:
9175:
9163:
9162:
9153:
9151:
9149:
9148:
9147:
9131:
9130:
9129:
9116:
9114:
9112:
9111:
9099:
9098:
9089:
9083:
9079:
9077:
9076:
9075:
9062:
9061:
9060:
9044:
9043:
9042:
9026:
9025:
9024:
9011:
9009:
9007:
9006:
8997:
8996:
8984:
8983:
8971:
8970:
8961:
8956:
8948:
8928:
8914:
8894:
8893:
8892:
8876:
8875:
8874:
8855:
8854:
8842:
8841:
8828:
8811:
8809:
8808:
8803:
8801:
8800:
8784:
8782:
8781:
8776:
8740:
8738:
8737:
8732:
8720:
8718:
8717:
8712:
8710:
8709:
8705:
8683:
8681:
8680:
8675:
8670:
8669:
8662:
8661:
8650:
8649:
8631:
8630:
8614:
8613:
8597:
8596:
8566:
8565:
8537:
8536:
8504:
8503:
8482:
8481:
8469:
8468:
8440:
8439:
8380:
8378:
8377:
8372:
8370:
8369:
8362:
8361:
8338:
8337:
8321:
8320:
8304:
8303:
8292:
8291:
8266:
8265:
8237:
8236:
8204:
8203:
8191:
8190:
8169:
8168:
8140:
8139:
8077:
8075:
8074:
8069:
8067:
8066:
8047:
8045:
8044:
8039:
8037:
8036:
8016:
8014:
8013:
8008:
8003:
8001:
7996:
7983:
7981:
7976:
7963:
7961:
7956:
7934:
7932:
7931:
7926:
7921:
7920:
7913:
7912:
7910:
7908:
7907:
7906:
7897:
7896:
7884:
7883:
7871:
7870:
7860:
7855:
7850:
7849:
7847:
7845:
7844:
7843:
7834:
7833:
7821:
7820:
7808:
7807:
7797:
7792:
7787:
7785:
7783:
7782:
7781:
7772:
7771:
7759:
7758:
7746:
7745:
7735:
7733:
7725:
7719:
7718:
7716:
7715:
7713:
7712:
7711:
7702:
7701:
7689:
7688:
7676:
7675:
7665:
7663:
7661:
7660:
7659:
7647:
7646:
7636:
7634:
7632:
7627:
7624:
7623:
7618:
7617:
7616:
7607:
7606:
7594:
7593:
7581:
7580:
7570:
7562:
7561:
7545:
7540:
7538:
7537:
7535:
7533:
7532:
7531:
7522:
7521:
7509:
7508:
7496:
7495:
7485:
7483:
7482:
7481:
7469:
7468:
7458:
7456:
7451:
7448:
7444:
7442:
7441:
7440:
7431:
7430:
7418:
7417:
7405:
7404:
7394:
7386:
7385:
7369:
7365:
7363:
7361:
7357:
7356:
7347:
7346:
7334:
7333:
7321:
7320:
7304:
7302:
7301:
7299:
7298:
7297:
7285:
7284:
7274:
7268:
7262:
7260:
7259:
7257:
7256:
7255:
7246:
7245:
7233:
7232:
7220:
7219:
7209:
7207:
7205:
7204:
7203:
7191:
7190:
7180:
7178:
7173:
7170:
7166:
7164:
7163:
7162:
7153:
7152:
7140:
7139:
7127:
7126:
7116:
7108:
7107:
7091:
7087:
7085:
7084:
7082:
7081:
7080:
7071:
7070:
7058:
7057:
7045:
7044:
7034:
7032:
7030:
7029:
7028:
7016:
7015:
7005:
7003:
6998:
6995:
6991:
6989:
6988:
6987:
6978:
6977:
6965:
6964:
6952:
6951:
6941:
6933:
6932:
6916:
6912:
6910:
6908:
6904:
6903:
6894:
6893:
6881:
6880:
6868:
6867:
6851:
6849:
6848:
6846:
6845:
6844:
6832:
6831:
6821:
6815:
6802:
6801:
6800:
6779:
6777:
6776:
6771:
6766:
6765:
6760:
6747:
6746:
6733:
6718:
6716:
6711:
6693:
6691:
6690:
6685:
6680:
6679:
6677:
6669:
6667:
6666:
6665:
6656:
6655:
6643:
6642:
6630:
6629:
6619:
6617:
6609:
6601:
6586:
6584:
6579:
6561:
6559:
6558:
6553:
6548:
6547:
6544:
6536:
6535:
6534:
6525:
6524:
6512:
6511:
6499:
6498:
6488:
6487:
6479:
6471:
6456:
6454:
6449:
6430:
6428:
6427:
6422:
6420:
6419:
6418:
6397:
6395:
6394:
6389:
6387:
6386:
6385:
6376:
6371:
6370:
6347:
6345:
6344:
6339:
6334:
6333:
6332:
6323:
6318:
6317:
6298:
6297:
6296:
6277:
6276:
6275:
6256:
6255:
6254:
6229:
6227:
6226:
6221:
6216:
6214:
6209:
6193:
6191:
6186:
6173:
6172:
6160:
6150:
6142:
6133:
6121:
6113:
6104:
6096:
6089:
6081:
6054:
6052:
6051:
6046:
6044:
6043:
6036:
6029:
6022:
6010:
6003:
5999:
5991:
5986:
5978:
5961:
5949:
5939:
5929:
5925:
5917:
5896:
5880:
5879:
5878:
5859:
5857:
5856:
5851:
5849:
5848:
5847:
5827:
5825:
5824:
5819:
5817:
5815:
5810:
5793:
5791:
5790:
5785:
5783:
5782:
5781:
5764:
5762:
5761:
5756:
5754:
5752:
5747:
5728:
5726:
5725:
5720:
5719:
5711:
5703:
5690:
5688:
5683:
5670:
5668:
5660:
5647:
5645:
5643:
5638:
5618:
5616:
5615:
5610:
5608:
5607:
5606:
5588:
5586:
5585:
5580:
5578:
5577:
5576:
5556:
5554:
5553:
5548:
5546:
5545:
5544:
5527:
5525:
5524:
5519:
5517:
5516:
5515:
5496:
5494:
5493:
5488:
5483:
5482:
5473:
5472:
5460:
5459:
5450:
5449:
5437:
5436:
5427:
5426:
5414:
5413:
5404:
5403:
5391:
5390:
5381:
5380:
5368:
5367:
5358:
5357:
5345:
5344:
5343:
5325:
5323:
5322:
5317:
5312:
5311:
5302:
5301:
5289:
5288:
5279:
5278:
5266:
5265:
5256:
5255:
5243:
5242:
5233:
5232:
5220:
5219:
5210:
5209:
5197:
5196:
5187:
5186:
5174:
5173:
5172:
5154:
5152:
5151:
5146:
5141:
5140:
5131:
5130:
5118:
5117:
5108:
5107:
5095:
5094:
5085:
5084:
5072:
5071:
5062:
5061:
5049:
5048:
5039:
5038:
5026:
5025:
5016:
5015:
5003:
5002:
5001:
4983:
4981:
4980:
4975:
4970:
4969:
4960:
4959:
4947:
4946:
4937:
4936:
4924:
4923:
4914:
4913:
4901:
4900:
4891:
4890:
4878:
4877:
4868:
4867:
4855:
4854:
4845:
4844:
4832:
4831:
4830:
4812:
4810:
4809:
4804:
4799:
4798:
4789:
4788:
4776:
4775:
4766:
4765:
4753:
4752:
4743:
4742:
4730:
4729:
4720:
4719:
4707:
4706:
4697:
4696:
4684:
4683:
4674:
4673:
4661:
4660:
4659:
4641:
4639:
4638:
4633:
4628:
4627:
4618:
4617:
4605:
4604:
4595:
4594:
4582:
4581:
4572:
4571:
4559:
4558:
4549:
4548:
4536:
4535:
4526:
4525:
4513:
4512:
4503:
4502:
4490:
4489:
4488:
4470:
4468:
4467:
4462:
4456:
4451:
4438:
4433:
4420:
4415:
4402:
4397:
4384:
4379:
4366:
4361:
4349:
4348:
4347:
4329:
4327:
4326:
4321:
4315:
4310:
4297:
4292:
4279:
4274:
4261:
4256:
4243:
4238:
4225:
4220:
4208:
4207:
4206:
4188:
4186:
4185:
4180:
4174:
4169:
4156:
4151:
4138:
4133:
4120:
4115:
4102:
4097:
4084:
4079:
4067:
4066:
4065:
4046:
4044:
4043:
4038:
4036:
4035:
4034:
4015:
4013:
4012:
4007:
4002:
4001:
3994:
3993:
3992:
3980:
3979:
3978:
3962:
3961:
3960:
3948:
3947:
3946:
3930:
3929:
3928:
3914:
3913:
3912:
3896:
3895:
3894:
3882:
3881:
3880:
3868:
3867:
3866:
3850:
3849:
3848:
3834:
3833:
3832:
3816:
3815:
3814:
3802:
3801:
3800:
3784:
3783:
3782:
3770:
3769:
3768:
3747:
3746:
3745:
3727:can be given by
3726:
3724:
3723:
3718:
3716:
3715:
3697:
3696:
3695:
3675:
3673:
3672:
3667:
3662:
3661:
3654:
3653:
3638:
3637:
3626:
3625:
3610:
3609:
3598:
3597:
3582:
3581:
3568:
3567:
3552:
3551:
3540:
3539:
3524:
3523:
3512:
3511:
3496:
3495:
3482:
3481:
3466:
3465:
3454:
3453:
3438:
3437:
3426:
3425:
3410:
3409:
3373:
3371:
3370:
3365:
3363:
3362:
3350:
3349:
3333:
3331:
3330:
3325:
3323:
3322:
3306:
3304:
3303:
3298:
3296:
3295:
3276:
3274:
3273:
3268:
3266:
3265:
3249:
3247:
3246:
3241:
3239:
3238:
3223:At least one of
3215:
3213:
3212:
3207:
3200:
3199:
3198:
3197:
3185:
3177:
3175:
3174:
3169:
3165:
3164:
3163:
3162:
3150:
3142:
3140:
3139:
3134:
3130:
3129:
3128:
3127:
3121:
3113:
3105:
3103:
3102:
3097:
3093:
3092:
3091:
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2032:
2015:
2007:
2005:
2004:
1999:
1992:
1986:
1978:
1976:
1975:
1970:
1966:
1965:
1964:
1956:
1951:
1943:
1941:
1940:
1935:
1928:
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1308:
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1289:
1230:
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1210:) were from the
1209:
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1177:
1169:
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1125:
1124:
1123:
1115:
1114:
1099:
1097:
1096:
1091:
1089:
1088:
1022:Belle Experiment
1014:BaBar experiment
980:
978:
977:
971:
968:
967:
958:
956:
955:
948:
947:
937:Feynman diagrams
744:electromagnetism
702:The idea behind
640:parity violation
583:resulted in the
548:particle physics
536:
529:
522:
408:Quantum geometry
363:Extra dimensions
46:
32:
31:
21:
14870:
14869:
14865:
14864:
14863:
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14699:Quantum gravity
14693:
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14575:
14566:Higgs mechanism
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14057:
14047:Clarendon Press
14034:
14013:
14011:Further reading
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14001:
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13815:
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13263:(12): 2515–22.
