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First Nucleon Gluon PDF from Large Momentum Effective Theory

We report the first nucleon gluon parton distribution function (PDF) using Large-Momentum Effective Theory (LaMET). We focus on the gluon operator which was demonstrated to have the best signal-to-noise in the previous attempt [1] in computing gluon PDFs using LaMET. We compute the corresponding Wilson coefficients needed for the hybrid-renormalized matrix elements and the matching kernel to convert the quasi-PDF to the lightcone one at the one-loop level. We demonstrate that with the proper Wilson coefficients in place, the counterterms for the renormalization are independent of the hadron and mass within statistical error. Using the resulting renormalization, we then compute the nucleon PDF using a HISQ ensemble generated by the MILC collaboration with $N_f=2+1+1$, $a \approx 0.12$ fm, with valence pion masses of 310 and 690 MeV and two gauge link smearing techniques. Despite the physics effects of the heavier than physical pion masses and gauge link smearing, this calculation provides excellent proof of principle and compares reasonably with selected global fit results.