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We present a calculation of $ _s$ for the strange quark in the nucleon. We also report the ratio of the strange $ $ to that of $u/d$ in the disconnected insertion which will be useful in constraining the global fit of parton distribution functions at small $x$. We adopt overlap fermion action on $2 + 1$ flavor domain-wall fermion configurations on the $24^3 \times 64$ lattice with a light sea quark mass which corresponds to $m_{\pi}=330$ MeV. Smeared grid $Z_3$ sources are deployed to calculate the nucleon propagator with low-mode substitution. Even-odd grid sources and time-dilution technique with stochastic noises are used to calculate the high mode contribution to the quark loop. Low mode averaging (LMA) for the quark loop is applied to reduce the statistical error of the disconnected insertion calculation. We find the ratio $ _s/ _{u/d}^{\mathrm{DI}}= 0.78(3)$ in this study.

Strange quark momentum fraction from overlap fermion