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12990:Nuclear Physics
12985:
12981:
12949:Physical Review
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12936:
12903:
12899:
12869:Physical Review
12860:
12856:
12828:Physical Review
12823:
12819:
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12795:
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12758:Physical Review
12749:
12745:
12715:Physical Review
12706:
12702:
12651:
12647:
12614:
12610:
12606:
12591:The video game
12588:
12570:Penguin diagram
12565:LHCb experiment
12555:BTeV experiment
12526:
12520:
12513:
12475:CPT reflections
12340:
12329:
12323:
12320:
12305:
12289:
12278:
12277:
12272:
12269:
12262:
12248:
12240:Main articles:
12238:
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12128:
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2083:
2075:
2068:
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2059:
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2055:
2022:
2018:
2013:
2010:
2009:
1984:
1981:
1980:
1955:
1954:
1949:
1946:
1945:
1919:
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1529:
1524:
1521:
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1469:
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1359:
1355:
1346:
1342:
1333:
1329:
1320:
1315:
1302:
1298:
1287:
1284:
1283:
1269:can be absorbed
1259:mixing, or the
1241:
1227:
1224:
1223:
1222:
1219:
1216:
1214:
1213:
1212:
1211:
1206:
1203:
1202:
1201:
1198:
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1193:
1192:
1191:
1190:
1185:
1182:
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1176:
1174:
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1138:
1135:
1132:
1130:
1129:
1128:
1127:
1122:
1119:
1118:
1117:
1113:
1111:
1110:
1109:
1108:
1084:
1080:
1078:
1075:
1074:
1068:strange B meson
1003:NA48 experiment
987:NA31 experiment
976:
974:
973:
972:
969:
966:
964:
963:
962:
960:
954:
952:
951:
950:
946:
944:
943:
942:
940:
921:
907:(in which each
873:
868:
853:transformations
823:John Riley Holt
811:Jerome Friedman
756:
736:Chien-Shiung Wu
700:
695:
624:
610:in the present
540:
511:
510:
466:
458:
457:
383:
381:Quantum gravity
373:
372:
328:
318:
317:
298:Massive gravity
203:Brane cosmology
138:
130:
129:
75:
60:
28:
23:
22:
15:
12:
11:
5:
14868:
14858:
14857:
14852:
14847:
14842:
14837:
14820:
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14817:
14816:
14804:
14791:
14788:
14787:
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14784:
14779:
14774:
14769:
14764:
14759:
14753:
14751:
14747:
14746:
14743:
14742:
14740:
14739:
14737:Twistor theory
14734:
14729:
14724:
14719:
14714:
14709:
14703:
14701:
14695:
14694:
14692:
14691:
14686:
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14676:
14670:
14668:
14662:
14661:
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14628:
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14622:
14617:
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14615:
14605:
14600:
14594:
14592:
14585:
14583:Standard Model
14577:
14576:
14574:
14573:
14568:
14563:
14558:
14552:
14550:
14546:
14545:
14538:
14536:
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14531:
14526:
14521:
14516:
14511:
14501:
14500:
14499:
14494:
14489:
14479:
14474:
14469:
14468:
14467:
14462:
14457:
14446:
14444:
14440:
14439:
14436:Standard Model
14432:
14431:
14424:
14417:
14409:
14400:
14399:
14397:
14396:
14391:
14386:
14380:
14377:
14376:
14374:
14373:
14368:
14363:
14357:
14354:
14353:
14351:
14350:
14345:
14340:
14334:
14331:
14330:
14325:
14324:
14317:
14310:
14302:
14296:
14295:
14288:
14287:External links
14285:
14283:
14282:
14277:
14252:
14223:hep-ph/9803479
14203:
14182:hep-ph/9712475
14162:
14156:
14136:
14127:
14110:
14101:
14084:
14078:
14061:
14055:
14038:
14032:
14014:
14012:
14009:
14007:
14006:
14000:978-0824717148
13999:
13977:
13947:hep-th/9803188
13922:
13869:
13813:
13750:
13695:
13668:
13605:
13560:(21): 211803.
13535:
13490:(22): 221601.
13477:
13468:
13413:
13392:
13371:
13333:hep-ex/0107061
13308:
13270:hep-ex/0102030
13245:
13215:hep-ex/9909022
13190:
13160:hep-ex/9905060
13140:
13131:
13120:
13082:
13068:
13030:
13016:
12997:(1): 127–131.
12979:
12956:(2): 340–345.
12934:
12897:
12854:
12817:
12786:
12743:
12722:(1): 254–258.
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11883:
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11871:Main article:
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9547:
9543:
9539:
9535:
9529:
9525:
9521:
9511:
9507:
9503:
9498:
9494:
9488:
9483:
9475:
9471:
9467:
9460:
9456:
9452:
9448:
9442:
9438:
9434:
9430:
9424:
9420:
9416:
9410:
9407:
9404:
9397:
9393:
9387:
9383:
9379:
9374:
9370:
9366:
9361:
9357:
9350:
9347:
9342:
9339:
9335:
9332:
9329:
9325:
9322:
9318:
9314:
9311:
9307:
9304:
9298:
9295:
9286:
9266:
9262:
9258:
9251:
9247:
9243:
9239:
9233:
9229:
9225:
9221:
9215:
9211:
9207:
9197:
9193:
9187:
9183:
9179:
9174:
9170:
9166:
9161:
9157:
9146:
9142:
9138:
9134:
9128:
9124:
9120:
9110:
9106:
9102:
9097:
9093:
9087:
9082:
9074:
9070:
9066:
9059:
9055:
9051:
9047:
9041:
9037:
9033:
9029:
9023:
9019:
9015:
9005:
9001:
8995:
8991:
8987:
8982:
8978:
8974:
8969:
8965:
8959:
8955:
8952:
8947:
8944:
8940:
8937:
8934:
8931:
8927:
8924:
8920:
8917:
8913:
8910:
8906:
8903:
8900:
8897:
8891:
8887:
8883:
8879:
8873:
8869:
8865:
8861:
8858:
8853:
8849:
8845:
8840:
8836:
8832:
8826:
8823:
8799:
8795:
8774:
8771:
8768:
8765:
8762:
8759:
8756:
8753:
8730:
8708:
8704:
8700:
8696:
8673:
8668:
8660:
8656:
8652:
8648:
8644:
8640:
8638:
8635:
8634:
8629:
8625:
8621:
8619:
8616:
8612:
8609:
8605:
8601:
8600:
8595:
8591:
8587:
8585:
8582:
8580:
8577:
8576:
8574:
8569:
8564:
8558:
8555:
8553:
8550:
8548:
8545:
8544:
8542:
8535:
8529:
8526:
8525:
8522:
8519:
8518:
8515:
8512:
8511:
8509:
8502:
8498:
8494:
8491:
8488:
8485:
8480:
8476:
8472:
8467:
8461:
8458:
8456:
8453:
8451:
8448:
8447:
8445:
8438:
8432:
8429:
8428:
8425:
8422:
8421:
8418:
8415:
8414:
8412:
8407:
8404:
8401:
