Complex fermion mass term, regularization and CP violation

TL;DR

This paper discusses how the CP violation in QCD can be managed through regularization choices, specifically using zeta function regularization, and explores implications for the strong CP problem.

Contribution

It demonstrates that a complex quark mass term can be regularized without violating CP, resolving a contradiction and highlighting the importance of regularization dependence.

Findings

Regularization choice affects CP violation in QCD

Zeta function regularization preserves CP symmetry

Implications for solving the strong CP problem

Abstract

It is well known that the CP violating theta term of QCD can be converted to a phase in the quark mass term. However, a theory with a complex mass term for quarks can be regularized so as not to violate CP, for example through a zeta function. The contradiction is resolved through the recognition of a dependence on the regularization or measure. The appropriate choice of regularization is discussed and implications for the strong CP problem are pointed out.