QCD evolution of (un)polarized gluon TMDPDFs and the Higgs $q_T$-distribution

Understand

We provide the proper definition of all the leading-twist (un)polarized gluon transverse momentum dependent parton distribution functions (TMDPDFs), by considering the Higgs boson transverse momentum distribution in hadron-hadron collisions and deriving the factorization theorem in terms of them.

• We show that the evolution of all the (un)polarized gluon TMDPDFs is driven by a universal evolution kernel, which can be resummed up to next-to-next-to-leading-logarithmic accuracy.
• Considering the proper definition of gluon TMDPDFs, we perform an explicit next-to-leading-order calculation of the unpolarized ($f_1^g$), linearly polarized ($h_1^{\perp g}$) and helicity ($g_{1L}^g$) gluon TMDPDFs, and show that, as expected, they are free from rapidity divergences.
• As a byproduct, we obtain the Wilson coefficients of the refactorization of these TMDPDFs at large transverse momentum.