An elegant and fast method to solve QCD evolution equations. Application to the determination of the gluon content of the Pomeron

We present an original implementation of a very elegant method to solve Q2 evolution equations of perturbative QCD at NLO: the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) equations. Based on a seminal idea of Furmanski and Petronzio, our numerical treatment consists in expanding parton distributions and splitting functions on Laguerre polynomials, which reduces DGLAP integro-differential equations to a set of ordinary differential equations defined by recurrence. Then, we apply our evolution method to determine the gluon content of the Pomeron by realizing QCD fits on diffractive structure function.