Novel loop-diagrammatic approach to QCD θ parameter and application to the left-right model

Abstract

When the QCD axion is absent in full theory, the strong CP problem has to be explained by an additional mechanism, e.g., the left-right symmetry. Even though tree-level QCD overline{theta} parameter is restricted by the mechanism, radiative corrections to overline{theta} are mostly generated, which leads to a dangerous neutron electric dipole moment (EDM). The ordinary method for calculating the radiative overline{theta} utilizes an equation overline{theta}=-arg det {m}_q^{textrm{loop}} based on the chiral rotations of complex quark masses. In this paper, we point out that when full theory includes extra heavy quarks, the ordinary method is unsettled for the extra quark contributions and does not contain its full radiative corrections. We formulate a novel method to calculate the radiative corrections to overline{theta} through a direct loop-diagrammatic approach, which should be more robust than the ordinary one. As an application, we investigate the radiative overline{theta} in the minimal left-right symmetric model. We first confirm a seminal result that two-loop level radiative overline{theta} completely vanishes (corresponding to one-loop corrections to the quark mass matrices). Furthermore, we estimate the size of a non-vanishing radiative overline{theta} at three-loop level. It is found that the resultant induced neutron EDM is comparable to the current experimental bound, and the expected size is restricted by the perturbative unitarity bound in the minimal left-right model.