Dec 1st, 2007 by anhaipeng
The strong CP phase is very small and might be zero, the main constraint is from the experiment of neutron electric dipole moment. This term can be explicitly written as 
, G is the field strength of the gluon field. This term proportional to 
, so it preserves C and violates P and CP. Therefore, if the theory at a higher energy automatically preserves parity then we could naturally get a small strong CP phase. This may be a hint that at higher energy level parity is preserved.
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I only know we can introduce a PQ symmetry to preserve CP in strong interaction, but do not know the details. Does that have anything to do with what you said? And I have another question: in cosmology, matter-antimatter asymmetry requires a not too small CP violation, but it is not observed in our experiments. Is there a possibility to find a mechanism which violates CP strongly in high energy but restore it in low energy?（sounds crazy)
PS: One more wondering: why can’t I see latex output any more? I tried the old theme and can not see either. Do you have the same problem?
is left-right symmetry model possible to solve this problem?
aa very naive thought:
Introduce a Higgs like tensor field [tex]H^{abcd}[/tex],
and an unrenormalized interaction term :[tex]H^{abcd}G_{ab}G{cd}[/tex]. This term is suppressed by some
large mass scale M. If H acquire vacuum expectation at some
high energy scale v: [tex]=v\epsilon^{abcd}[/tex], then CP violation
arises. The problem is that, in order to have a very small theta, M should be much much larger than v.
Phiphy:
The idea you proposed here is not crazy. The baryogenesis CP and EDM CP are related, but not exactly the same. To describe cosmological evolution, we need one additional parameter–temperature. The baryogenesis CP is finite temperature CP and EDM CP is zero temperature CP (i.e., CP observed or to be observed on Colliders). If the CP symmetry is broken explicitly, these two CPs generally are idential. But, if the CP is broken spontaneously (e.g., together with EW phase transition), these two CPs can be very different. In the latter case, the CP is related to the VEV of a vacuum, and hence is time-dependent, which implies a possibility that we have large CP at the baryogenesis time and a small or trivial one today (so no EDM problem).
LT:
I am confused. If we want a large CPV at finite T and a small one at T=0, what will be the relation between CPV and VEV(which is large at T=0)?
pekingli:
Gauge theory requires that scalar fileld must be complex. Besides the amplitude component, higgs field also has a phase component. It is the VEV of the latter that may cause spontaneous CP breaking (as a comparison, the particle mass spectra are more closely related to the VEV of the former). Spontaneous CP breaking extensively exists in the extended version of MSSM, e.g., NMSSM, UMSSM…, but not in MSSM (it is easy to check that, up to a unitary gauge, the VEVs of higgs phases are trivial in this case).