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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.02312 |
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| _version_ | 1866917308274835456 |
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| author | Bonvini, Marco Frixione, Stefano Stagnitto, Giovanni |
| author_facet | Bonvini, Marco Frixione, Stefano Stagnitto, Giovanni |
| contents | We revisit the basic steps necessary to obtain next-to-leading-logarithmic accurate small-$x$ results for the DGLAP splitting functions, and their implementations within the HELL framework. We derive new analytical all-order results for the leading-logarithmic $gg$ anomalous dimension, the $qg$ and $gg$ finite Green functions, and most importantly for the $qg$ anomalous dimension, which allows us to arrive for the first time at a properly resummed $qg$ splitting kernel. We use these results as cornerstones of a new implementation of small-$x$ splitting-function resummation which is more solid and numerically better behaved with respect to those available thus far. All of these novelties are included in the upcoming 4.0 version of HELL. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02312 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | New results on small-x resummation for splitting functions Bonvini, Marco Frixione, Stefano Stagnitto, Giovanni High Energy Physics - Phenomenology We revisit the basic steps necessary to obtain next-to-leading-logarithmic accurate small-$x$ results for the DGLAP splitting functions, and their implementations within the HELL framework. We derive new analytical all-order results for the leading-logarithmic $gg$ anomalous dimension, the $qg$ and $gg$ finite Green functions, and most importantly for the $qg$ anomalous dimension, which allows us to arrive for the first time at a properly resummed $qg$ splitting kernel. We use these results as cornerstones of a new implementation of small-$x$ splitting-function resummation which is more solid and numerically better behaved with respect to those available thus far. All of these novelties are included in the upcoming 4.0 version of HELL. |
| title | New results on small-x resummation for splitting functions |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2603.02312 |