Ratio of strange to $u/d$ momentum fraction in disconnected insertions

Understand

The ratio of the strange quark momentum fraction $\langle x\rangle_{s+\bar{s}}$ to that of light quark $u$ or $d$ in disconnected insertions (DI) 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.
• A complete nonperturbative renormalization and the mixing between the quark and glue operators are taken into account.
• We find the ratio to be $\langle x\rangle_{s+\bar{s}}/\langle x\rangle_{u+\bar{u}} ({\rm DI})=0.795(79)(77)$ at $\mu = 2$ GeV in the $\overline{{\rm MS}}$ scheme.