8398:
8395:
8392:
8368:
8360:
8356:
8352:
8350:
8347:
8345:
8342:
8341:
8336:
8332:
8328:
8326:
8323:
8319:
8316:
8312:
8308:
8307:
8302:
8298:
8294:
8290:
8286:
8282:
8280:
8277:
8276:
8274:
8269:
8264:
8258:
8255:
8253:
8250:
8248:
8245:
8244:
8242:
8235:
8229:
8226:
8225:
8222:
8219:
8218:
8215:
8212:
8211:
8209:
8202:
8198:
8194:
8189:
8185:
8181:
8178:
8175:
8172:
8167:
8161:
8158:
8156:
8153:
8151:
8148:
8147:
8145:
8138:
8132:
8129:
8128:
8125:
8122:
8121:
8118:
8115:
8114:
8112:
8107:
8104:
8101:
8098:
8095:
8092:
8065:
8062:
8058:
8035:
8031:
8006:
8000:
7995:
7991:
7986:
7980:
7975:
7971:
7966:
7960:
7955:
7951:
7946:
7924:
7919:
7905:
7901:
7895:
7891:
7887:
7882:
7878:
7874:
7869:
7865:
7858:
7852:
7842:
7838:
7832:
7828:
7824:
7819:
7815:
7811:
7806:
7802:
7795:
7789:
7780:
7776:
7770:
7766:
7762:
7757:
7753:
7749:
7744:
7740:
7732:
7729:
7723:
7722:
7710:
7706:
7700:
7696:
7692:
7687:
7683:
7679:
7674:
7670:
7658:
7654:
7650:
7645:
7641:
7631:
7621:
7615:
7611:
7605:
7601:
7597:
7592:
7588:
7584:
7579:
7575:
7568:
7565:
7560:
7556:
7552:
7549:
7542:
7530:
7526:
7520:
7516:
7512:
7507:
7503:
7499:
7494:
7490:
7480:
7476:
7472:
7467:
7463:
7454:
7447:
7439:
7435:
7429:
7425:
7421:
7416:
7412:
7408:
7403:
7399:
7392:
7389:
7384:
7380:
7376:
7373:
7367:
7360:
7355:
7351:
7345:
7341:
7337:
7332:
7328:
7324:
7319:
7315:
7311:
7308:
7296:
7292:
7288:
7283:
7279:
7272:
7266:
7265:
7254:
7250:
7244:
7240:
7236:
7231:
7227:
7223:
7218:
7214:
7202:
7198:
7194:
7189:
7185:
7176:
7169:
7161:
7157:
7151:
7147:
7143:
7138:
7134:
7130:
7125:
7121:
7114:
7111:
7106:
7102:
7098:
7095:
7089:
7079:
7075:
7069:
7065:
7061:
7056:
7052:
7048:
7043:
7039:
7027:
7023:
7019:
7014:
7010:
7001:
6994:
6986:
6982:
6976:
6972:
6968:
6963:
6959:
6955:
6950:
6946:
6939:
6936:
6931:
6927:
6923:
6920:
6914:
6907:
6902:
6898:
6892:
6888:
6884:
6879:
6875:
6871:
6866:
6862:
6858:
6855:
6843:
6839:
6835:
6830:
6826:
6819:
6813:
6812:
6810:
6805:
6799:
6795:
6769:
6763:
6759:
6756:
6753:
6750:
6745:
6741:
6737:
6731:
6728:
6725:
6721:
6715:
6710:
6706:
6683:
6676:
6673:
6664:
6660:
6654:
6650:
6646:
6641:
6637:
6633:
6628:
6624:
6615:
6612:
6607:
6604:
6599:
6596:
6593:
6589:
6583:
6578:
6574:
6551:
6543:
6540:
6533:
6529:
6523:
6519:
6515:
6510:
6506:
6502:
6497:
6493:
6485:
6482:
6477:
6474:
6469:
6466:
6463:
6459:
6453:
6448:
6444:
6417:
6413:
6402:Diagonalizing
6384:
6380:
6375:
6369:
6365:
6361:
6358:
6337:
6331:
6327:
6322:
6316:
6312:
6308:
6305:
6301:
6295:
6291:
6287:
6284:
6280:
6274:
6270:
6266:
6263:
6259:
6253:
6249:
6245:
6242:
6219:
6213:
6208:
6204:
6199:
6196:
6190:
6185:
6181:
6176:
6171:
6165:
6162:
6159:
6155:
6152:
6148:
6145:
6140:
6137:
6136:
6132:
6128:
6126:
6123:
6119:
6116:
6111:
6108:
6107:
6102:
6099:
6094:
6091:
6087:
6084:
6079:
6077:
6074:
6073:
6071:
6066:
6063:
6042:
6035:
6031:
6028:
6024:
6021:
6018:
6014:
6013:
6009:
6005:
6002:
5997:
5994:
5989:
5984:
5981:
5976:
5973:
5970:
5967:
5963:
5960:
5957:
5953:
5952:
5948:
5945:
5941:
5938:
5935:
5931:
5928:
5923:
5920:
5915:
5912:
5909:
5906:
5903:
5899:
5895:
5891:
5890:
5888:
5883:
5877:
5873:
5846:
5842:
5814:
5809:
5805:
5780:
5776:
5751:
5746:
5742:
5718:
5715:
5710:
5707:
5702:
5698:
5693:
5687:
5682:
5678:
5673:
5667:
5664:
5659:
5655:
5650:
5642:
5637:
5633:
5605:
5601:
5575:
5571:
5543:
5539:
5514:
5510:
5486:
5481:
5477:
5471:
5467:
5463:
5458:
5454:
5448:
5444:
5440:
5435:
5431:
5425:
5421:
5417:
5412:
5408:
5402:
5398:
5394:
5389:
5385:
5379:
5375:
5371:
5366:
5362:
5356:
5352:
5348:
5342:
5338:
5315:
5310:
5306:
5300:
5296:
5292:
5287:
5283:
5277:
5273:
5269:
5264:
5260:
5254:
5250:
5246:
5241:
5237:
5231:
5227:
5223:
5218:
5214:
5208:
5204:
5200:
5195:
5191:
5185:
5181:
5177:
5171:
5167:
5144:
5139:
5135:
5129:
5125:
5121:
5116:
5112:
5106:
5102:
5098:
5093:
5089:
5083:
5079:
5075:
5070:
5066:
5060:
5056:
5052:
5047:
5043:
5037:
5033:
5029:
5024:
5020:
5014:
5010:
5006:
5000:
4996:
4973:
4968:
4964:
4958:
4954:
4950:
4945:
4941:
4935:
4931:
4927:
4922:
4918:
4912:
4908:
4904:
4899:
4895:
4889:
4885:
4881:
4876:
4872:
4866:
4862:
4858:
4853:
4849:
4843:
4839:
4835:
4829:
4825:
4802:
4797:
4793:
4787:
4783:
4779:
4774:
4770:
4764:
4760:
4756:
4751:
4747:
4741:
4737:
4733:
4728:
4724:
4718:
4714:
4710:
4705:
4701:
4695:
4691:
4687:
4682:
4678:
4672:
4668:
4664:
4658:
4654:
4631:
4626:
4622:
4616:
4612:
4608:
4603:
4599:
4593:
4589:
4585:
4580:
4576:
4570:
4566:
4562:
4557:
4553:
4547:
4543:
4539:
4534:
4530:
4524:
4520:
4516:
4511:
4507:
4501:
4497:
4493:
4487:
4483:
4460:
4455:
4450:
4446:
4442:
4437:
4432:
4428:
4424:
4419:
4414:
4410:
4406:
4401:
4396:
4392:
4388:
4383:
4378:
4374:
4370:
4365:
4360:
4356:
4352:
4346:
4342:
4319:
4314:
4309:
4305:
4301:
4296:
4291:
4287:
4283:
4278:
4273:
4269:
4265:
4260:
4255:
4251:
4247:
4242:
4237:
4233:
4229:
4224:
4219:
4215:
4211:
4205:
4201:
4178:
4173:
4168:
4164:
4160:
4155:
4150:
4146:
4142:
4137:
4132:
4128:
4124:
4119:
4114:
4110:
4106:
4101:
4096:
4092:
4088:
4083:
4078:
4074:
4070:
4064:
4060:
4033:
4029:
4005:
4000:
3991:
3987:
3982:
3977:
3973:
3968:
3965:
3959:
3955:
3950:
3945:
3941:
3936:
3933:
3927:
3923:
3918:
3917:
3911:
3907:
3902:
3899:
3893:
3889:
3884:
3879:
3875:
3870:
3865:
3861:
3856:
3853:
3847:
3843:
3838:
3837:
3831:
3827:
3822:
3819:
3813:
3809:
3804:
3799:
3795:
3790:
3787:
3781:
3777:
3772:
3767:
3763:
3758:
3757:
3755:
3750:
3744:
3740:
3714:
3710:
3706:
3703:
3700:
3694:
3690:
3665:
3660:
3652:
3648:
3644:
3641:
3636:
3632:
3628:
3624:
3620:
3616:
3613:
3608:
3604:
3600:
3596:
3592:
3588:
3585:
3580:
3576:
3572:
3571:
3566:
3562:
3558:
3555:
3550:
3546:
3542:
3538:
3534:
3530:
3527:
3522:
3518:
3514:
3510:
3506:
3502:
3499:
3494:
3490:
3486:
3485:
3480:
3476:
3472:
3469:
3464:
3460:
3456:
3452:
3448:
3444:
3441:
3436:
3432:
3428:
3424:
3420:
3416:
3413:
3408:
3404:
3400:
3399:
3397:
3392:
3389:
3376:
3375:
3361:
3357:
3353:
3348:
3344:
3321:
3317:
3294:
3290:
3278:
3264:
3260:
3237:
3233:
3216:respectively.
