A collinear shower algorithm for NSL non-singlet fragmentation
Abstract
We formulate a collinear partonic shower algorithm that achieves next-to-single-logarithmic (NSL, αsn Ln-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 2 branching probability, using a formula that can be applied more generally also to future full showers with 13 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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