$ν$-point energy correletors with FastEEC: small-$x$ physics from LHC jets
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arXiv
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2024
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| _version_ | 1866910771849461760 |
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| author | Budhraja, Ankita Chen, Hao Waalewijn, Wouter J. |
| author_facet | Budhraja, Ankita Chen, Hao Waalewijn, Wouter J. |
| contents | In recent years, energy correlators have emerged as a powerful tool for studying jet substructure, with promising applications such as probing the hadronization transition, analyzing the quark-gluon plasma, and improving the precision of top quark mass measurements. The projected $N$-point correlator measures correlations between $N$ final-state particles by tracking the largest separation between them, showing a scaling behavior related to DGLAP splitting functions. These correlators can be analytically continued in $N$, commonly referred to as $ν$-correlators, allowing access to non-integer moments of the splitting functions. Of particular interest is the $ν\to 0$ limit, where the small momentum fraction behavior of the splitting functions requires resummation. Originally, the computational complexity of evaluating $ν$-correlators for $M$ particles scaled as $2^{2M}$, making it impractical for real-world analyses. However, by using recursion, we reduce this to $M 2^M$, and through the FastEEC method of dynamically resolving subjets, $M$ is replaced by the number of subjets. This breakthrough enables, for the first time, the computation of $ν$-correlators for LHC data. In practice, limiting the number of subjets to 16 is sufficient to achieve percent-level precision, which we validate using known integer-$ν$ results and convergence tests for non-integer $ν$. We have implemented this in an update to FastEEC and conducted an initial study of power-law scaling in the perturbative regime as a function of $ν$, using CMS Open Data on jets. The results agree with DGLAP evolution, except at small $ν$, where the anomalous dimension saturates to a value that matches the BFKL anomalous dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12235 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $ν$-point energy correletors with FastEEC: small-$x$ physics from LHC jets Budhraja, Ankita Chen, Hao Waalewijn, Wouter J. High Energy Physics - Phenomenology High Energy Physics - Experiment Nuclear Experiment Nuclear Theory In recent years, energy correlators have emerged as a powerful tool for studying jet substructure, with promising applications such as probing the hadronization transition, analyzing the quark-gluon plasma, and improving the precision of top quark mass measurements. The projected $N$-point correlator measures correlations between $N$ final-state particles by tracking the largest separation between them, showing a scaling behavior related to DGLAP splitting functions. These correlators can be analytically continued in $N$, commonly referred to as $ν$-correlators, allowing access to non-integer moments of the splitting functions. Of particular interest is the $ν\to 0$ limit, where the small momentum fraction behavior of the splitting functions requires resummation. Originally, the computational complexity of evaluating $ν$-correlators for $M$ particles scaled as $2^{2M}$, making it impractical for real-world analyses. However, by using recursion, we reduce this to $M 2^M$, and through the FastEEC method of dynamically resolving subjets, $M$ is replaced by the number of subjets. This breakthrough enables, for the first time, the computation of $ν$-correlators for LHC data. In practice, limiting the number of subjets to 16 is sufficient to achieve percent-level precision, which we validate using known integer-$ν$ results and convergence tests for non-integer $ν$. We have implemented this in an update to FastEEC and conducted an initial study of power-law scaling in the perturbative regime as a function of $ν$, using CMS Open Data on jets. The results agree with DGLAP evolution, except at small $ν$, where the anomalous dimension saturates to a value that matches the BFKL anomalous dimension. |
| title | $ν$-point energy correletors with FastEEC: small-$x$ physics from LHC jets |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment Nuclear Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2409.12235 |