3205:
3196:
3191:
3161:
3156:
3126:
3120:
3089:
3083:
3058:
3050:
3044:
3038:
3027:
3021:
3016:
3010:
3007:
3004:
2998:
2968:
2962:
2957:
2953:
2949:
2944:
2940:
2936:
2933:
2930:
2924:
2919:
2915:
2911:
2906:
2902:
2898:
2895:
2892:
2885:
2879:
2875:
2870:
2862:
2856:
2852:
2847:
2840:
2837:
2834:
2829:
2824:
2816:
2813:
2806:
2802:
2797:
2792:
2787:
2783:
2754:
2744:
2740:
2736:
2733:
2729:
2718:
2714:
2710:
2706:
2698:
2692:
2688:
2683:
2679:
2676:
2674:
2667:
2663:
2659:
2656:
2652:
2641:
2637:
2633:
2629:
2621:
2615:
2611:
2606:
2602:
2599:
2597:
2592:
2589:
2583:
2582:
2575:
2571:
2567:
2563:
2552:
2548:
2544:
2540:
2532:
2526:
2522:
2517:
2513:
2510:
2508:
2501:
2497:
2493:
2489:
2478:
2474:
2470:
2466:
2458:
2452:
2448:
2443:
2439:
2436:
2434:
2432:
2429:
2428:
2406:
2400:
2397:
2394:
2391:
2388:
2362:
2359:
2356:
2353:
2350:
2324:
2319:
2316:
2311:
2285:
2280:
2277:
2272:
2245:
2237:
2232:
2227:
2223:
2191:
2188:
2185:
2181:
2172:
2169:
2165:
2157:
2153:
2149:
2145:
2142:
2140:
2135:
2132:
2126:
2125:
2120:
2117:
2114:
2110:
2101:
2098:
2094:
2086:
2082:
2078:
2074:
2071:
2069:
2067:
2064:
2063:
2039:
2031:
2028:
2025:
2021:
1997:
1991:
1962:
1959:
1933:
1925:
1922:
1918:
1894:
1886:
1883:
1879:
1871:
1867:
1863:
1859:
1856:
1823:
1820:
1791:
1768:
1759:
1756:
1750:
1744:
1741:
1712:
1709:
1706:
1683:
1674:
1671:
1639:
1636:
1610:
1604:
1578:
1553:
1547:
1544:
1540:
1536:
1532:
1508:
1502:
1496:
1485:
1477:
1474:
1468:
1463:
1459:
1432:
1407:
1401:
1395:
1389:
1386:
1383:
1375:
1371:
1362:
1358:
1349:
1345:
1336:
1332:
1323:
1318:
1314:
1305:
1301:
1297:
1294:
1245:Standard Model
1240:
1237:
1225:
1215:
1204:
1194:
1183:
1175:
1164:
1156:
1141:
1131:
1120:
1112:
1087:
1083:
1059:experiment at
1046:Standard Model
975:
965:
953:
945:
920:
917:
915:CP violation.
872:
869:
867:
864:
795:Boris L. Ioffe
791:Reinhard Oehme
755:
752:
720:Chen-Ning Yang
699:
696:
694:
691:
623:
620:
570:symmetry) and
542:
541:
539:
538:
531:
524:
516:
513:
512:
509:
508:
503:
498:
493:
488:
483:
478:
473:
467:
464:
463:
460:
459:
456:
455:
450:
445:
440:
435:
430:
425:
420:
415:
410:
405:
400:
395:
390:
384:
379:
378:
375:
374:
371:
370:
365:
360:
355:
350:
345:
340:
335:
329:
324:
323:
320:
319:
316:
315:
310:
305:
300:
295:
290:
285:
280:
275:
270:
265:
260:
255:
250:
245:
240:
235:
230:
225:
220:
215:
210:
205:
200:
195:
190:
185:
180:
175:
170:
165:
160:
155:
150:
145:
139:
136:
135:
132:
131:
128:
127:
122:
117:
112:
107:
105:Dark radiation
102:
100:Phantom energy
97:
92:
87:
82:
76:
73:
72:
69:
68:
66:Standard Model
62:
61:
47:
39:
38:
26:
9:
6:
4:
3:
2:
14867:
14856:
14853:
14851:
14848:
14846:
14843:
14841:
14838:
14836:
14833:
14832:
14830:
14815:
14814:
14805:
14803:
14802:
14793:
14792:
14789:
14783:
14780:
14778:
14775:
14773:
14770:
14768:
14765:
14763:
14760:
14758:
14755:
14754:
14752:
14748:
14738:
14735:
14733:
14730:
14728:
14725:
14723:
14720:
14718:
14715:
14713:
14710:
14708:
14707:String theory
14705:
14704:
14702:
14700:
14696:
14690:
14687:
14685:
14682:
14680:
14677:
14675:
14672:
14671:
14669:
14667:
14666:Supersymmetry
14663:
14657:
14654:
14652:
14649:
14647:
14644:
14642:
14639:
14638:
14636:
14632:
14626:
14623:
14621:
14618:
14614:
14611:
14610:
14609:
14606:
14604:
14601:
14599:
14596:
14595:
14593:
14589:
14586:
14584:
14578:
14572:
14569:
14567:
14564:
14562:
14559:
14557:
14554:
14553:
14551:
14547:
14530:
14527:
14525:
14522:
14520:
14517:
14515:
14512:
14510:
14507:
14506:
14505:
14502:
14498:
14495:
14493:
14490:
14488:
14485:
14484:
14483:
14480:
14478:
14475:
14473:
14470:
14466:
14463:
14461:
14458:
14456:
14453:
14452:
14451:
14448:
14447:
14445:
14441:
14437:
14430:
14425:
14423:
14418:
14416:
14411:
14410:
14407:
14395:
14392:
14390:
14387:
14385:
14382:
14381:
14378:
14372:
14369:
14367:
14364:
14362:
14359:
14358:
14355:
14349:
14346:
14344:
14341:
14339:
14336:
14335:
14332:
14323:
14318:
14316:
14311:
14309:
14304:
14303:
14300:
14294:
14291:
14290:
14281:
14278:
14267:on 3 May 2014
14266:
14262:
14258:
14253:
14249:
14245:
14241:
14237:
14233:
14229:
14224:
14219:
14215:
14211:
14210:
14204:
14200:
14196:
14192:
14188:
14183:
14178:
14174:
14170:
14169:
14163:
14159:
14153:
14149:
14145:
14141:
14137:
14135:
14130:
14124:
14120:
14116:
14111:
14109:
14104:
14098:
14094:
14090:
14085:
14081:
14075:
14071:
14067:
14062:
14058:
14052:
14048:
14044:
14039:
14035:
14029:
14025:
14021:
14016:
14015:
14002:
13996:
13992:
13991:Marcel Dekker
13988:
13981:
13973:
13969:
13965:
13961:
13957:
13953:
13948:
13943:
13940:(6): 066004.
13939:
13935:
13934:
13926:
13917:
13912:
13908:
13904:
13899:
13894:
13890:
13886:
13885:
13880:
13873:
13865:
13861:
13857:
13853:
13849:
13845:
13840:
13835:
13831:
13827:
13826:
13817:
13809:
13805:
13801:
13797:
13793:
13789:
13785:
13781:
13776:
13771:
13768:(5): 051801.
13767:
13763:
13762:
13754:
13746:
13742:
13738:
13734:
13730:
13726:
13721:
13716:
13713:(1): 013004.
13712:
13708:
13707:
13699:
13691:
13687:
13683:
13679:
13672:
13664:
13660:
13656:
13652:
13648:
13644:
13640:
13636:
13631:
13626:
13622:
13618:
13617:
13609:
13601:
13597:
13593:
13589:
13585:
13581:
13577:
13573:
13568:
13563:
13559:
13555:
13554:
13546:
13539:
13531:
13527:
13523:
13519:
13515:
13511:
13507:
13503:
13498:
13493:
13489:
13485:
13484:
13472:
13464:
13460:
13456:
13452:
13448:
13444:
13439:
13434:
13430:
13426:
13425:
13417:
13408:
13403:
13396:
13389:. p. 11.
13388:
13387:
13386:Physics World
13382:
13375:
13367:
13363:
13359:
13355:
13351:
13347:
13343:
13339:
13334:
13329:
13326:(9): 091802.
