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1. Systematic improvement of $x$ -dependent unpolarized nucleon generalized parton distributions in lattice-QCD calculation

   https://doi.org/10.1103/PhysRevD.110.034503  

   Holligan, Jack; Lin, Huey-Wen (August 2024, Physical Review D)

   We present a first study of the effects of renormalization-group resummation (RGR) and leading-renormalon resummation (LRR) on the systematic errors of the unpolarized isovector nucleon generalized parton distribution in the framework of large-momentum effective theory. This work is done using lattice gauge ensembles generated by the MILC Collaboration, consisting of $2+1+1$flavors of highly improved staggered quarks with a physical pion mass at lattice spacing $a\approx 0.09\mathrm{fm}$and a box width $L\approx 5.76\mathrm{fm}$. We present results for the nucleon $H$and $E$generalized parton distributions (GPDs) with average boost momentum $P_z\approx 2\mathrm{GeV}$at momentum transfers $Q^2=[0,0.97]{\mathrm{GeV}}^2$at skewness $\xi =0$as well as $Q^2\in 0.23{\mathrm{GeV}}^2$at $\xi =0.1$, renormalized in the modified minimal subtraction ( $\overline{\mathrm{MS}}$) scheme at scale $\mu =2.0\mathrm{GeV}$, with two- and one-loop matching, respectively. We demonstrate that the simultaneous application of RGR and LRR significantly reduces the systematic errors in renormalized matrix elements and distributions for both the zero and nonzero skewness GPDs, and that it is necessary to include both RGR and LRR at higher orders in the matching and renormalization processes. Published by the American Physical Society2024 

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2. Parton Distribution Functions and Lattice QCD

   https://doi.org/10.1051/epjconf/201920601003  

   Lin, Huey-Wen; Yang, A.; Wang, W.Y.; Ng, S.C.C.; Chan, A.H.; Oh, C.H.; Phua, K.K. (January 2019, EPJ Web of Conferences)

   Recently, there have been rapid developments in lattice-QCD calculations of proton structure, especially in the parton distribution functions (PDFs). We overcame a longstanding obstacle and for the first time in lattice-QCD are able to directly calculate the Bjorken- x dependence of the quark, helicity and transversity distributions. The PDFs are obtained using the large-momentum effective field theory (LaMET) framework where the full Bjorken- x dependence of finite-momentum PDFs, called “quasi-PDFs”, can be calculated on the lattice. The quasi-PDF nucleon matrix elements are renormalized non-perturbatively in RI/MOM-scheme. Following a nonperturbative renormalization of the parton quasi-distribution in a regularization-independent momentum-subtraction scheme, we establish its matching to the $$ \overline {{\rm{MS}}} $$ PDF and calculate the non-singlet matching coefficient at next-to-leading order in perturbation theory. In this proceeding, I will show the progress that has been made in recent years, highlighting the latest state-of-the art PDF calculations at the physical pion mass. Future impacts on the large- x global PDF fits are also discussed. 

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3. Gluon moment and parton distribution function of the pion from $N_f=2+1+1$ lattice QCD

   https://doi.org/10.1103/PhysRevD.109.114509  

   Good, William; Hasan, Kinza; Chevis, Allison; Lin, Huey-Wen (June 2024, Physical Review D)

   We present the first calculation of the pion gluon moment from lattice QCD in the continuum-physical limit. The calculation is done using clover fermions for the valence action with three pion masses, 220, 310 and 690 MeV, and three lattice spacings, 0.09, 0.12, and 0.15 fm, using ensembles generated by MILC Collaboration with $2+1+1$flavors of highly improved staggered quarks (HISQ). On the lattice, we nonperturbatively renormalize the gluon operator in RI/MOM scheme using the cluster-decomposition error reduction (CDER) technique to enhance the signal-to-noise ratio of the renormalization constant. We extrapolate the pion gluon moment to the continuum-physical limit and obtain $⟨x{⟩}_g=0.394\left(58{)}_{\mathrm{stat}+\mathrm{NPR}}\right(39{)}_{\text{mixing}}$in the $\overline{\mathrm{MS}}$scheme at 2 GeV, with first error being the statistical error and uncertainties in nonperturbative renormalization, and the second being a systematic uncertainty estimating the effect of ignoring quark mixing. Our pion gluon momentum fraction has a central value lower than two recent single-ensemble lattice-QCD results near physical pion mass but is consistent with the recent global fits by JAM and xFitter and with most QCD-model estimates. Published by the American Physical Society2024 

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4. Lattice QCD calculation of $x$ -dependent meson distribution amplitudes at physical pion mass with threshold logarithm resummation

   https://doi.org/10.1103/PhysRevD.110.114502  

   Cloët, Ian; Gao, Xiang; Mukherjee, Swagato; Syritsyn, Sergey; Karthik, Nikhil; Petreczky, Peter; Zhang, Rui; Zhao, Yong (December 2024, Physical Review D)

   We present a lattice quantum chromodynamics (QCD) calculation of the $x$-dependent pion and kaon distribution amplitudes (DA) in the framework of large momentum effective theory. This calculation is performed on a fine lattice of $a=0.076\mathrm{fm}$at physical pion mass, with the pion boosted to 1.8 GeV and kaon boosted to 2.3 GeV. We renormalize the matrix elements in the hybrid scheme and match to $\overline{\mathrm{MS}}$with a subtraction of the leading renormalon in the Wilson-line mass. The perturbative matching is improved by resumming the large logarithms related to the small quark and gluon momenta in the soft-gluon limit. After resummation, we demonstrate that we are able to calculate a range of $x\in [x_0,1-x_0]$with $x_0=0.25$for pion and $x_0=0.2$for kaon with theoretical systematic errors under control. The kaon DA is shown to be slighted skewed, and narrower than pion DA. Although the $x$-dependence cannot be direct calculated beyond these ranges, we estimate higher moments of the pion and kaon DAs by complementing our calculation with short-distance factorization. Published by the American Physical Society2024 

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5. Toward the first gluon parton distribution from the LaMET

   https://doi.org/10.1088/1361-6471/ada815  

   Good, William; Hasan, Kinza; Lin, Huey-Wen (February 2025, Journal of Physics G: Nuclear and Particle Physics)

   Abstract We present progress towards the first unpolarized gluon quasi-parton distribution function (PDF) from lattice quantum chromodynamics using high-statistics measurements for hadrons at two valence pion massesM_π ≈ 310 and 690 MeV computed on ana ≈ 0.12 fm ensemble with 2 + 1 + 1-flavors of highly improved staggered quark generated by the MILC collaboration. In this study, we consider two gluon operators for which the hybrid-ratio renormalization matching kernels have been recently derived and a third operator that has been used in prior pseudo-PDF studies of the gluon PDFs. We compare the matrix elements for each operator for both the nucleon and pion, at both pion masses, and using two gauge-smearing techniques. Focusing on the more phenomenologically studied nucleon gluon PDF, we compare the ratio and hybrid-ratio renormalized matrix elements at both pion masses and both smearings to those reconstructed from the nucleon gluon PDF from the CT18 global analysis. We identify the best choice of operator to study the gluon PDF and present the first gluon quasi-PDF under some caveats. Additionally, we explore the recent idea of Coulomb gauge fixing to improve signal at large Wilson-line displacement and find it could be a major help in improving the signal in the gluon matrix elements. This work helps identify the best operator for studying the gluon quasi-PDF, shows higher hadron boost momentum is needed to implement hybrid-ratio renormalization reliably, and suggests the need to study more diverse set of operators with their corresponding perturbative calculations for hybrid-ratio renormalization to further gluon quasi-PDF study. 

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