Chiral Properties of $(2\!+\!1)$-Flavor QCD in Magnetic Fields at Zero Temperature

TL;DR

This lattice QCD study investigates how strong magnetic fields influence chiral symmetry breaking, meson properties, and decay constants in $(2+1)$-flavor QCD at zero temperature, revealing magnetic catalysis and complex meson mass behaviors.

Contribution

First comprehensive lattice QCD analysis of chiral and meson properties under magnetic fields with physical pion masses and controlled continuum extrapolation.

Findings

Chiral condensates increase monotonically with magnetic field, showing magnetic catalysis.

Neutral pseudoscalar meson masses decrease with magnetic field, charged mesons show nonmonotonic behavior.

Neutral pseudoscalar decay constants are significantly enhanced by magnetic fields.

Abstract

We present a lattice QCD study of the chiral properties of $(2\!+\!1)$-flavor QCD in background magnetic fields at zero temperature with physical pion masses. Simulations are performed using the highly improved staggered quark action across four different lattice spacings to enable a controlled continuum extrapolation. We compute the renormalized chiral condensates together with pseudoscalar meson masses and decay constants for pions, kaons, and the fictitious $\eta^0_{s\bar{s}}$ pseudoscalar as functions of the magnetic-field strength $eB$ up to $eB\simeq1.2$ $\mathrm{GeV}^2$. The chiral condensates exhibit clear magnetic catalysis, increasing monotonically with the field strength. In the meson sector, neutral pseudoscalar masses decrease steadily with $eB$, whereas charged pseudoscalar masses display a nonmonotonic response: They rise at small fields, consistent with the lowest-Landau-level expectation, but then saturate and slightly decrease at larger fields, signaling sizable internal-structure effects. At the same time, neutral pseudoscalar decay constants are strongly enhanced by the magnetic field. To quantify deviations from chiral symmetry relations, we isolate the magnetic-field-induced shift in the Gell-Mann--Oakes--Renner corrections and find it to remain small for the neutral pion but to become sizable for the neutral kaon. To elucidate the origin of the magnetic response, we separately analyze the sea- and valence-quark contributions to both neutral and charged meson masses, finding that valence effects dominate at zero temperature. These results provide new insights into the interplay between QCD chiral symmetry breaking and strong magnetic fields.