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Three-dimensional Imaging of Pion using Lattice QCD: Generalized Parton Distributions

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arxiv 2407.03516 v2 pith:26NPZXJZ submitted 2024-07-03 hep-lat hep-phnucl-exnucl-th

Three-dimensional Imaging of Pion using Lattice QCD: Generalized Parton Distributions

Heng-Tong Ding , Xiang Gao , Swagato Mukherjee , Peter Petreczky , Qi Shi , Sergey Syritsyn , Yong Zhao This is my paper
classification hep-lat hep-phnucl-exnucl-th
keywords latticepionmomentumvalenceasymmetriccalculationsdistributionselements
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In this work, we report a lattice calculation of $x$-dependent valence pion generalized parton distributions (GPDs) at zero skewness with multiple values of the momentum transfer $-t$. The calculations are based on an $N_f=2+1$ 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 $-t$.

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Cited by 4 Pith papers

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