Topological susceptibility in two-flavor lattice QCD with exact chiral symmetry

Abstract

We determine the topological susceptibility $\ddot{I}{‡}_t$ in two-flavor QCD using the lattice simulations at a fixed topological sector. The topological charge density is unambiguously defined on the lattice using the overlap-Dirac operator which possesses exact chiral symmetry. Simulations are performed on a $16^3\times 32$ lattice at lattice spacing $\sim$ 0.12 fm at six sea quark masses $m_q$ ranging in $m_s/6$--$m_s$ with $m_s$ the physical strange quark mass. The $\ddot{I}{‡}_t$ is extracted from the constant behavior of the time-correlation of flavor-singlet pseudo-scalar meson two-point function at large distances, which arises from the finite size effect due to the fixed topology. In the small $m_q$ regime, our result of $\ddot{I}{‡}_t$ is proportional to $m_q$ as expected from chiral effective theory. Using the formula $\ddot{I}{‡}_t=m_q\hat{I}\pounds /N_f$ by Leutwyler-Smilga, we obtain the chiral condensate in $N_f=2$ QCD as $\hat{I}{\pounds }^{\overline{\mathrm{MS}}}(2GeV)=[252(5)(10)\mathrm{MeV}{]}^3$, in good agreement with our previous result obtained in the $\hat{I}\mu$-regime.

11 pages, 3 figures, v2: accepted for publication in PLB