We calculate the strange quark content of the nucleon $⟨N|\overline{s}s|N⟩$ in $2+1$ -flavor lattice QCD. Chirally symmetric overlap fermion formulation is used to avoid the contamination from up and down quark contents due to an operator mixing between strange and light scalar operators, $\overline{s}s$ and $\overline{u}u+\overline{d}d$. At a lattice spacing $a=0.112(1)\mathrm{fm}$, we perform calculations at four values of degenerate up and down quark masses $m_{ud}$, which cover a range of the pion mass $M_{\pi }\simeq 300–540\mathrm{MeV}$. We employ two different methods to calculate $⟨N|\overline{s}s|N⟩$. One is a direct method where we calculate $⟨N|\overline{s}s|N⟩$ by directly inserting the $\overline{s}s$ operator. The other is an indirect method where $⟨N|\overline{s}s|N⟩$ is extracted from a derivative of the nucleon mass in terms of the strange quark mass. With these two methods we obtain consistent results for $⟨N|\overline{s}s|N⟩$ with each other. Our best estimate $f_{T_s}=m_s⟨N|\overline{s}s|N⟩/M_N=0.009(15{)}_{\mathrm{stat}}(16{)}_{\mathrm{sys}}$ is in good agreement with our previous studies in two-flavor QCD.

• Received 21 August 2012

DOI:https://doi.org/10.1103/PhysRevD.87.034509