Streamlining resummed QCD calculations using Monte Carlo integration

TL;DR

This paper demonstrates how existing Monte Carlo programs like MadGraph can be leveraged to streamline and automate the hard process calculations in precision resummed QCD computations, reducing complexity and error.

Contribution

It introduces a method to use Monte Carlo event generators for producing partonic distributions with color structures to facilitate resummed QCD calculations.

Findings

Only about 1000 unweighted events needed for precise distributions.

Validated approach with $e^+e^-$ jet shape examples.

Code provided to adapt MadGraph for resummed calculations.

Abstract

Some of the most arduous and error-prone aspects of precision resummed calculations are related to the partonic hard process, having nothing to do with the resummation. In particular, interfacing to parton-distribution functions, combining various channels, and performing the phase space integration can be limiting factors in completing calculations. Conveniently, however, most of these tasks are already automated in many Monte Carlo programs, such as MadGraph, Alpgen or Sherpa. In this paper, we show how such programs can be used to produce distributions of partonic kinematics with associated color structures representing the hard factor in a resummed distribution. These distributions can then be used to weight convolutions of jet, soft and beam functions producing a complete resummed calculation. In fact, only around 1000 unweighted events are necessary to produce precise distributions. A number of examples and checks are provided, including $e^+e^-$ two- and four-jet event shapes, $n$-jettiness and jet-mass related observables at hadron colliders. Attached code can be used to modify MadGraph to export the relevant leading-order hard functions and color structures for arbitrary processes.