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Closer look at the matching condition for radiative QCD θθ parameter

Published 14 Nov 2023 in hep-ph | (2311.07817v2)

Abstract: In this paper, we scrutinize a radiatively generated QCD θ\theta parameter at the two-loop level based on both full analytical loop functions with the Fock-Schwinger gauge method and the effective field theory approach, using simplified models. We observe that the radiatively generated θ\theta parameters at the low energy scale precisely match between them. It provides validity to perturbative loop calculations of the QCD θ\theta parameter with the Fock-Schwinger gauge method. Furthermore, it is also shown that the ordinary Fujikawa method for the radiative θ\theta parameter by using θˉ=−argdetMq<sup>loop\bar\theta = - arg det M_q<sup>{loop} does not cover all contributions in the simplified models. But, we also find that when there is a scale hierarchy in CPCP-violating sector, evaluation of the Fujikawa method is numerically sufficient. As an application, we calculate the radiative θ\theta parameter at the two-loop level in a slightly extended Nelson-Barr model, where the spontaneous CPCP violation occurs to solve the strong CPCP problem. It is found a part of the radiative θ\theta parameters cannot be described by the Fujikawa method.

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