Gluon Unpolarized, Polarized, and Transversity GPDs from Lattice QCD: Lorentz-Covariant Parametrization (Part I)
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| Format: | Preprint |
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2024
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| author | Schoenleber, Jakob Sufian, Raza Sabbir Izubuchi, Taku Yang, Yi-Bo |
| author_facet | Schoenleber, Jakob Sufian, Raza Sabbir Izubuchi, Taku Yang, Yi-Bo |
| contents | We identify the matrix elements necessary to determine the leading-twist gluon generalized parton distributions (GPDs) $H_g,~E_g,~\wt{H}_g,~\wt{E}_g,~H^T_g,~E^T_g, \wt{H}^T_g ,~\wt{E}^T_g$ in lattice QCD calculations. We present a method to achieve a Lorentz-covariant parameterization of the matrix elements in terms of a linearly independent basis of tensor structures. This parameterization is crucial for projecting lattice QCD matrix elements onto light cone distributions. For the first time, we determine the corresponding components that project onto the linear combinations of invariant amplitudes, which reduce to the different gluon GPDs in the light cone limit and enable their separation in a lattice QCD calculation for spin-$0$ and spin-$\frac{1}{2}$ hadrons. Hence, this work lays the foundation for the numerical determination of the gluon GPDs from first-principle lattice QCD calculations, directly advancing our understanding of the mass and spin structures and mechanical properties of the nucleon, as well as the physics underlying deeply virtual Compton scattering and deeply virtual meson production in a range of experimental processes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_14110 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gluon Unpolarized, Polarized, and Transversity GPDs from Lattice QCD: Lorentz-Covariant Parametrization (Part I) Schoenleber, Jakob Sufian, Raza Sabbir Izubuchi, Taku Yang, Yi-Bo High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory We identify the matrix elements necessary to determine the leading-twist gluon generalized parton distributions (GPDs) $H_g,~E_g,~\wt{H}_g,~\wt{E}_g,~H^T_g,~E^T_g, \wt{H}^T_g ,~\wt{E}^T_g$ in lattice QCD calculations. We present a method to achieve a Lorentz-covariant parameterization of the matrix elements in terms of a linearly independent basis of tensor structures. This parameterization is crucial for projecting lattice QCD matrix elements onto light cone distributions. For the first time, we determine the corresponding components that project onto the linear combinations of invariant amplitudes, which reduce to the different gluon GPDs in the light cone limit and enable their separation in a lattice QCD calculation for spin-$0$ and spin-$\frac{1}{2}$ hadrons. Hence, this work lays the foundation for the numerical determination of the gluon GPDs from first-principle lattice QCD calculations, directly advancing our understanding of the mass and spin structures and mechanical properties of the nucleon, as well as the physics underlying deeply virtual Compton scattering and deeply virtual meson production in a range of experimental processes. |
| title | Gluon Unpolarized, Polarized, and Transversity GPDs from Lattice QCD: Lorentz-Covariant Parametrization (Part I) |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2412.14110 |