CP Violation |

**In General** > s.a. atomic physics;
early-universe cosmology; matter [antimatter];
neutrino mixing; particle statistics.

* __Idea__: One of several
possible explanations for the matter-antimatter asymmetry (baryon
asymmetry) observed in the universe.

* __Theory__: Both strong and
weak interactions can violate CP (charge-parity) symmetry; The effect can be
described in terms of mixing in the CKM matrix (three angles *α*,
*β* and *γ* which form a non-degenerate CKM unitarity
triangle–the amount of violation is proportional to the area), but
could also be due to other physics; The standard model "predicts" a value
of sin(2*β*) between 0.66 and 0.84; Violations are likely to
be connected to baryon asymmetry, and maybe neutrino oscillations.

* __CKM matrix and unitarity__:
The entries *V*_{ij}
of the CKM matrix, where *i* = *u*, *c*, *t*,
and *j* = *d*, *s*, *b*, are the
amplitudes for the corresponding flavor-changing processes, and must
be unitary; The "unitarity triangle" is the expression one obtains
when one writes explicitly one of the unitarity conditions,
*V*_{ub}
*V*_{ud}*
+ *V*_{cb}
*V*_{cd}*
+ *V*_{tb}
*V*_{td}* = 0 (so this
vanishing of the sum of three complex numbers is one of six such triangles
one can get from *V*_{ij},
but it is the one that contains the two most significant phases).

* __Idea, experiment__:
Can't measure all three CKM angles in the same experiment (BaBar and Belle measure
*α* and *β* – although *α* will require
much more data –, but need *B*_{s}s
to measure *γ*; Weak effects are esier to compare with theory.

* __In 2+1 dimensions__:
P and T are violated by particles with fractional statistics.

> __Online resources__:
see Wikipedia page.

**History, Status**

* __1957__: L Landau argues that,
although P can be violated, CP should not be; A Pais & M Gell-Mann suggest that
the K^{0} and K^{0}-bar
mesons are linear combinations of parity eigenstates K_{1}
(−1, long-lived, decays into 3*π*) and K_{2}
(+1, short-lived, decays into 2*π*); K_{1}
found by L Lederman et al.

* __1964__: Unexpected, first indirect evidence
found by Fitch & Cronin (CCFT) in K_{1} meson decay
into 2*π* [@ news pn(99)mar].

* __1998__:
Indications found by CDF in B meson decay.

* __1999__: Direct evidence
in K meson decay at Fermilab, *ε*'/*ε* = (28
± 4) × 10^{−4}, and CERN,
(18.5 ± 7) × 10^{−4}.

* __2000__: RHIC is now online, will
search for violations due to strong interaction, as opposed to weak interactions;
Results from B meson decay give sin(2*β*) = 0.45 ± 0.44
± 0.45 (KEK) and 0.45 ± 0.44 ± 0.45 (BaBar at SLAC).

* __2001__:
Measurements from B meson decays give sin(2*β*) = 0.59 ±
0.14 (BaBar at SLAC) and 0.99 ± 0.14 (Belle at KEK); Aleph and CDF
give intermediate values; Strong interaction effects not yet seen.

* __2001__: Direct violation –
Differences between decays B mesons and their antiparticle equivalents at BaBar.

* __2006__: The amount of CP
violation observed so far is insufficient to account for matter domination
(there may be more in quark, neutrino, or Higgs physics).

* __2012__:
Unexpectedly large violation seen in charmed meson decay.

* __2017__: CP violation seen in heavy baryon decays.

* __2019__: CP violation seen in the charm sector, D mesons.

**References**
> s.a. CPT [including T-reversal]; modified QED;
parity [violation]; theta sectors.

@ __Reviews, news__: Adair SA(88)feb;
news PT(88)oct;
Harrison pw(03)jul;
news pw(06)apr;
Ibrahim & Nath RMP(08);
Kobayashi IJMPA(09);
Maskawa IJMPA(09);
Frère CRP(12)-a1201 [rev].

@ __Books__: Jarlskog 89;
Wolfenstein ed-90;
Castelo Branco et al 99 [r PT(00)aug];
Bigi & Sanda 09;
Sozzi 12.

@ __General articles__:
Fitch RMP(81);
Cronin RMP(81);
Rosner AJP(96)aug [demo];
Rosner & Slezak AJP(01)jan [classical analog];
Sozzi & Mannelli RNC(03) [measurements];
Smit JHEP(04)hp [and standard model effective action];
Gershon pw(07)apr [unitarity triangle];
Ashtekar SHPMP-a1307-conf [new perspective].

@ __Lepton sector__: Branco & Rebelo NJP(05) [and neutrino mass];
Dita PRD(06)-a1101;
Farzan & Smirnov JHEP(07);
Pascoli et al PRD(07) [and leptogenesis];
Winter PLB(09) [neutrino propagation];
Branco et al RMP(12) [rev];
Fogli et al PRD(12)-a1205 [neutrino masses, mixings and phases];
Miller PT(20)jun [in the neutrino sector];
> s.a. neutrino mixing.

@ __Spontaneous violation__: Dorey et al JPA(01) [and supersymmetry];
Frampton IJMPA(02);
Balaji et al PLB(04) [dynamical, early universe].

@ __ B-meson decays__:
Green & McMahon CP(01);
Peruzzi RNC(04);
Gronau IJMPA(07);
Roney Phys(20) [re observation];
> s.a. Weak Measurements.

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**Related Topics**

> s.a. Charge Conjugation; electromagnetism
[dipole moments]; matter [mirror matter]; realism;
uncertainty relations.

* __Strong CP problem__: The Peccei-Quinn
mechanism is the most popular resolution, with the Nelson-Barr considered the most
viable alternative.

@ __Strong CP problem__:
Fort & Gambini ht/97 [in loop formulation];
Dine hp/00-ln;
Hsu & Sannino PLB(05);
Mitra hp/05-conf [no problem];
Takahashi PTP(09)-a0804 [anthropic solution];
Peccei AIP(10)-a1005 [history, and spontaneously-broken chiral symmetry];
Swain a1005 [and the existence of black holes];
Lattanzi & Mercuri PRD(10)-a1006 [solution via the Peccei-Quinn mechanism];
Acharya et al JHEP(10) [M-theory solution];
Hook PRL(15)-a1411 [anomalous solutions].

@ __Other__: Home & Majumdar FP(99)qp [and Bohmian insert];
Huggett PhSc(00)jun [*P* violation];
Bertlmann et al PLA(01)qp [and Bell inequalities];
Caliceti et al PLA(05)mp/04 [with CPT symmetry];
Brauner et al PRL(12)-a1110 [temperature dependence of CP violation effects in the Standard Model].

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