A collinear shower algorithm for NSL non-singlet fragmentation

TL;DR

This paper introduces a collinear partonic shower algorithm that achieves next-to-single-logarithmic accuracy for non-singlet fragmentation, incorporating advanced splitting functions and double-collinear corrections, advancing towards NNLL precision.

Contribution

The paper develops a novel collinear shower algorithm with NSL accuracy, including triple-collinear splitting and one-loop double-collinear corrections, applicable to future full showers.

Findings

Demonstrates improved accuracy for non-singlet fragmentation functions.

Validates the shower's performance with small-R quark jet spectra.

Provides a framework for future NNLL-level shower developments.

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.