Invariant mass line shape of B -> PP decays at LHCb

The family of B meson decays into pairs of charmless charged pseudo-scalar mesons comprises many different channels. In order to disentagle the overlapped mass peaks of the various decay modes, an accurate description of the invariant mass distribution of each mode is required. In particular, the invariant mass parameterization must take into account the effect of QED final state radiation, which leads to the presence of a long tail on the lower side of the mass peak. In this document we propose a new parameterization based on a complete QED calculation of the photon emission rate and we compare it to a simpler one based on phenomenological arguments. Furthermore, we show how the shape of the invariant mass distributions under the pi+pi- mass hypothesis, for every decay mode of interest, can be described very precisely by means of analytical calculations.