Exponentiating virtual imaginary contributions in a parton shower

TL;DR

This paper explores exponentiating the imaginary part of virtual contributions in a parton shower to improve color treatment, demonstrating the method's feasibility with minimal impact on specific observables.

Contribution

It introduces a method to exponentiate the phase operator in a parton shower, handling matrices up to 14x14 in size, and tests its effect on jet gap probabilities.

Findings

Exponentiation of the phase operator is feasible within the given matrix size.

The net effect of exponentiating the phase operator is small for the tested observable.

Perturbative treatment remains sufficient for the studied scenario.

Abstract

The operator in a parton shower algorithm that represents the imaginary part of virtual Feynman graphs has a non-trivial color structure and is large because it is proportional to a factor of $4\pi$. In order to improve the treatment of color in a parton shower, it may help to exponentiate this phase operator. We show that it is possible to do so by exponentiating matrices that are no larger than $14\times14$. Using the example of the probability to have a gap in the rapidity interval between two high transverse momentum jets, we test this exponentiation algorithm by comparing to the result of treating the phase operator perturbatively. We find that the exponentiation works, but that the net effect of the exponentiated phase operator is quite small for this problem, so that one can as well use the perturbative approach.