13325:
13321:
13320:
13312:
13304:
13300:
13296:
13292:
13288:
13284:
13280:
13276:
13271:
13266:
13262:
13258:
13257:
13249:
13241:
13237:
13233:
13229:
13225:
13221:
13216:
13211:
13207:
13203:
13202:
13194:
13186:
13182:
13178:
13174:
13170:
13166:
13161:
13156:
13152:
13148:
13147:
13135:
13129:
13124:
13115:
13110:
13106:
13102:
13098:
13094:
13093:
13088:
13087:Meson System"
13072:
13053:
13049:
13045:
13044:
13036:
13035:meson decays"
13020:
13012:
13008:
13004:
13000:
12996:
12992:
12991:
12983:
12975:
12971:
12967:
12963:
12959:
12955:
12951:
12950:
12945:
12938:
12930:
12926:
12922:
12918:
12914:
12910:
12909:
12901:
12892:
12887:
12883:
12879:
12875:
12871:
12870:
12865:
12858:
12850:
12846:
12842:
12838:
12834:
12830:
12829:
12821:
12813:
12809:
12808:
12800:
12793:
12791:
12781:
12776:
12772:
12768:
12764:
12760:
12759:
12754:
12747:
12738:
12733:
12729:
12725:
12721:
12717:
12716:
12711:
12704:
12696:
12692:
12688:
12684:
12680:
12676:
12671:
12666:
12662:
12658:
12657:
12649:
12641:
12637:
12633:
12629:
12625:
12621:
12620:
12619:Physics Today
12612:
12608:
12598:
12594:
12590:
12589:
12581:
12578:
12576:
12573:
12571:
12568:
12566:
12563:
12561:
12558:
12556:
12553:
12551:
12548:
12546:
12543:
12541:
12538:
12536:
12533:
12531:
12528:
12527:
12517:
12510:
12508:
12504:
12500:
12496:
12492:
12486:
12484:
12480:
12479:arrow of time
12476:
12472:
12467:
12464:
12459:
12457:
12453:
12449:
12444:
12440:
12436:
12432:
12428:
12424:
12420:
12416:
12412:
12408:
12403:
12399:
12394:
12392:
12388:
12384:
12380:
12376:
12372:
12367:
12365:
12361:
12357:
12353:
12349:
12338:
12335:
12327:
12324:November 2020
12317:
12313:
12309:
12303:
12302:
12298:
12293:This section
12291:
12287:
12282:
12281:
12276:
12261:
12257:
12256:Arrow of time
12253:
12247:
12243:
12233:
12231:
12227:
12223:
12219:
12214:
12212:
12208:
12184:
12170:
12157:
12153:
12145:
12141:
12136:
12133:
12129:
12125:
12121:
12118:
12113:
12109:
12103:
12099:
12095:
12091:
12081:
12075:
12070:
12067:
12057:
12048:
12045:
12041:
12032:
12028:
12024:
12019:
12014:
12010:
12004:
12000:
11993:
11988:
11985:
11981:
11975:
11972:
11968:
11962:
11959:
11954:
11951:
11936:
11934:
11929:
11927:
11923:
11919:
11915:
11911:
11907:
11902:
11900:
11896:
11889:
11874:
11864:
11860:
11847:
11844:
11834:
11831:
11827:
11813:
11799:
11796:
11793:
11783:
11780:
11776:
11767:
11757:
11754:
11750:
11741:
11731:
11728:
11724:
11715:
11705:
11702:
11698:
11684:
11671:
11668:
11665:
11655:
11652:
11648:
11639:
11629:
11626:
11622:
11608:
11595:
11592:
11589:
11579:
11576:
11572:
11563:
11553:
11550:
11546:
11532:
11529:
11516:
11505:
11501:
11497:
11490:
11486:
11482:
11478:
11472:
11468:
11464:
11460:
11454:
11450:
11446:
11436:
11432:
11426:
11422:
11418:
11413:
11409:
11405:
11400:
11396:
11387:
11384:
11379:
11376:
11372:
11369:
11366:
11362:
11359:
11355:
11352:
11348:
11345:
11341:
11335:
11332:
11324:
11311:
11300:
11296:
11292:
11285:
11281:
11277:
11273:
11267:
11263:
11259:
11255:
11249:
11245:
11241:
11230:
11226:
11222:
11218:
11212:
11208:
11204:
11194:
11190:
11184:
11180:
11176:
11171:
11167:
11163:
11158:
11154:
11146:
11134:
11130:
11126:
11119:
11115:
11111:
11107:
11101:
11097:
11093:
11089:
11083:
11079:
11075:
11066:
11062:
11059:
11055:
11051:
11048:
11044:
11038:
11035:
11026:
11023:
11019:
11016:
11006:
11002:
10998:
10994:
10991:
10985:
10982:
10978:
10975:
10965:
10961:
10957:
10953:
10944:
10935:
10926:
10913:
10902:
10898:
10894:
10887:
10883:
10879:
10875:
10869:
10865:
10861:
10857:
10851:
10847:
10843:
10833:
10829:
10823:
10819:
10815:
10810:
10806:
10802:
10797:
10793:
10783:
10779:
10775:
10770:
10766:
10758:
10747:
10743:
10737:
10733:
10729:
10724:
10720:
10716:
10711:
10707:
10698:
10694:
10691:
10687:
10683:
10680:
10676:
10670:
10667:
10657:
10654:
10650:
10647:
10639:
10635:
10630:
10627:
10623:
10616:
10613:
10609:
10606:
10598:
10594:
10589:
10586:
10576:
10573:
10552:
10541:
10537:
10533:
10526:
10522:
10518:
10514:
10508:
10504:
10500:
10496:
10490:
10486:
10482:
10472:
10468:
10462:
10458:
10454:
10449:
10445:
10441:
10436:
10432:
10421:
10417:
10413:
10409:
10403:
10399:
10395:
10385:
10381:
10377:
10372:
10368:
10362:
10349:
10345:
10341:
10334:
10330:
10326:
10322:
10316:
10312:
10308:
10304:
10298:
10294:
10290:
10284:
10281:
10278:
10271:
10267:
10261:
10257:
10253:
10248:
10244:
10240:
10235:
10231:
10224:
10221:
10216:
10213:
10203:
10199:
10196:
10192:
10188:
10185:
10181:
10172:
10169:
10161:
10140:
10136:
10132:
10125:
10121:
10117:
10113:
10107:
10103:
10099:
10095:
10089:
10085:
10081:
10071:
10067:
10061:
10057:
10053:
10048:
10044:
10040:
10035:
10031:
10020:
10016:
10012:
10008:
10002:
9998:
9994:
9984:
9980:
9976:
9971:
9967:
9961:
9948:
9944:
9940:
9933:
9929:
9925:
9921:
9915:
9911:
9907:
9903:
9897:
9893:
9889:
9879:
9875:
9869:
9865:
9861:
9856:
9852:
9848:
9843:
9839:
9833:
9829:
9826:
9821:
9818:
9814:
9811:
9801:
9798:
9794:
9791:
9787:
9784:
9780:
9774:
9765:
9761:
9757:
9753:
9747:
9743:
9739:
9727:
9723:
9719:
9714:
9710:
9700:
9697:
9676:
9665:
9661:
9657:
9650:
9646:
9642:
9638:
9632:
9628:
9624:
9620:
9614:
9610:
9606:
9596:
9592:
9586:
9582:
9578:
9573:
9569:
9565:
9560:
9556:
9545:
9541:
9537:
9533:
9527:
9523:
9519:
9509:
9505:
9501:
9496:
9492:
9486:
9473:
9469:
9465:
9458:
9454:
9450:
9446:
9440:
9436:
9432:
9428:
9422:
9418:
9414:
9408:
9405:
9402:
9395:
9391:
9385:
9381:
9377:
9372:
9368:
9364:
9359:
9355:
9348:
9345:
9340:
9337:
9327:
9323:
9320:
9316:
9312:
9309:
9305:
9296:
9293:
9285:
9264:
9260:
9256:
9249:
9245:
9241:
9237:
9231:
9227:
9223:
9219:
9213:
9209:
9205:
9195:
9191:
9185:
9181:
9177:
9172:
9168:
9164:
9159:
9155:
9144:
9140:
9136:
9132:
9126:
9122:
9118:
9108:
9104:
9100:
9095:
9091:
9085:
9072:
9068:
9064:
9057:
9053:
9049:
9045:
9039:
9035:
9031:
9027:
9021:
9017:
9013:
9003:
8999:
8993:
8989:
8985:
8980:
8976:
8972:
8967:
8963:
8957:
8953:
8950:
8945:
8942:
8938:
8935:
8925:
8922:
8918:
8915:
8911:
8908:
8904:
8898:
8889:
8885:
8881:
8877:
8871:
8867:
8863:
8851:
8847:
8843:
8838:
8834:
8824:
8821:
8813:
8812:are given by
8793:
8772:
8769:
8766:
8763:
8760:
8757:
8754:
8751:
8742:
8728:
8706:
8702:
8698:
8694:
8684:
8671:
8666:
8658:
8654:
8646:
8642:
8636:
8623:
8617:
8610:
8603:
8593:
8589:
8583:
8578:
8572:
8567:
8562:
8556:
8551:
8546:
8540:
8533:
8527:
8520:
8513:
8507:
8500:
8496:
8492:
8486:
8478:
8474:
8470:
8465:
8459:
8454:
8449:
8443:
8436:
8430:
8423:
8416:
8410:
8405:
8402:
8396:
8390:
8382:
8366:
8358:
8354:
8348:
8343:
8330:
8324:
8317:
8310:
8300:
8296:
8288:
8284:
