Next-to-leading logarithms and the PHOTOS Monte Carlo

The PHOTOS Monte Carlo program is often used for the simulation of experimental, selection-sensitive, QED radiative corrections in decays of Z bosons and other heavy resonances and particles. The present paper will be devoted to those parts of the next-to-leading order corrections for leptonic Z decays which are normally missing in PHOTOS. The analytical form of the exact and truncated, standard, kernel used in PHOTOS will be explicitly given. The correction, being the ratio of the exact to the approximate kernel, can be activated as an optional contribution to the internal weight of PHOTOS. We will quantify the numerical effect of the approximation with the help of a multitude of distributions. The numerical size of the effect is in general below 0.1%; however, in some corners of the phase space (well defined and contributing less than 0.5% to the total rate), it may reach up to about 20% of their relative size.