Parton shower evolution with subleading color

TL;DR

This paper introduces the LC+ approximation for parton shower evolution, incorporating some subleading color effects beyond the leading color approximation, improving the accuracy of Monte Carlo event generators.

Contribution

The LC+ approximation extends traditional leading color methods by including certain subleading color contributions with manageable computational costs.

Findings

LC+ treats soft and collinear singularities exactly in color.

Events can have weights due to the approximation.

The method allows starting from mismatched color states.

Abstract

Parton shower Monte Carlo event generators in which the shower evolves from hard splittings to soft splittings generally use the leading color approximation, which is the leading term in an expansion in powers of $1/N_c^2$, where $N_c = 3$ is the number of colors. We introduce a more general approximation, the LC+ approximation, that includes some of the color suppressed contributions. There is a cost: each generated event comes with a weight. There is a benefit: at each splitting the leading soft$\times$collinear singularity and the leading collinear singularity are treated exactly with respect to color. In addition, an LC+ shower can start from a state of the color density matrix in which the bra state color and the ket state color do not match.