In physics, and specifically particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics. It plays an important role in theories of cosmology that attempt to explain the dominance of matter over antimatter in the present Universe. 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. The study of CP violation remains a vibrant area of theoretical and experimental work today.

What is CP?

---

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 are invariant under the 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. Until the 1940s, physicists believed all reactions demonstrated parity conservation. In the 1950s, scientists found an exception to P symmetry. Studies on radioactive reactions revealed that some reactions do not demonstrate 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 simple symmetry between particles and antiparticles, and so CP symmetry was proposed as the true symmetry between matter and antimatter.

CP Violation

---

In 1964, James Cronin and Val Fitch provided clear evidence that CP symmetry could be broken, too, winning them the 1980 Nobel Prize. Their discovery showed that weak interactions violate both the charge-conjugation symmetry C between particles and antiparticles and at the same time also violate P or parity. 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 nearly a symmetry created a great puzzle.

It was discovered in 1964 by the group of Christenson, Cronin, Fitch and Turlay in a kaon decay experiment that CP symmetry was violated, and only a weaker version of the symmetry could be preserved by physical phenomena, which was CPT-symmetry. Besides C and P, there is a third operation, time reversal (T), which corresponds to reversal of motion. Invariance under time implies that whenever a motion is allowed by the laws of physics, the reversed motion is also an allowed one. Therefore, the combination of CPT is thought to constitute an exact symmetry of all types of fundamental interactions. Because of the CPT-symmetry, a violation of the CP-symmetry is equivalent to a violation of the T-symmetry. CP violation implied nonconservation of T, provided that the long-held CPT theorem was valid. In this theorem, regarded as one of the basic principles of quantum field theory, charge conjugation, parity, and time reversal are applied together.

Recently, a new generation of experiments, including the BaBar Experiment at the Stanford Linear Accelerator Center (SLAC) and the Belle Experiment at the High Energy Accelerator Research Organisation (KEK), Japan, have observed CP violation using B mesons //physicsweb.org/articles/world/14/8/9. Before these experiments, it was a logical possibility that all CP violation was confined to kaon physics. These experiments dispelled any doubt that the interactions of the Standard Model violated CP.

The CP violation of the Standard model is incorporated by including a complex phase in the CKM matrix. A necessary condition for the appearance of the complex phase, and thus for CP-violation, is the presence of at least three generations of quarks.

There is no experimentally known violation of the CP-symmetry in quantum chromodynamics; see below.

Strong CP problem

---

In particle physics, the strong CP problem is the puzzling question why quantum chromodynamics (QCD) does not seem to break the CP-symmetry.

QCD does not violate the CP-symmetry as easily as the electroweak theory; unlike the electroweak theory where the gauge fields couple to chiral currents constructed from the fermionic 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 electric dipole moment of the neutron which would be comparable to $10^\{-18\}$ e.m (electrons multiplied by meters) while the experimental upper bound is roughly a trillion times smaller.

This is a problem because at the end, there are natural terms in the QCD Lagrangian that are able to break the CP-symmetry.

$\{\backslash mathcal\; L\}\; =\; -\backslash frac\{1\}\{4\}\; \{\backslash mathrm\; \{tr\}\backslash ,\}\; F\_\{\backslash mu\backslash nu\}F^\{\backslash mu\backslash nu\}-\backslash frac\{n\_f\; g^2\backslash theta\}\{32\backslash pi^2\}$

{\mathrm {tr}\,}F_{\mu\nu}\tilde F^{\mu\nu}+\bar \psi(i\gamma^\mu D_\mu - m e^{i\theta'\gamma_5})\psi

For a nonzero choice of the QCD $\backslash theta$-angle and the chiral quark mass phase $\backslash theta\text{'}$ 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 $\backslash tilde\backslash theta$-angle, but it remains to be explained why Nature chooses an unbelievably small value of this angle instead of an angle of order one; the special choice of the $\backslash theta$-angle that must be very close to zero (in this case) is an example of fine-tuning in physics.

The most famous solution that has been proposed to solve the strong CP problem is the Peccei-Quinn theory, involving new scalar particles called axions.

CP violation and the existence of the universe

---

One of the unsolved theoretical questions in physics is why the universe is made chiefly of matter, rather than consisting of equal parts of matter and antimatter. With a series of plausible assumptions, it can be demonstrated that the observed matter-antimatter ratio may have been produced by the occurrence of CP violation in the first seconds after the Big Bang, the event in which the universe was formed.

In the Standard Model, the Big Bang should have produced equal amounts of matter and anti-matter if CP-symmetry was preserved; as such, there should have been total cancellation of both. In other words, protons should have cancelled with anti-protons, electrons with positrons, neutrons with anti-neutrons, and so on for all elementary particles. This would have resulted in a sea of photons in the universe with no matter. Since this is quite evidently not the case, during the Big Bang, physical laws must have acted differently for matter and antimatter, and since CP-Symmetry would dictate that physics would act identically to both classes of matter, it cannot hold in all cases.

Therefore, it is postulated that a force must have acted in such a way to make baryon number and lepton number no longer conserved. While the weak force can account for a small percentage of CP-violation, it is predicted to be sufficient for only a single galaxy's equivalent mass of matter.

Since the Standard Model does not accurately predict this discrepancy (along with the problems presented by dark matter and dark energy), it would seem that the current Standard Model is incomplete or physics is otherwise in error. This has lead to a great deal of interest in experimental particle physics, and hopes for various theories of astrophysics, such as inflationary theory and baryogenesis, to explain the violation.

References

---

• (A collection of essays introducing the subject, with an emphasis on experimental results.)
• (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.)
• I. Bigi, CP violation, an essential mystery in Nature's grand design. Invited lecture given at the XXV ITEP Winter school of Physics, February 18-27, 1997, Moscow, Russia, at 'Frontiers in Contemporary Physics', May 11-16, 1997, Vanderbilt University, Nashville, USA, and at the International School of Physics 'Enrico Fermi', CXXXVII Course 'Heavy Flavour Physics: A Probe of Nature's Grand Design', Varenna, Italy, July 8-18, 1997. hep-ph/9803479.
• Davide Castelvecchi, What is direct CP-violation?, Stanford Linear Accelerator (SLAC)

Quantum field theory | Particle physics | Symmetry | Conservation laws

CP-Verletzung | Violation de la symétrie CP | Simmetria CP | CP-szimmetria | CP-symmetrie