{\tt ee$\in$MC}: Arbitrary Initial Spin States for the Production of $\bf e^{+}e^{-} \to \tau^{+}\tau^{-} (\gamma) $ Events and the Impact on Spin Correlations

Abstract

We present a modified spin algorithm, including spin correlations, which has been implemented in {\tt ee$\in$MC} for the simulation of $e^{+}e^{-} \to \tau^{+}\tau^{-} (\gamma)$ events with an arbitrary initial spin configuration. This algorithm is suitable for the proposed BELLE-II polarization upgrade to SuperKEKB, both for the ideal case and for the case where there are misalignments, radiative effects and allows for changing polarization conditions. The spin $1/2$ states of the polarized beams are constructed in terms of a super-positioning of the helicity states corresponding to the polarimetric-vector describing the overall beam polarization and implemented both through a modification of the initial state in the modified Altrelli-Parsis Density Function as well as a change of basis of the helicity states.