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<p>We study the renormalization of the QCD <i>θ</i> angle at the two-loop level focusing on divergent and finite <i>CP</i>-violating contributions from evanescent operators, using dimensional regularization with the BMHV scheme. When one considers the Lagrangian in <i>d</i>-dimensional space-time instead of four dimensions in dimensional regularization, evanescent operators that break the chiral symmetry are induced. Consequently, <i>T</i>-odd and <i>P</i>-odd fermion loops in the BMHV scheme generate evanescent contributions to the QCD <i>θ</i> angle. We carefully classify the evanescent contributions into two types: one originating from the evanescent operators at the one-loop level and the other directly produced by two-loop calculations. We show that renormalization of the parameters in the BMHV scheme keeps removing those unphysical contributions to the QCD <i>θ</i> angle at any scale at the two-loop level. We also discuss how the rephasing invariance of the radiative correction to the QCD <i>θ</i> angle is realized in the BMHV scheme.</p>

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Two-loop corrections to QCD θ angle from evanescent operator in the BMHV scheme

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月17日

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  • Tatsuya Banno,
  • Junji Hisano,
  • Teppei Kitahara,
  • Kiyoto Ogawa,
  • Naohiro Osamura

摘要

We study the renormalization of the QCD θ angle at the two-loop level focusing on divergent and finite CP-violating contributions from evanescent operators, using dimensional regularization with the BMHV scheme. When one considers the Lagrangian in d-dimensional space-time instead of four dimensions in dimensional regularization, evanescent operators that break the chiral symmetry are induced. Consequently, T-odd and P-odd fermion loops in the BMHV scheme generate evanescent contributions to the QCD θ angle. We carefully classify the evanescent contributions into two types: one originating from the evanescent operators at the one-loop level and the other directly produced by two-loop calculations. We show that renormalization of the parameters in the BMHV scheme keeps removing those unphysical contributions to the QCD θ angle at any scale at the two-loop level. We also discuss how the rephasing invariance of the radiative correction to the QCD θ angle is realized in the BMHV scheme.