The Metropolis algorithm for on-shell four-momentum phase space

TL;DR

This paper introduces multiple implementations of the Metropolis Monte Carlo algorithm tailored for calculating complex multi-dimensional integrals over on-shell four-momentum phase space, especially useful in high energy particle physics processes.

Contribution

It presents novel adaptations of the Metropolis algorithm for on-shell four-momentum phase space integration, improving efficiency in high-dimensional, constrained problems.

Findings

Metropolis method effectively handles high-dimensional phase space integrals.

Compared performance shows advantages over existing numerical tools.

Suitable for complex high-energy physics calculations.

Abstract

We present several implementations of the Metropolis method, an adaptive Monte Carlo algorithm, which allow for the calculation of multi-dimensional integrals over arbitrary on-shell four-momentum phase space. The Metropolis technique reveals itself very suitable for the treatment of high energy processes in particle physics, particularly when the number of final state objects and of kinematic constraints on the latter gets larger. We compare the performances of the Metropolis algorithm with those of other programs widely used in numerical simulations.