Chiral Response of QCD Topology across the Thermal Crossover

Abstract

We introduce a novel relation connecting the light-quark-mass derivative of the topological susceptibility in quantum chromodynamics (QCD) to the connected correlation between the squared topological charge and the integrated light-quark scalar density. This relation gives direct access to the chiral response of QCD topology---the local logarithmic light-quark-mass derivative of the susceptibility---from a single ensemble at fixed quark masses for each temperature, without additional simulations at shifted masses. Applying this relation to $(2+1)$-flavor lattice QCD at $m_π\simeq220\,\mathrm{MeV}$ over temperatures ranging from well below to well above the chiral crossover, we find that the response rises rapidly through the crossover from approximately unity toward two. This evolution corresponds to a change from nearly linear to nearly quadratic dependence of the topological susceptibility on the light-quark mass. Using the chiral response as the exponent of a local power law in the light-quark mass, we determine its effective amplitude from the topological susceptibility. This amplitude exhibits a maximum near the crossover temperature, reflecting the competition between the decreasing topological susceptibility and the increasing chiral response. These results reveal a thermal reorganization of the quark-mass dependence of QCD topology beyond the suppression of topological fluctuations alone.