TAUOLA update for decay channels with $e^+e^-$ pairs in the final state

Abstract: With the arrival of high luminosity B-factories like the Belle II experiment, $\tau$ decay measurements have become more precise than ever, allowing rarer processes to be explored, and finer details of $\tau$ decays to be studied. These are important to understand the spectrum of intermediate particles produced in $\tau$ decays. Therefore Monte Carlo generators, like the TAUOLA program, have to facilitate precision analysis as well as confront new models that constantly emerge with the availability of high statistics experimental data. New decay channels and models may lead to large variation of matrix elements size within the available phase space, as in the case when $e^+e^-$ pairs are present in final state. It requires appropriate presampler of the phase space generator and a proper documentation to help users introduce their own models. While releasing a new update, it is important for the TAUOLA Monte Carlo library to maintain the general structure of the previous versions to preserve backward compatibility. The aim is to minimize changes from the user perspective. This paper presents a demonstration of new models implementation facilitated by the current update.