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arXiv · 2409.08316

A collinear shower algorithm for NSL non-singlet fragmentation

Melissa van Beekveld·Mrinal Dasgupta·Basem Kamal El-Menoufi·Jack Helliwell·Pier Francesco Monni·Gavin P. Salam
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Abstract

We formulate a collinear partonic shower algorithm that achieves next-to-single-logarithmic (NSL, $\alpha_s^n L^{n-1}$) accuracy for collinear-sensitive non-singlet fragmentation observables. This entails the development of an algorithm for nesting triple-collinear splitting functions. It also involves the inclusion of the one-loop double-collinear corrections, through a $z$-dependent NLO-accurate effective $1\to 2$ branching probability, using a formula that can be applied more generally also to future full showers with $1\to3$ splitting kernels. The specific NLO branching probability is calculated in two ways, one based on slicing, the other using a subtraction approach based on recent analytical calculations. We close with demonstrations of the shower's accuracy for non-singlet partonic fragmentation functions and the energy spectrum of small-$R$ quark jets. This work represents an important conceptual step towards general NNLL accuracy in parton showers.

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Melissa van Beekveld, Mrinal Dasgupta, Basem Kamal El-Menoufi, Jack Helliwell, Pier Francesco Monni, Gavin P. Salam. 2024-09-12. A collinear shower algorithm for NSL non-singlet fragmentation. https://arxiv.org/abs/2409.08316

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