An official website of the United States government
A<sc>bstract</sc> In this work, we present a lattice QCD calculation of the Mellin moments of the twist-2 axial-vector generalized parton distribution (GPD),$$ \overset{\sim }{H}\left(x,\xi, t\right) $$ , at zero skewness,ξ, with multiple values of the momentum transfer,t. Our analysis employs the short-distance factorization framework on ratio-scheme renormalized quasi-GPD matrix elements. The calculations are based on anNf= 2 + 1 + 1 twisted mass fermions ensemble with clover improvement, a lattice spacing ofa= 0.093 fm, and a pion mass ofmπ= 260 MeV. We consider both the iso-vector and iso-scalar cases, utilizing next-to-leading-order perturbative matching while omitting the disconnected contributions and gluon mixing in the iso-scalar case. For the first time, we determine the Mellin moments of$$ \overset{\sim }{H} $$ up to the fifth order. From these moments, we discuss the quark helicity and orbital angular momentum contributions to the nucleon spin, as well as the spin-orbit correlations of the quarks. Additionally, we perform a Fourier transform over the momentum transfer, which allows us to explore the spin structure in the impact-parameter space.
more »
« less
This content will become publicly available on February 1, 2026
Three-dimensional imaging of pion using lattice QCD: generalized parton distributions
A<sc>bstract</sc> In this work, we report a lattice calculation ofx-dependent valence pion generalized parton distributions (GPDs) at zero skewness with multiple values of the momentum transfer −t. The calculations are based on anNf= 2 + 1 gauge ensemble of highly improved staggered quarks with Wilson-Clover valence fermion. The lattice spacing is 0.04 fm, and the pion valence mass is tuned to be 300 MeV. We determine the Lorentz-invariant amplitudes of the quasi-GPD matrix elements for both symmetric and asymmetric momenta transfers with similar values and show the equivalence of both frames. Then, focusing on the asymmetric frame, we utilize a hybrid scheme to renormalize the quasi-GPD matrix elements obtained from the lattice calculations. After the Fourier transforms, the quasi-GPDs are then matched to the light-cone GPDs within the framework of large momentum effective theory with improved matching, including the next-to-next-to-leading order perturbative corrections, and leading renormalon and renormalization group resummations. We also present the 3-dimensional image of the pion in impact-parameter space through the Fourier transform of the momentum transfer −t.
more »
« less
- Award ID(s):
- 2412963
- PAR ID:
- 10600545
- Publisher / Repository:
- JHEP
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2025
- Issue:
- 2
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
A<sc>bstract</sc> Large-momentum effective theory (LaMET) provides an approach to directly calculate thex-dependence of generalized parton distributions (GPDs) on a Euclidean lattice through power expansion and a perturbative matching. When a parton’s momentum becomes soft, the corresponding logarithms in the matching kernel become non-negligible at higher orders of perturbation theory, which requires a resummation. But the resummation for the off-forward matrix elements at nonzero skewnessξis difficult due to their multi-scale nature. In this work, we demonstrate that these logarithms are important only in the threshold limit, and derive the threshold factorization formula for the quasi-GPDs in LaMET. We then propose an approach to resum all the large logarithms based on the threshold factorization, which is implemented on a GPD model. We demonstrate that the LaMET prediction is reliable for [−1 +x0,−ξ−x0] ∪ [−ξ+x0, ξ−x0] ∪ [ξ+x0,1 −x0], wherex0is a cutoff depending on hard parton momenta. Through our numerical tests with the GPD model, we demonstrate that our method is self-consistent and that the inverse matching does not spread the nonperturbative effects or power corrections to the perturbatively calculable regions.more » « less
-
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 massesMπ ≈ 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.more » « less
-
Abstract We present a state-of-the-art calculation of the unpolarized pion valence-quark distribution in the framework of large-momentum effective theory (LaMET) with improved handling of systematic errors as well as two-loop perturbative matching. We use lattice ensembles generated by the MILC collaboration at lattice spacinga≈ 0.09 fm, lattice volume 643× 96,Nf= 2 + 1 + 1 flavors of highly-improved staggered quarks and a physical pion mass. The LaMET matrix elements are calculated with pions boosted to momentumPz≈ 1.72 GeV with high-statistics ofO(106) measurements. We study the pion PDF in both hybrid-ratio and hybrid-regularization-independent momentum subtraction (hybrid-RI/MOM) schemes and also compare the systematic errors with and without the addition of leading-renormalon resummation (LRR) and renormalization-group resummation (RGR) in both the renormalization and lightcone matching. The final lightcone PDF results are presented in the modified minimal-subtraction scheme at renormalization scaleμ= 2.0 GeV. We show that thex-dependent PDFs are compatible between the hybrid-ratio and hybrid-RI/MOM renormalization with the same improvements. We also show that systematics are greatly reduced by the simultaneous inclusion of RGR and LRR and that these methods are necessary if improved precision is to be reached with higher-order terms in renormalization and matching.more » « less
-
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.more » « less
