Historical and mathematical aspects of iterative solutions for Monte Carlo simulations

TL;DR

This paper reviews the mathematical and historical development of Monte Carlo simulation programs developed in Cracow over 25 years, focusing on phase space parametrization and spin amplitudes in various projects.

Contribution

It provides a detailed analysis of the mathematical design and historical evolution of Monte Carlo programs like PHOTOS, MUSTRAAL, TAUOLA, and KKMC, highlighting their similarities and differences.

Findings

Mathematical aspects of phase space parametrization elucidated

Historical development of Monte Carlo programs documented

Comparison of solution methods across different projects provided

Abstract

Over the last 25 years Monte Carlo programs were being developped in Cracow in the group guided by Prof. Stanislaw Jadach. Many of those programs became standard in their application domains. In the following let us review some aspects of such projects which were probably at the foundation of their success. We will concentrate on mathematical aspects of their design and history of their construction. It is rather difficult to cover 25 years of the research in a single talk. That is why, I have organized my presentation around Monte Carlo PHOTOS but stressing its relation to other activities and projects often realized together with Prof. Jadach. Many of omitted aspects will find their way into other perentations collected in this volume. I will concentrate on issues related to phasespace parametrization and spin amplitudes as used in our Monte Carlo programs such as MUSTRAAL, TAUOLA or KKMC and their similarities and differences with respect to solution used in PHOTOS.