CP violation

In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge conjugation symmetry) and P-symmetry (parity 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 kaons resulted in the Nobel Prize in Physics in 1980 for its discoverers James Cronin and Val Fitch. It plays an important role both in the attempts of cosmology to explain the dominance of matter over antimatter in the present Universe, and in the study of weak interactions in particle physics. CP-symmetry, often called just CP, is the product of two symmetries: C for charge conjugation, which transforms a particle into its antiparticle, and P for parity, which creates the mirror image of a physical system. The strong interaction and electromagnetic interaction seem to be invariant under the combined CP transformation operation, but this symmetry is slightly violated during certain types of weak decay. Historically, CP-symmetry was proposed to restore order after the discovery of parity violation in the 1950s. The idea behind parity symmetry is that the equations of particle physics are invariant under mirror inversion. This leads to the prediction that the mirror image of a reaction (such as a chemical reaction or radioactive decay) occurs at the same rate as the original reaction. Parity symmetry appears to be valid for all reactions involving electromagnetism and strong interactions. Until 1956, parity conservation was believed to be one of the fundamental geometric conservation laws (along with conservation of energy and conservation of momentum). However, in 1956 a careful critical review of the existing experimental data by theoretical physicists Tsung-Dao Lee and Chen-Ning Yang 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. The first test based on beta decay of cobalt-60 nuclei was carried out in 1956 by a group led by Chien-Shiung Wu, 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. Overall, the symmetry of a quantum mechanical system can be restored if another symmetry S can be found such that the combined symmetry PS remains unbroken. This rather subtle point about the structure of Hilbert space was realized shortly after the discovery of P violation, and it was proposed that charge conjugation was the desired symmetry to restore order. Simply speaking, charge conjugation is a symmetry between particles and antiparticles, and so CP-symmetry was proposed in 1957 by Lev Landau as the true symmetry between matter and antimatter.In other words, a process in which all particles are exchanged with their antiparticles was assumed to be equivalent to the mirror image of the original process. 'Direct' CP violation is allowed in the Standard Model if a complex phase appears in the CKM matrix describing quark mixing, or the PMNS matrix describing neutrino mixing. A necessary condition for the appearance of the complex phase is the presence of at least three generations of quarks. If fewer generations are present, the complex phase parameter can be absorbed into redefinitions of the quark fields. A popular rephasing invariant whose vanishing signals absence of CP violation and occurs in most CP violating amplitudes is the Jarlskog invariant, J = c 12 c 13 2 c 23 s 12 s 13 s 23 sin ⁡ δ ≈ 3   10 − 5 . {displaystyle J=c_{12}c_{13}^{2}c_{23}s_{12}s_{13}s_{23}sin delta approx 3~10^{-5}.} 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) a {displaystyle a} and b {displaystyle b} , and their antiparticles a ¯ {displaystyle {ar {a}}} and b ¯ {displaystyle {ar {b}}} . Now consider the processes a → b {displaystyle a ightarrow b} and the corresponding antiparticle process a ¯ → b ¯ {displaystyle {ar {a}} ightarrow {ar {b}}} , and denote their amplitudes M {displaystyle M} and M ¯ {displaystyle {ar {M}}} respectively. Before CP violation, these terms must be the same complex number. We can separate the magnitude and phase by writing M = | M | e i θ {displaystyle M=|M|e^{i heta }} . If a phase term is introduced from (e.g.) the CKM matrix, denote it e i ϕ {displaystyle e^{iphi }} . Note that M ¯ {displaystyle {ar {M}}} contains the conjugate matrix to M {displaystyle M} , so it picks up a phase term e − i ϕ {displaystyle e^{-iphi }} .