Topological susceptibility in 2-flavor lattice QCD with fixed topology

TL;DR

This study measures the topological susceptibility in two-flavor lattice QCD with fixed topology, confirming its proportionality to quark mass and estimating the chiral condensate with high precision.

Contribution

It provides a precise lattice calculation of topological susceptibility and chiral condensate in two-flavor QCD using overlap fermions and fixed topology.

Findings

Topological susceptibility proportional to quark mass at small masses

Chiral condensate estimated as (252 MeV)^3

Results agree with previous epsilon-regime calculations

Abstract

We determine the topological susceptibility $ \chi_t $ in the trivial topological sector generated by lattice simulations of two-flavor QCD with overlap Dirac fermion, on a $16^3 \times 32$ lattice with lattice spacing $\sim$ 0.12 fm, at six sea quark masses $m_q$ ranging from $m_s/6$ to $m_s$ (where $m_s$ is the physical strange quark mass). The $ \chi_t $ is extracted from the plateau (at large time separation) of the time-correlation function of the flavor-singlet pseudoscalar meson ($\eta'$), which arises from the finite size effect due to fixed topology. In the small $m_q$ regime, our result of $\chi_t$ is proportional to $m_q$ as expected from chiral effective theory. Using the formula $\chi_t=m_q\Sigma/N_f$ by Leutwyler-Smilga, we obtain the chiral condensate in $N_f=2$ QCD as $\Sigma^{\bar{\mathrm{MS}}}(\mathrm{2 GeV})=[252(5)(10) \mathrm{MeV}]^3 $, in good agreement with our previous result obtained in the $\epsilon$-regime.