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

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.

1+22 pages, 5 figures; matches published version; fixed title page for inspire record; The library is distributed via https://github.com/cbpark/YAM2

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• DeeLeMa: Missing information search with Deep Learning for Mass estimation
• A new approach to semi-leptonic tags in $B$-meson semi-invisible decays
• Could $M_{T2}$ be a singularity variable?