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arXiv · 2607.17816

Renormalization of meson susceptibilities and RG-invariant symmetry ratios in QCD

Ting-Wai Chiu
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Abstract

We analyze the ultraviolet divergence structure of meson susceptibilities in finite-temperature QCD, for lattice formulations with exact chiral symmetry. The bare susceptibility separates into additive divergences and a multiplicative renormalization $Z_\Gamma^{2}$. The additive divergences are temperature-independent, and are removed by the temperature subtraction. They consist of the leading power divergence $\alpha_\Gamma/(2a^2)$ from the identity operator, together with a mass-dependent logarithmic term $\propto m^2\ln(1/(am))$. Exact chiral symmetry forbids all mass-dependent \emph{power} divergences of the susceptibility. The multiplicative factor $Z_\Gamma^{2}$ has a logarithmic dependence on the lattice spacing, controlled by the operator anomalous dimension. We show that the symmetry ratio $\kappa_{AB} = (\chi_A^{\rm reg} - \chi_B^{\rm reg})/ (\chi_A^{\rm reg} + \chi_B^{\rm reg})$, built from temperature-subtracted susceptibilities of symmetry partners, is exactly renormalization-group invariant and scheme-independent. The additive divergence is removed by the subtraction, and the multiplicative factor cancels through the equality $Z_A = Z_B$. This equality holds for any number of flavors and any quark masses in a mass-independent scheme, unaffected by spontaneous symmetry breaking or the $U(1)_A$ anomaly. We derive the complete $Z$-factor chains for all meson channels and contrast the divergence structure with that of Wilson fermions, for which the explicit chiral-symmetry breaking induces a chiral-odd power-divergent mixing and spoils the equality $Z_A = Z_B$ on which the construction relies.

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Ting-Wai Chiu. 2026-07-20. Renormalization of meson susceptibilities and RG-invariant symmetry ratios in QCD. https://arxiv.org/abs/2607.17816

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