$J/ψ$ meson production in SIDIS: matching high and low transverse momentum

Daniël Boer; Umberto D'Alesio; Francesco Murgia; Cristian Pisano; Pieter Taels

Paper

$J/ψ$ meson production in SIDIS: matching high and low transverse momentum

Abstract

We consider the transverse momentum spectrum and the

azimuthal distribution of

mesons produced in semi-inclusive, deep-inelastic electron-proton scattering, where the electron and the proton are unpolarized. At low transverse momentum, we propose factorized expressions in terms of transverse momentum dependent gluon distributions and shape functions. We show that our formulae, at the order

correctly match with the collinear factorization results at high transverse momentum. The latter are computed at the order

in the framework of nonrelativistic QCD (NRQCD), with the inclusion of the intermediate

color-singlet Fock state, as well as the subleading color-octet ones that are relatively suppressed by a factor

in the NRQCD velocity parameter

. We show that the

and

(

) contributions diverge in the small transverse momentum region and allow us to determine the perturbative tails of the shape functions, which carry the same quantum numbers. These turn out to be identical, except for the overall magnitude given by the appropriate NRQCD long distance matrix element.