8278:
8272:
8267:
8262:
8256:
8251:
8246:
8240:
8233:
8227:
8220:
8213:
8207:
8200:
8196:
8192:
8187:
8179:
8173:
8170:
8165:
8159:
8154:
8149:
8143:
8136:
8130:
8123:
8116:
8110:
8105:
8102:
8096:
8090:
8082:
8079:
8063:
8060:
8056:
8033:
8029:
8018:
7984:
7964:
7935:
7922:
7917:
7452:
7270:
7174:
6999:
6817:
6808:
6803:
6783:
6780:
6767:
6719:
6694:
6681:
6587:
6562:
6549:
6457:
6432:
6399:
6359:
6335:
6306:
6299:
6285:
6278:
6264:
6257:
6243:
6230:
6217:
6197:
6194:
6174:
6169:
6163:
6153:
6138:
6124:
6109:
6092:
6075:
6069:
6064:
6061:
6040:
5897:
5886:
5881:
5861:
5829:
5729:
5691:
5671:
5648:
5620:
5558:
5497:
5484:
5479:
5475:
5469:
5465:
5461:
5456:
5452:
5446:
5442:
5438:
5433:
5429:
5423:
5419:
5415:
5410:
5406:
5400:
5396:
5392:
5387:
5383:
5377:
5373:
5369:
5364:
5360:
5354:
5350:
5346:
5326:
5313:
5308:
5304:
5298:
5294:
5290:
5285:
5281:
5275:
5271:
5267:
5262:
5258:
5252:
5248:
5244:
5239:
5235:
5229:
5225:
5221:
5216:
5212:
5206:
5202:
5198:
5193:
5189:
5183:
5179:
5175:
5155:
5142:
5137:
5133:
5127:
5123:
5119:
5114:
5110:
5104:
5100:
5096:
5091:
5087:
5081:
5077:
5073:
5068:
5064:
5058:
5054:
5050:
5045:
5041:
5035:
5031:
5027:
5022:
5018:
5012:
5008:
5004:
4984:
4971:
4966:
4962:
4956:
4952:
4948:
4943:
4939:
4933:
4929:
4925:
4920:
4916:
4910:
4906:
4902:
4897:
4893:
4887:
4883:
4879:
4874:
4870:
4864:
4860:
4856:
4851:
4847:
4841:
4837:
4833:
4813:
4800:
4795:
4791:
4785:
4781:
4777:
4772:
4768:
4762:
4758:
4754:
4749:
4745:
4739:
4735:
4731:
4726:
4722:
4716:
4712:
4708:
4703:
4699:
4693:
4689:
4685:
4680:
4676:
4670:
4666:
4662:
4642:
4629:
4624:
4620:
4614:
4610:
4606:
4601:
4597:
4591:
4587:
4583:
4578:
4574:
4568:
4564:
4560:
4555:
4551:
4545:
4541:
4537:
4532:
4528:
4522:
4518:
4514:
4509:
4505:
4499:
4495:
4491:
4471:
4458:
4453:
4448:
4444:
4440:
4435:
4430:
4426:
4422:
4417:
4412:
4408:
4404:
4399:
4394:
4390:
4386:
4381:
4376:
4372:
4368:
4363:
4358:
4354:
4350:
4330:
4317:
4312:
4307:
4303:
4299:
4294:
4289:
4285:
4281:
4276:
4271:
4267:
4263:
4258:
4253:
4249:
4245:
4240:
4235:
4231:
4227:
4222:
4217:
4213:
4209:
4189:
4176:
4171:
4166:
4162:
4158:
4153:
4148:
4144:
4140:
4135:
4130:
4126:
4122:
4117:
4112:
4108:
4104:
4099:
4094:
4090:
4086:
4081:
4076:
4072:
4068:
4048:
4016:
4003:
3998:
3966:
3963:
3934:
3931:
3900:
3897:
3854:
3851:
3820:
3817:
3788:
3785:
3753:
3748:
3728:
3712:
3708:
3704:
3701:
3698:
3676:
3663:
3658:
3650:
3646:
3642:
3639:
3634:
3630:
3622:
3618:
3614:
3611:
3606:
3602:
3594:
3590:
3586:
3583:
3578:
3574:
3564:
3560:
3556:
3553:
3548:
3544:
3536:
3532:
3528:
3525:
3520:
3516:
3508:
3504:
3500:
3497:
3492:
3488:
3478:
3474:
3470:
3467:
3462:
3458:
3450:
3446:
3442:
3439:
3434:
3430:
3422:
3418:
3414:
3411:
3406:
3402:
3395:
3390:
3387:
3379:
3359:
3355:
3351:
3346:
3342:
3319:
3315:
3292:
3288:
3279:
3262:
3258:
3235:
3231:
3222:
3221:
3220:
3217:
3203:
3189:
3154:
3056:
3048:
3014:
2982:
2979:
2966:
2955:
2951:
2947:
2942:
2938:
2931:
2928:
2917:
2913:
2909:
2904:
2900:
2893:
2890:
2877:
2873:
2854:
2850:
2838:
2835:
2832:
2827:
2811:
2800:
2795:
2785:
2772:
2769:
2752:
2742:
2738:
2734:
2731:
2727:
2716:
2712:
2708:
2704:
2690:
2686:
2677:
2675:
2665:
2661:
2657:
2654:
2650:
2639:
2635:
2631:
2627:
2613:
2609:
2600:
2598:
2587:
2573:
2569:
2565:
2561:
2550:
2546:
2542:
2538:
2524:
2520:
2511:
2509:
2499:
2495:
2491:
2487:
2476:
2472:
2468:
2464:
2450:
2446:
2437:
2435:
2430:
2418:
2417:Now we have:
2404:
2398:
2392:
2386:
2360:
2354:
2348:
2322:
2317:
2309:
2283:
2278:
2270:
2259:
2243:
2235:
2225:
2208:
2189:
2186:
2183:
2179:
2170:
2167:
2163:
2151:
2143:
2141:
2130:
2118:
2115:
2112:
2108:
2099:
2096:
2092:
2080:
2072:
2070:
2065:
2053:
2050:
2037:
2029:
2026:
2023:
2019:
1995:
1989:
1957:
1931:
1923:
1920:
1916:
1892:
1884:
1881:
1877:
1865:
1857:
1854:
1843:
1818:
1789:
1766:
1754:
1739:
1710:
1704:
1681:
1669:
1634:
1608:
1602:
1576:
1564:
1551:
1545:
1542:
1534:
1506:
1500:
1494:
1483:
1475:
1472:
1466:
1457:
1430:
1418:
1405:
1399:
1393:
1387:
1384:
1381:
1373:
1369:
1360:
1356:
1347:
1343:
1334:
1330:
1321:
1316:
1312:
1303:
1299:
1295:
1292:
1281:
1279:
1278:
1272:
1270:
1266:
1262:
1258:
1254:
1250:
1246:
1236:
1234:
1150:
1106:
1103:In 2020, the
1101:
1085:
1081:
1071:
1069:
1064:
1062:
1058:
1054:
1049:
1047:
1043:
1039:
1035:
1031:
1027:
1023:
1019:
1015:
1010:
1008:
1004:
1000:
996:
992:
988:
979:
957:
938:
933:
925:
916:
914:
910:
906:
905:antiparticles
902:
897:
894:
890:
886:
882:
878:
863:
860:
858:
857:antiparticles
854:
850:
846:
842:
838:
834:
830:
828:
824:
820:
816:
812:
808:
804:
803:Wu experiment
800:
796:
792:
787:
785:
781:
777:
773:
772:Hilbert space
769:
765:
761:
751:
749:
745:
741:
737:
733:
729:
724:
721:
717:
716:Tsung-Dao Lee
713:
709:
705:
690:
688:
684:
680:
676:
672:
666:
664:
660:
655:
653:
649:
645:
641:
637:
633:
629:
619:
617:
613:
609:
605:
601:
596:
594:
590:
586:
582:
577:
573:
569:
565:
561:
557:
553:
549:
537:
532:
530:
525:
523:
518:
517:
515:
514:
507:
504:
502:
499:
497:
494:
492:
489:
487:
484:
482:
479:
477:
474:
472:
469:
468:
462:
461:
454:
451:
449:
446:
444:
441:
439:
436:
434:
431:
429:
426:
424:
421:
419:
416:
414:
411:
409:
406:
404:
401:
399:
396:
394:
393:String theory
391:
389:
386:
385:
382:
377:
376:
369:
366:
364:
361:
359:
356:
354:
351:
349:
346:
344:
341:
339:
336:
334:
331:
330:
327:
326:Supersymmetry
322:
321:
314:
311:
309:
306:
304:
301:
299:
296:
294:
291:
289:
286:
284:
281:
279:
276:
274:
271:
269:
266:
264:
261:
259:
256:
254:
251:
249:
246:
244:
241:
239:
236:
234:
231:
229:
228:Mirror matter
226:
224:
221:
219:
216:
214:
211:
209:
208:String theory
206:
204:
201:
199:
196:
194:
191:
189:
186:
184:
181:
179:
176:
174:
171:
169:
166:
164:
161:
159:
156:
154:
151:
149:
146:
144:
141:
140:
134:
133:
126:
123:
121:
118:
116:
113:
111:
108:
106:
103:
101:
98:
96:
93:
91:
88:
86:
83:
81:
78:
77:
71:
70:
67:
64:
63:
58:
54:
51:
45:
41:
40:
37:
34:
33:
30:
19:
14811:
14799:
14689:Supergravity
14619:
14549:Constituents
14529:Weak isospin
14487:Color charge
14477:Gauge theory
14371:CPT symmetry
14269:. Retrieved
14265:the original
14213:
14207:
14172:
14166:
14143:
14133:
14115:CP violation
14114:
14107:
14088:
14066:CP violation
14065:
14043:CP violation
14042:
14019:
13986:
13980:
13937:
13931:
13925:
13888:
13882:
13872:
13829:
13823:
13816:
13765:
13759:
13753:
13710:
13704:
13698:
13682:Neutrino2020
13681:
13671:
13620:
13614:
13608:
13557:
13551:
13538:
13487:
13481:
13471:
13428:
13422:
13416:
13395:
13384:
13374:
13323:
13317:
13311:
13260:
13254:
13248:
13205:
13199:
13193:
13153:(1): 22–27.
