### CP Violation and CPT symmetry

CPT stands for three operators in quantum mechanics. The C operator is called the charge conjugation operator. It changes every particle into its antiparticle. The P operator is called the spatial inversion operator. It flips the direction of each of the three spatial axes and is equivalent to a combination of a mirror reflection and rotation. The T operator is called the time reversal operator. It reverses the direction of the flow of time. For a long time, it was thought that the laws of Nature are invariant under each of those operations. The P-symmetry (a.k.a. Parity) was the first to fall in 1956, while the symmetry was thought to be preserved by the combined operation of CP as well as by T. This picture, however, only survived until 1964, when the CP was first shown to be violated in experiment carried out by J. Cronin, V. Fitch and R. Turlay [1]. They showed that kaon decays do not preserve CP symmetry. For this discovery, Cronin and Fitch received the 1980 Nobel Prize in Physics.

The symmetry with respect to the combined CPT transformation holds for now, although it is being put to more and more stringent experimental tests.

### CP Violation in the Standard Model

The CP violating effects can be introduced in the electroweak sector of the Standard Model through the Cabibbo-Kobayashi-Maskawa (CKM) matrix. The strong interactions theory (called quantum chromodynamics, or QCD), on the other hand, contains CP violation in the non-perturbative sector, and it presents a formidable theoretical challenge to explain why CP violation is actually observed to be so small (the so-called the strong CP problem) [2,3]. A solution proposed by R. Peccei and H. Quinn in 1976 [4] is a scalar particle that was later called the axion (allegedly after a popular cleaning fluid that is supposed to solve tough problems).

### The CASPEr experiment

# References

- [1] J. H. Christenson et al. Evidence for the 2π Decay of the K20 Meson. Physical Review Letters, 13(4):138-140, 1964.
- [2] M. Kaku. Quantum field theory, a modern introduction. 1993.
- [3] M. Pospelov and A. Ritz. Theta vacua, QCD sum rules, and the neutron electric dipole moment. Nuclear Physics B, 573(1):177–200, 2000, 2000.
- [4] R. Peccei and H. Quinn. CP Conservation in the Presence of Pseudoparticles. Physical Review Letters, 38(25):1440–1443, 1977.
- [5] P. Graham and S. Rajendran. New observables for direct detection of axion dark matter. Physical Review D, 88(3):23-35, 2013.
- [6]. D. Budker, P. Graham, M. Ledbetter, S. Rajendran, A. Sushkov. Proposal for a Cosmic Axion Spin Precession Experiment (CASPEr). Physical Review X, 4(2):21-30, 2014.