Chiral condensates and screening masses of neutral pseudoscalar mesons from lattice QCD at physical quark masses

TL;DR

This study uses lattice QCD simulations to analyze how temperature and magnetic fields influence chiral condensates and screening masses of neutral pseudoscalar mesons, revealing complex behaviors relevant to QCD in magnetic environments.

Contribution

First lattice QCD investigation of temperature and magnetic field effects on neutral pseudoscalar meson screening masses with physical quark masses.

Findings

Screening masses of $c0^0$ and $K^0$ show non-monotonic dependence on magnetic field.

Chiral condensates exhibit magnetic catalysis and inverse magnetic catalysis effects.

Monotonic decrease of $b7_{s\bar{s}}^0$ screening mass with increasing magnetic field.

Abstract

We investigate the effects of temperature $T$ and external magnetic fields $eB$ on the chiral condensates and screening masses of neutral pseudoscalar mesons, including $\pi^0$, $K^0$, and $\eta_{s\bar{s}}^0$, in (2+1)-flavor lattice QCD with physical quark masses. The chiral condensates are intrinsically connected to the screening masses via Ward-Takahashi identities, with the latter characterizing the inverse of the spatial correlation length in the pseudoscalar channel. Using highly improved staggered quarks, we perform simulations on lattices with temporal extents $N_\tau = 8, 12, 16$ and an aspect ratio of 4, covering five temperatures from 145 MeV to 166 MeV. For each temperature, eight magnetic field strengths are simulated, reaching up to $eB \sim 0.8$ GeV$^2$. These simulations allow us to provide continuum estimates for the chiral condensates and screening masses. We observe intricate behavior in the light ($ud$), strange-light ($ds$) and strange ($s$) quark condensates as functions of the magnetic field and temperature, reflecting the competition between magnetic catalysis and inverse magnetic catalysis effects. This complex behavior is also mirrored in the screening masses of the neutral pseudoscalar mesons. Notably, the screening masses of $\pi^0$ and $K^0$ exhibit a non-monotonic dependence on $eB$, closely following the variations in their corresponding chiral condensates. Meanwhile, the screening mass of $\eta_{s\bar{s}}^0$ decreases monotonically with increasing $eB$. These findings provide valuable insights for understanding the behavior of QCD in a thermomagnetic medium and can serve as benchmarks for low-energy QCD models and effective theories.