LAUSR

The ratio of the strange momentum fraction $\langle x\rangle_{s+\bar{s}}$ to that of $u/d$ in the disconnected insertion is calculated on the lattice with overlap fermions on four domain wall fermion ensembles. These ensembles cover three lattice spacings, three volumes and several pion masses including the physical one, from which a global fitting is carried out where a complete nonperturbative renormalization and mixing between the quark and glue operators are taken into account. We find the ratio to be $\langle x\rangle_{s+\bar{s}}/\langle x\rangle_{u+\bar{u}} ({\rm DI})=0.795(79)(53)$ at $\mu = 2$ GeV in the $\overline{\rm MS}$ scheme. This ratio can be used as a constraint to better determine the strange parton distribution in the global fitting of PDF's when the connected and disconnected sea are fitted and evolved separately. We also compare this momentum fraction ratio with several recent global analyses of the PDF ratio $(s(x) + \bar{s}(x))/(\bar{u}(x) + \bar{d}(x))$ at the same $\mu$ and discuss its consequences.