2026/07/20 by Ting-Wai Chiu
#hep-lat #hep-ph #hep-th
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 ZΓ2. The additive divergences are temperature-independent, and are removed by the temperature subtraction. They consist of the leading power divergence αΓ/(2a2) from the identity operator, together with a mass-dependent logarithmic term ∝ m2ln(1/(am)). Exact chiral symmetry forbids all mass-dependent power divergences of the susceptibility. The multiplicative factor ZΓ2 has a logarithmic dependence on the lattice spacing, controlled by the operator anomalous dimension. We show that the symmetry ratio κAB = (χA\rm reg - χB\rm reg)/ (χA\rm reg + χB\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 ZA = ZB. 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 ZA = ZB on which the construction relies.