YAM2: Yet another library for the $M_2$ variables using sequential quadratic programming

TL;DR

This paper introduces YAM2, a new software library that efficiently computes $M_2$ variables using sequential quadratic programming, outperforming existing methods in numerical performance.

Contribution

The paper presents YAM2, a novel library for calculating $M_2$ variables with multiple algorithms, notably improving computational efficiency over previous software.

Findings

Sequential quadratic programming performs well for $M_2$ calculation.

YAM2 outperforms existing software in numerical efficiency.

YAM2 provides multiple algorithms for flexible $M_2$ computation.

Abstract

The $M_2$ variables are devised to extend $M_{T2}$ by promoting transverse masses to Lorentz-invariant ones and making explicit use of on-shell mass relations. Unlike simple kinematic variables such as the invariant mass of visible particles, where the variable definitions directly provide how to calculate them, the calculation of the $M_2$ variables is undertaken by employing numerical algorithms. Essentially, the calculation of $M_2$ corresponds to solving a constrained minimization problem in mathematical optimization, and various numerical methods exist for the task. We find that the sequential quadratic programming method performs very well for the calculation of $M_2$, and its numerical performance is even better than the method implemented in the existing software package for $M_2$. As a consequence of our study, we have developed and released yet another software library, YAM2, for calculating the $M_2$ variables using several numerical algorithms.