13150:
13144:
13134:
13123:
13096:
13090:
13071:
13059:. Retrieved
13052:the original
13047:
13041:
13019:
12994:
12988:
12982:
12974:the original
12953:
12947:
12937:
12912:
12906:
12900:
12873:
12867:
12857:
12832:
12826:
12820:
12811:
12805:
12762:
12756:
12746:
12719:
12713:
12703:
12660:
12654:
12648:
12626:(2): 19–20.
12623:
12617:
12611:
12597:CP Violation
12550:CPT symmetry
12515:
12506:
12502:
12498:
12494:
12490:
12488:
12482:
12474:
12470:
12468:
12460:
12456:leptogenesis
12395:
12391:antineutrons
12368:
12345:
12330:
12321:
12306:Please help
12294:
12246:Baryogenesis
12215:
12171:
11937:
11930:
11903:
11892:
11861:
11814:
11685:
11609:
11533:
11530:
11325:
10927:
10566:
9690:
8814:
8743:
8685:
8383:
8083:
8080:
8019:
7936:
6784:
6781:
6695:
6563:
6433:
6400:
6231:
5862:
5830:
5730:
5621:
5559:
5498:
5327:
5156:
4985:
4814:
4643:
4472:
4331:
4190:
4049:
4017:
3729:
3677:
3380:
3377:
3218:
2983:
2980:
2773:
2770:
2419:
2257:
2209:
2054:
2051:
1841:
1565:
1419:
1282:
1275:
1273:
1242:
1102:
1072:
1065:
1050:
1041:
1011:
994:
984:
912:
898:
892:
888:
877:James Cronin
874:
861:
848:
844:
840:
835:
831:
788:
784:antiparticle
779:
775:
767:
763:
757:
725:
701:
667:
662:
659:CPT symmetry
656:
630:(along with
625:
597:
589:James Cronin
559:
555:
552:CP violation
551:
545:
403:Quantum foam
388:False vacuum
353:Supergravity
313:CPT symmetry
119:
95:Quintessence
29:
14750:Experiments
14641:Technicolor
14603:Dark matter
14497:Quark model
14465:Higgs boson
14460:Gauge boson
14366:CP symmetry
13891:(5): 1051.
12593:Half-Life 2
12443:PMNS matrix
12375:antiprotons
12348:dark matter
5560:The M and
1263:describing
1261:PMNS matrix
1255:describing
1149:accelerator
981:oscillation
849:CP-symmetry
841:CP-symmetry
754:CP-symmetry
556:CP-symmetry
465:Experiments
438:Causal sets
283:Graviscalar
278:Graviphoton
178:Technicolor
153:Fifth force
110:Dark photon
90:Dark energy
85:Dark matter
57:Higgs boson
18:CP-symmetry
14829:Categories
14757:Gran Sasso
14581:Beyond the
14556:CKM matrix
14443:Background
14348:T-symmetry
14343:P-symmetry
14338:C-symmetry
13898:2209.12490
13839:2010.08245
13775:2008.01110
13720:2007.08526
13630:1910.03887
13567:1903.08726
13099:(4): 138.
12915:(2): 169.
12814:: 328–330.
12604:References
12545:T-symmetry
12540:C-symmetry
12356:antimatter
12252:T-symmetry
12250:See also:
11933:Lagrangian
1944:Note that
1253:CKM matrix
1020:) and the
837:Lev Landau
728:beta decay
698:P-symmetry
652:weak decay
608:antimatter
572:P-symmetry
564:C-symmetry
476:Gran Sasso
248:Dark fluid
48:Simulated
14840:Asymmetry
14389:Pin group
14384:Chirality
13864:245641205
13808:220961778
13745:220633488
13663:203951445
13497:1304.6173
13480:Mesons".
13463:118510475
13438:1405.2797
13431:(7): 41.
13407:1210.8257
13185:119333352
12695:117740717
12670:1409.5998
12530:B-factory
12383:positrons
12379:electrons
12295:does not
12188:~
12185:θ
12158:ψ
12142:γ
12134:θ
12119:−
12114:μ
12104:μ
12100:γ
12085:¯
12082:ψ
12071:ν
12068:μ
12061:~
12049:ν
12046:μ
12029:π
12020:θ
11994:−
11989:ν
11986:μ
11976:ν
11973:μ
11955:−
11914:fermionic
11845:∼
11794:∼
11666:∼
11590:∼
11056:−
11024:−
10983:−
10940:′
10688:−
10651:−
10610:−
10279:−
10193:−
9834:−
9317:−
8798:′
8729:λ
8695:λ
8659:∗
8647:∗
8628:′
8611:∗
8608:′
8594:∗
8501:∗
8479:∗
8359:∗
8335:′
8318:∗
8315:′
8301:∗
8289:∗
8201:∗
8188:∗
7564:−
7271:−
6935:−
6818:−
6595:−
6481:−
6465:−
6360:≡
6307:≡
6286:≡
6265:≡
6244:≡
6175:≡
6154:−
6110:−
6093:−
5988:−
5914:−
5692:⋅
5672:−
5649:⋅
5462:−
5416:−
5370:−
5291:−
5245:−
5199:−
5120:−
5074:−
5028:−
3964:−
3932:−
3852:−
3705:⋅
3352:≠
3049:†
2952:ϕ
2948:−
2939:ϕ
2932:
2914:θ
2910:−
2901:θ
2894:
2836:−
2815:¯
2801:−
2739:ϕ
2732:−
2713:θ
2662:ϕ
2655:−
2636:θ
2591:¯
2570:ϕ
2547:θ
2496:ϕ
2473:θ
2396:→
2390:→
2358:→
2352:→
2315:⟶
2276:⟶
2190:ϕ
2184:−
2171:θ
2134:¯
2119:ϕ
2100:θ
2030:ϕ
2024:−
1961:¯
1924:ϕ
1885:θ
1822:¯
1758:¯
1749:→
1743:¯
1708:→
1673:¯
1638:¯
1495:≈
1394:≈
1388:δ
1385:
1038:B-factory
881:Val Fitch
875:In 1964,
732:cobalt-60
600:cosmology
593:Val Fitch
398:Spin foam
293:Gravitino
14801:Category
14782:Tevatron
14634:Theories
14591:Evidence
14455:Fermions
14248:17275359
14142:(1987).
14093:Springer
13884:Symmetry
13800:33605742
13655:32296192
13600:84842008
13592:31283320
13530:20486226
13522:23767711
13358:11531561
13303:24606837
13295:11289970
13240:15277360
12663:: 1–38.
12524:See also
12512:—
12387:neutrons
12364:Big Bang
12346:The non-
12137:′
11797:0.122023
11502:′
11487:′
11469:′
11451:′
11388:′
11380:′
11363:′
11349:′
11297:′
11282:′
11264:′
11246:′
11227:′
11209:′
11131:′
11116:′
11098:′
11080:′
11063:′
11052:′
11020:′
11003:′
10979:′
10962:′
10899:′
10884:′
10866:′
10848:′
10695:′
10684:′
10658:′
10631:′
10617:′
10590:′
10538:′
10523:′
10505:′
10487:′
10418:′
10400:′
10346:′
10331:′
10313:′
10295:′
10225:′
10217:′
10200:′
10189:′
10137:′
10122:′
10104:′
10086:′
10017:′
9999:′
9945:′
9930:′
9912:′
9894:′
9830:′
9822:′
9802:′
9788:′
9762:′
9744:′
9662:′
9647:′
9629:′
9611:′
9542:′
9524:′
9470:′
9455:′
9437:′
9419:′
9349:′
9341:′
9324:′
9313:′
9261:′
9246:′
9228:′
9210:′
9141:′
9123:′
9069:′
9054:′
9036:′
9018:′
8954:′
8946:′
8926:′
8912:′
8886:′
8868:′
1265:neutrino
1070:decays.
1053:D mesons
1030:B mesons
1001:and the
999:Fermilab
913:indirect
819:Lederman
799:Lev Okun
789:In 1956
687:Fermilab
622:Overview
612:universe
501:Tevatron
348:M-theory
288:Graviton
218:M-theory
158:F-theory
137:Theories
74:Evidence
14813:Commons
14777:Super-K
14613:problem
14228:Bibcode
14187:Bibcode
13972:8314164
13952:Bibcode
13903:Bibcode
13844:Bibcode
13780:Bibcode
13725:Bibcode
13635:Bibcode
13572:Bibcode
13502:Bibcode
13443:Bibcode
13366:3197654
13338:Bibcode
13275:Bibcode
13220:Bibcode
13165:Bibcode
13101:Bibcode
13061:3 April
12999:Bibcode
12958:Bibcode
12917:Bibcode
12878:Bibcode
12837:Bibcode
12767:Bibcode
12724:Bibcode
12675:Bibcode
12628:Bibcode
12518:(1982).
12509:> 0.
12413:in the
12400:in the
12371:protons
12316:removed
12301:sources
12224:called
11922:neutron
11920:of the
11848:0.9845.
