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

## TL;DR

This study calculates the ratio of strange to light quark momentum fractions in disconnected insertions using lattice QCD, providing a nonperturbative constraint to improve global parton distribution function fits.

## Contribution

It presents the first lattice QCD determination of the strange to light quark momentum fraction ratio in disconnected insertions with comprehensive renormalization and mixing effects.

## Key findings

- Ratio of strange to light quark momentum fractions: 0.795(79)(77) at 2 GeV
- Provides a new nonperturbative constraint for global PDF analyses
- Connects lattice QCD results with phenomenological global fits

## Abstract

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. This ratio can be used as a constraint to better determine the strange parton distribution especially in the small $x$ region in the global fittings of PDFs when the connected and disconnected sea are fitted and evolved separately, demonstrating a new way that connects lattice calculations with global analyses.