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arXiv · 2101.09479

Renormalization of the flavor-singlet axial-vector current and its anomaly in dimensional regularization

Taushif Ahmed·Long Chen·Michał Czakon
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Abstract

The renormalization constant $Z_J$ of the flavor-singlet axial-vector current with a non-anticommuting $γ_5$ in dimensional regularization is determined to order $α_s^3$ in QCD with massless quarks. The result is obtained by computing the matrix elements of the operators appearing in the axial-anomaly equation $\big[\partial_μ J^μ_{5} \big]_{R} = \frac{α_s}{4 π}\, n_f\, {\displaystyle \mathrm{T}_{F}} \, \big[F \tilde{F} \big]_{R}$ between the vacuum and a state of two (off-shell) gluons to 4-loop order. Furthermore, through this computation, the conjectured equality between the $\overline{\mathrm{MS}}$ renormalization constant $Z_{F\tilde{F}}$ associated with the operator $\big[F \tilde{F} \big]_{R}$ and that of $α_s$ is verified explicitly to hold true at 4-loop order. This equality automatically ensures a relation between the respective anomalous dimensions, $γ_{\scriptscriptstyle J} = \frac{α_s}{4 π}\, n_f\, {\displaystyle \mathrm{T}_{F}} \, γ_{\scriptscriptstyle FJ} $, at order $α_s^4$ given the validity of the axial-anomaly equation which was used to determine the non-$\overline{\mathrm{MS}}$ piece of $Z_J$ for the particular $γ_5$ prescription in use.

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Taushif Ahmed, Long Chen, Michał Czakon. 2021-05-11. Renormalization of the flavor-singlet axial-vector current and its anomaly in dimensional regularization. https://doi.org/10.1007/jhep05(2021)087

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