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

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 treelevel QCD theta($) over bar parameter is restricted by the mechanism, radiative corrections to theta($) over bar are mostly generated, which leads to a dangerous neutron electric dipole moment (EDM). The ordinary method for calculating the radiative theta($) over bar utilizes an equation theta($) over bar = -arg detmloop q 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 theta($) over bar through a direct loop-diagrammatic approach, which should be more robust than the ordinary one. As an application, we investigate the radiative theta($) over bar in the minimal left-right symmetric model. We first confirm a seminal result that two-loop level radiative theta($) over bar completely vanishes (corresponding to oneloop corrections to the quark mass matrices). Furthermore, we estimate the size of a nonvanishing radiative theta($) over bar 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.