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

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.

M_2变量旨在通过提升横质量为洛伦兹不变质量，并明确利用粒子的在壳质量关系来扩展M_T2。与诸如可见粒子的不变质量等简单的动力学变量不同，其中变量定义直接提供了计算方法，M_2变量的计算则通过采用数值算法来完成。本质上，M_2的计算相当于在数学优化中解决一个约束最小化问题，并且存在多种数值方法来完成这一任务。我们发现，序列二次规划法在M_2的计算中表现卓越，其数值性能甚至优于现有软件包中实现的M_2方法。作为我们研究的结果，我们已开发并发布了一个新的软件库，名为YAM2，该库通过多种数值算法计算M_2变量。