Three-dimensional Imaging of Pion using Lattice QCD: Generalized Parton Distributions
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909491612614656 |
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| author | Ding, Heng-Tong Gao, Xiang Mukherjee, Swagato Petreczky, Peter Shi, Qi Syritsyn, Sergey Zhao, Yong |
| author_facet | Ding, Heng-Tong Gao, Xiang Mukherjee, Swagato Petreczky, Peter Shi, Qi Syritsyn, Sergey Zhao, Yong |
| contents | 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 $-t$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03516 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three-dimensional Imaging of Pion using Lattice QCD: Generalized Parton Distributions Ding, Heng-Tong Gao, Xiang Mukherjee, Swagato Petreczky, Peter Shi, Qi Syritsyn, Sergey Zhao, Yong High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Experiment Nuclear Theory 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 $-t$. |
| title | Three-dimensional Imaging of Pion using Lattice QCD: Generalized Parton Distributions |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2407.03516 |