Kaon Gluon Parton Distribution and Momentum Fraction from 2+1+1 Lattice-QCD with High Statistics

TL;DR

This paper provides a high-precision lattice-QCD calculation of the kaon gluon parton distribution function and momentum fraction, offering insights into the gluonic structure of the kaon relevant for understanding hadronic physics.

Contribution

The study introduces a novel high-statistics lattice-QCD approach to determine the kaon gluon PDF and momentum fraction, including detailed analysis of gauge-link smearing effects and nonperturbative renormalization.

Findings

Kaon gluon momentum fraction is approximately 0.557 at 2 GeV.

Effective gauge-link smearing balances signal quality and physics preservation.

Comparison with Dyson-Schwinger and pion PDFs shows consistency and differences.

Abstract

We present a high-statistics lattice-QCD determination of the kaon gluon parton distribution function and gluon momentum fraction. We use clover valence fermion action to take 1,296,640 kaon-correlator measurements on a HISQ ensemble with $a \approx 0.12$~fm and 310-MeV pion mass, generated by the MILC collaboration. A detailed investigation into the impact of gauge-link smearing on the gluonic matrix elements indicates that five steps of hypercubic smearing offer an effective balance between signal quality and preservation of long-distance physics. We report a nonperturbatively renormalized kaon gluon momentum fraction of $\langle x \rangle_g^{\overline{\text{MS}}, K} = 0.557(18)_\text{stat}(24)_\text{NPR}(56)_\text{mixing}$ at $\mu = 2$ GeV in in the $\overline{\text{MS}}$ scheme. Using reduced pseudo-ITD matrix elements and pseudo-PDF matching, we extract the kaon gluon PDF and compare with the prediction from the Dyson-Schwinger equation and with the pion PDF obtained from the same ensemble.