Symmetries and their breaking are essential topics in modern physics, among which the discrete symmetries C (charge conjugation), P (parity), and T (time reversal) are of special importance. This is partially because the violation of the combined C and P symmetries is one of the three Sakharov conditions that are necessary to give rise to the baryon asymmetry of the universe (BAU). However, despite the great success of the standard model (SM), the weak baryogenesis mechanism from the CP violation within the SM contributes negligibly (∼ 16 orders of magnitude smaller than the observed BAU). This poses a hint that, besides the possible θ term in QCD, there could exist beyond-standard-model (BSM) sources of CP violation and thus the study of CP violation plays an important role in the efforts of searching for BSM physics.
The first experimental upper limit on the neutron EDM (nEDM) was given in 1957 as ∼ 10^−20 e·cm. During the past 60 years of experiments, this upper limit has been improved by 6 orders of magnitude. The most recent experimental result of the nEDM is 0.0(1.1)(0.2) × 10^−26 e·cm, which is still around 5 orders of magnitude larger than the contribution that can be offered by the weak CP violating phase. Currently, several experiments are aiming at improving the limit down to 10^−28 e·cm in the next ∼10 years.
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By using the most recent experimental upper limit of dn, our results indicate that θ¯ < 10^−10.
This limit is equivalent to less than ± 1.2 x 10^-13 e·fm, which implies that the magnitude of the θ term must be less than about ± 10^-10, a constraint that will improve by about two orders of magnitude in the next decade.
This is too small by more than ten orders of magnitude to make a meaningful dent in the Sakharov conditions. The θ term would have to be roughly on O(1) after running to extremely high energy scales to explain the matter-antimatter asymmetry of the universe. But, the strong force becomes weaker, not stronger, at higher energy scales, so CP violation in the strong force should be less important at these energy scales, not more important.
Personally, I'm confident that the θ term is exactly zero, and that there are no new CP violating physics at higher energies, at least up to about the GUT scale, that explain the matter-antimatter asymmetry of the universe.
Neither the zero value of the θ term, nor the existence of matter-antimatter asymmetry in the universe at a infinitesimal time after the Big Bang are "problems" in physics to be solved. They are simply descriptive features of our reality.
We calculate the nucleon electric dipole moment (EDM) from the θ term with overlap fermions on three domain wall lattices with different sea pion masses at lattice spacing 0.11 fm. Due to the chiral symmetry conserved by the overlap fermions, we have well defined topological charge and chiral limit for the EDM. Thus, the chiral extrapolation can be carried out reliably at nonzero lattice spacings. We use three to four different partially quenched valence pion masses for each sea pion mass and find that the EDM dependence on the valence and sea pion masses behaves oppositely, which can be described by partially quenched chiral perturbation theory. With the help of the cluster decomposition error reduction (CDER) technique, we determine the neutron and proton EDM at the physical pion mass to be dn=−0.00148(14)(31)θ¯ e⋅fm and dp=0.0038(11)(8)θ¯ e⋅fm. This work is a clear demonstration of the advantages of using chiral fermions in the nucleon EDM calculation and paves the road to future precise studies of the strong CP violation effects.
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