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

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.