Next to Leading Logarithms and the PHOTOS Monte Carlo

With the approaching start-up of the experiments at LHC, the urgency to quantify systematic uncertainties of the generators, used in the interpretation of the data, is becoming pressing. The PHOTOS Monte Carlo program is often used for the simulation of experimental, selectionsensitive, QED radiative corrections in decays of Z bosons and other heavy resonances and particles. Thanks to its complete phase-space coverage it is possible, with no approximations for any decay channel, to implement the matrix-element. The present paper will be devoted to those parts of the next-to-leading order corrections for 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. To calculate the weight, the information on the effective Born-level Z/γ∗ couplings and even directions of the incoming beams, is needed. A universal implementation would have made the PHOTOS solution less modular and less convenient for the users. That is why, for the time being, we will keep the correcting weight as an extra option, available for special tests only. 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. CERN-PH-TH/2006-056, IFJPAN-IV-2006-3 April, 2006 Supported in part by the EU grant MTKD-CT-2004-510126, in partnership with the CERN Physics Department, and the Polish State Committee for Scientific Research (KBN) grant 2 P03B 091 27 for years 2004–2006.