Matching NLO parton shower matrix element with exact phase space: case of W→lν(γ) and γ ∗→π + π −(γ)

Abstract

The PHOTOS Monte Carlo is often used for simulation of QED effects in decay of intermediate particles and resonances. Momenta are generated in such a way that samples of events cover the whole bremsstrahlung phase space. With the help of selection cuts, experimental acceptance can be then taken into account. The program is based on an exact multiphoton phase space. Crude matrix element is obtained by iteration of a universal multidimensional kernel. It ensures exact distribution in the soft photon region. Algorithm is compatible with exclusive exponentiation. To evaluate the program's precision, it is necessary to control the kernel with the help of perturbative results. If available, kernel is constructed from the exact first order matrix element. This ensures that all terms necessary for non-leading logarithms are taken into account. In the present paper we will focus on the W -> l nu and gamma^* -> pi^+ pi^- decays. The Born level cross sections for both processes approach zero in some points of the phase space. A process dependent compensating weight is constructed to incorporate the exact matrix element, but is recommended for use in tests only. In the hard photon region, where scalar QED is not expected to be reliable, the compensating weight for gamma^* decay can be large. With respect to the total rate, the effect remains at the permille level. It is nonetheless of interest. The terms leading to the effect are analogous to some terms appearing in QCD. The present paper can be understood either as a contribution to discussion on how to match two collinear emission chains resulting from charged sources in a way compatible with the exact and complete phase space, exclusive exponentiation and the first order matrix element of QED (scalar QED), or as the practical study of predictions for accelerator experiments.