Threshold resummation for computing large-$x$ parton distribution through large-momentum effective theory
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arXiv
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| Natura: | Preprint |
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2023
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| _version_ | 1866915424020463616 |
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| author | Ji, Xiangdong Liu, Yizhuang Su, Yushan |
| author_facet | Ji, Xiangdong Liu, Yizhuang Su, Yushan |
| contents | Parton distribution functions (PDFs) at large $x$ are poorly constrained by high-energy experimental data, but extremely important for probing physics beyond standard model at colliders. We study the calculation of PDFs at large-$x$ through large-momentum $P^z$ expansion of the lattice quasi PDFs. Similar to deep-inelastic scattering, there are two distinct perturbative scales in the threshold limit where the matching coefficient can be factorized into a space-like jet function at scale $P^z|1-y|$ and a pair of heavy-light Sudakov form factors at scale $P^z$. The matching formula allows us to derive a full renormalization group resummation of large threshold logarithms, and the result is consistent with the known calculation to the next-to-next to leading order (NNLO). This paves the way for direct large-$x$ PDFs calculations in lattice QCD. As by-products, we find that the space-like jet function is related to a time-like version calculated previously through analytic continuation, and the heavy-light Sudakov form factor, calculated here to NNLO, is a universal object appearing as well in the large momentum expansion of quasi transverse-momentum-dependent PDFs and quasi wave-function amplitudes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_04416 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Threshold resummation for computing large-$x$ parton distribution through large-momentum effective theory Ji, Xiangdong Liu, Yizhuang Su, Yushan High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory Nuclear Theory Parton distribution functions (PDFs) at large $x$ are poorly constrained by high-energy experimental data, but extremely important for probing physics beyond standard model at colliders. We study the calculation of PDFs at large-$x$ through large-momentum $P^z$ expansion of the lattice quasi PDFs. Similar to deep-inelastic scattering, there are two distinct perturbative scales in the threshold limit where the matching coefficient can be factorized into a space-like jet function at scale $P^z|1-y|$ and a pair of heavy-light Sudakov form factors at scale $P^z$. The matching formula allows us to derive a full renormalization group resummation of large threshold logarithms, and the result is consistent with the known calculation to the next-to-next to leading order (NNLO). This paves the way for direct large-$x$ PDFs calculations in lattice QCD. As by-products, we find that the space-like jet function is related to a time-like version calculated previously through analytic continuation, and the heavy-light Sudakov form factor, calculated here to NNLO, is a universal object appearing as well in the large momentum expansion of quasi transverse-momentum-dependent PDFs and quasi wave-function amplitudes. |
| title | Threshold resummation for computing large-$x$ parton distribution through large-momentum effective theory |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2305.04416 |