1400:0.00003
1249:complex
1034:B meson
825:at the
693:History
496:Super-K
14271:1 July
14246:
14154:
14125:
14099:
14076:
14053:
14030:
13997:
13970:
13862:
13806:
13798:
13743:
13661:
13653:
13616:Nature
13598:
13590:
13528:
13520:
13461:
13364:
13356:
13301:
13293:
13238:
13183:
12693:
12471:before
12441:, the
12415:lepton
12352:matter
12258:, and
12226:axions
11910:chiral
11669:0.0075
11593:0.9925
6232:where
3201:
3186:
3166:
3151:
3131:
3114:
3094:
3077:
3069:where
3054:
3032:
2992:
2964:
2926:
2888:
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2647:
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2016:
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1967:
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1309:
1290:
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1121:μ
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6682:,
6675:y
6672:x
6663:2
6659:y
6653:2
6649:x
6645:+
6640:2
6636:y
6632:+
6627:2
6623:x
6614:C
6611:+
6606:y
6603:x
6598:B
6592:A
6588:=
6582:2
6577:2
6573:m
6550:,
6542:y
6539:x
6532:2
6528:y
6522:2
6518:x
6514:+
6509:2
6505:y
6501:+
6496:2
6492:x
6484:C
6476:y
6473:x
6468:B
6462:A
6458:=
6452:2
6447:1
6443:m
6416:2
6412:M
6383:3
6379:B
6374:/
6368:1
6364:B
6357:y
6336:,
6330:3
6326:B
6321:/
6315:2
6311:B
6304:x
6300:,
6294:3
6290:C
6283:C
6279:,
6273:3
6269:B
6262:B
6258:,
6252:3
6248:A
6241:A
6218:,
6212:2
6207:I
6203:M
6198:i
6195:+
6189:2
6184:R
6180:M
6170:]
6164:0
6158:C
6147:x
6144:C
6139:i
6131:C
6125:0
6118:y
6115:C
6101:x
6098:C
6086:y
6083:C
6076:0
6070:[
6065:i
6062:+
6041:]
6034:A
6027:B
6020:B
6017:x
6008:B
6001:)
5996:y
5993:x
5983:x
5980:y
5975:(
5972:B
5969:+
5966:A
5959:B
5956:y
5947:B
5944:x
5937:B
5934:y
5927:)
5922:y
5919:x
5911:y
5908:x
5905:(
5902:B
5898:+
5894:A
5887:[
5882:=
5876:2
5872:M
5845:2
5841:M
5813:2
5808:I
5804:M
5779:2
5775:M
5750:2
5745:R
5741:M
5717:0
5714:=
5709:+
5706:2
5701:R
5697:M
5686:2
5681:I
5677:M
5666:+
5663:2
5658:I
5654:M
5641:2
5636:R
5632:M
5604:2
5600:M
5574:2
5570:M
5542:2
5538:M
5513:2
5509:M
5485:.
5480:3
5476:D
5470:3
5466:B
5457:3
5453:C
5447:3
5443:A
5439:+
5434:6
5430:C
5424:2
5420:A
5411:6
5407:B
5401:2
5397:D
5393:+
5388:5
5384:C
5378:4
5374:B
5365:5
5361:B
5355:4
5351:C
5347:=
5341:3
5337:C
5314:,
5309:3
5305:D
5299:2
5295:B
5286:2
5282:C
5276:3
5272:A
5268:+
5263:6
5259:C
5253:1
5249:B
5240:1
5236:C
5230:6
5226:B
5222:+
5217:5
5213:C
5207:1
5203:A
5194:5
5190:B
5184:1
5180:D
5176:=
5170:2
5166:C
5143:,
5138:3
5134:C
5128:2
5124:B
5115:2
5111:C
5105:3
5101:B
5097:+
5092:2
5088:D
5082:1
5078:B
5069:1
5065:C
5059:2
5055:A
5051:+
5046:4
5042:C
5036:1
5032:A
5023:4
5019:B
5013:1
5009:D
5005:=
4999:1
4995:C
4972:,
4967:3
4963:C
4957:3
4953:D
4949:+
4944:3
4940:B
4934:3
4930:A
4926:+
4921:2
4917:D
4911:6
4907:C
4903:+
4898:2
4894:A
4888:6
4884:B
4880:+
4875:5
4871:C
4865:4
4861:C
4857:+
4852:5
4848:B
4842:4
4838:B
4834:=
4828:3
4824:B
4801:,
4796:3
4792:D
4786:2
4782:C
4778:+
4773:3
4769:A
4763:2
4759:B
4755:+
4750:6
4746:C
4740:1
4736:C
4732:+
4727:6
4723:B
4717:1
4713:B
4709:+
4704:5
4700:C
4694:1
4690:D
4686:+
4681:5
4677:B
4671:1
4667:A
4663:=
4657:2
4653:B
4630:,
4625:3
4621:C
4615:2
4611:C
4607:+
4602:3
4598:B
4592:2
4588:B
4584:+
4579:2
4575:D
4569:1
4565:C
4561:+
4556:2
4552:A
4546:1
4542:B
4538:+
4533:4
4529:C
4523:1
4519:D
4515:+
4510:4
4506:B
4500:1
4496:A
4492:=
4486:1
4482:B
4459:,
4454:2
4449:6
4445:C
4441:+
4436:2
4431:6
4427:B
4423:+
4418:2
4413:5
4409:C
4405:+
4400:2
4395:5
4391:B
4387:+
4382:2
4377:3
4373:D
4369:+
4364:2
4359:3
4355:A
4351:=
4345:3
4341:A
4318:,
4313:2
4308:4
4304:C
4300:+
4295:2
4290:4
4286:B
4282:+
4277:2
4272:3
4268:C
4264:+
4259:2
4254:3
4250:B
4246:+
4241:2
4236:2
4232:D
4228:+
4223:2
4218:2
4214:A
4210:=
4204:2
4200:A
4177:,
4172:2
4167:2
4163:C
4159:+
4154:2
4149:2
4145:B
4141:+
4136:2
4131:1
4127:C
4123:+
4118:2
4113:1
4109:B
4105:+
4100:2
4095:1
4091:D
4087:+
4082:2
4077:1
4073:A
4069:=
4063:1
4059:A
4032:2
4028:M
4004:,
3999:]
3990:3
3986:A
3976:3
3972:C
3967:i
3958:3
3954:B
3944:2
3940:C
3935:i
3926:2
3922:B
3910:3
3906:C
3901:i
3898:+
3892:3
3888:B
3878:2
3874:A
3864:1
3860:C
3855:i
3846:1
3842:B
3830:2
3826:C
3821:i
3818:+
3812:2
3808:B
3798:1
3794:C
3789:i
3786:+
3780:1
3776:B
3766:1
3762:A
3754:[
3749:=
3743:2
3739:M
3713:+
3709:M
3702:M
3699:=
3693:2
3689:M
3664:.
3659:]
3651:6
3647:D
3643:i
3640:+
3635:3
3631:A
3623:6
3619:C
3615:i
3612:+
3607:6
3603:B
3595:5
3591:C
3587:i
3584:+
3579:5
3575:B
3565:3
3561:C
3557:i
3554:+
3549:3
3545:B
3537:2
3533:D
3529:i
3526:+
3521:2
3517:A
3509:4
3505:C
3501:i
3498:+
3493:4
3489:B
3479:2
3475:C
3471:i
3468:+
3463:2
3459:B
3451:1
3447:C
3443:i
3440:+
3435:1
3431:B
3423:1
3419:D
3415:i
3412:+
3407:1
3403:A
3396:[
3391:=
3388:M
3360:d
3356:U
3347:u
3343:U
3320:d
3316:U
3293:u
3289:U
3263:d
3259:U
3236:u
3232:U
3204:,
3195:d
3190:M
3160:u
3155:M
3125:d
3119:U
3088:u
3082:U
3057:,
3043:d
3037:U
3026:u
3020:U
3015:=
3009:M
3006:K
3003:C
2997:V
2967:.
2961:)
2956:2
2943:1
2935:(
2923:)
2918:2
2905:1
2897:(
2884:|
2878:2
2874:M
2869:|
2861:|
2855:1
2851:M
2846:|
2839:4
2833:=
2828:2
2823:|
2812:M
2805:|
2796:2
2791:|
2786:M
2782:|
2753:.
2743:2
2735:i
2728:e
2717:2
2709:i
2705:e
2697:|
2691:2
2687:M
2682:|
2678:+
2666:1
2658:i
2651:e
2640:1
2632:i
2628:e
2620:|
2614:1
2610:M
2605:|
2601:=
2588:M
2574:2
2566:i
2562:e
2551:2
2543:i
2539:e
2531:|
2525:2
2521:M
2516:|
2512:+
2500:1
2492:i
2488:e
2477:1
2469:i
2465:e
2457:|
2451:1
2447:M
2442:|
2438:=
2431:M
2405:.
2399:b
2393:2
2387:a
2361:b
2355:1
2349:a
2323:b
2318:2
2310:a
2284:b
2279:1
2271:a
2244:,
2236:2
2231:|
2226:M
2222:|
2187:i
2180:e
2168:i
2164:e
2156:|
2152:M
2148:|
2144:=
2131:M
2116:i
2113:+
2109:e
2097:i
2093:e
2085:|
2081:M
2077:|
2073:=
2066:M
2038:.
2027:i
2020:e
1996:,
1990:M
1958:M
1932:.
1921:i
1917:e
1893:.
1882:i
1878:e
1870:|
1866:M
1862:|
1858:=
1855:M
1819:M
1790:M
1767:,
1755:b
1740:a
1711:b
1705:a
1682:.
1670:b
1635:a
1609:,
1603:b
1577:a
1552:.
1539:|
1535:J
1531:|
1507:.
1484:3
1476:6
1473:1
1467:=
1458:J
1406:,
1370:s
1357:s
1344:s
1331:c
1322:2
1313:c
1300:c
1296:=
1293:J
1205:e
1165:e
1086:0
1082:D
970:K
959:-
949:K
893:P
889:C
780:C
776:P
764:S
663:T
574:(
566:(
535:e
528:t
521:v
20:)
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