Chiral phase in fermionic measure and the resolution of the strong CP problem

The fermionic measure in the functional integral of a gauge theory suffers from an ambiguity in the form of a chiral phase. By fixing it, one is led once again to the conclusion that a chiral phase in the quark mass term of QCD has no effect and cannot cause CP violation. At present, a popular approach to anomalies is in the functional integral formalism. Here an integration is carried out over different field configurations. The integrand involves the classical action which possesses all classical symmetries, but the measure of integration may break some of these [1], and lead to anomalies, which can be calculated if a regularization is employed. The measure of integration over fermions has been extensively studied in connection with chiral anomalies, but as will be demonstrated here, there is still a certain ambiguity left. This ambiguity relates to the case when the fermion mass is non-vanishing, and is practically relevant in the important context of QCD. In the standard model, the parity-violating electroweak sector gives rise to an unknown chiral phase in the quark mass term of QCD, and this has been at the basis of the strong CP problem. The ambiguity in the fermion measure would imply an ambiguity in the amount of CP violation caused by the chiral phase in the fermion mass term. The natural way of fixing the ambiguity makes the CP violation disappear. This is in consonance with the results obtained by explicit regularization of the action, namely the generalized Pauli-Villars regularization [2] and lattice regularizations [3]. This reconfirms the basic idea [email protected]