YAM2: Yet another library for the [formula omitted] variables using sequential quadratic programming

Abstract

The M2 variables are devised to extend MT2 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 M2 variables is undertaken by employing numerical algorithms. Essentially, the calculation of M2 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 M2, and its numerical performance is even better than the method implemented in the existing software package for M2. As a consequence of our study, we have developed and released yet another software library, YAM2, for calculating the M2 variables using several numerical algorithms. Program summaryProgram title: YAM2CPC Library link to program files:https://doi.org/10.17632/4g7wfd5fpb.1Developer’s repository link:https://github.com/cbpark/YAM2Licensing provisions: BSD 3-ClauseProgramming language: C ++Nature of problem: The value and the solution of the M2 variables can be obtained from the optimality and feasibility conditions of the nonlinearly constrained minimization problem in numerical optimization. To perform the calculation properly, one should employ suitable numerical algorithms with the appropriate formulation of the variables, having in mind the algorithmic efficiency and the computational cost.Solution method: There exist various numerical methods for solving constrained optimization problems. We have chosen the sequential quadratic programming method with the derivative-dependent quasi-Newton algorithm since it performs very efficiently to find the local minimum using derivative information. The method has been codified by using the implementation of the numerical algorithms in the NLopt library [1]. The new library also includes the routines using other algorithms for calculating M2, such as the augmented Lagrangian method.