Search for dark matter at high-power laser facilities : flawed luminosity calculations in QPS -- Quasi parallel scattering

I point the erroneous use, in several papers published recently, of the well known expression for the luminosity of the head-on collision of two particle bunches, in a QPS – Quasi parallel scattering – configuration, in which the two beams are co-propagating, and the collision of individual particles takes place at a small angle wrt co-propagation.