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By applying the effective field theory machinery we factorize the transverse momentum spectrum of Higgs boson production, where the main hadronic quantities are the gluon transverse momentum dependent parton distribution functions (TMDPDFs). We properly define those quantities, showing explicitly, in the case of an unpolarized hadron, that they are free from rapidity divergences, and extract their evolution properties. It turns out that the evolution for all eight (un-)polarized leading-twist gluon TMDPDFs is driven by the same evolution kernel, for which we derive the necessary ingredients to obtain a resummation of large logarithms at next-tonext-to-leading-logarithmic accuracy. We make predictions for the contribution of linearly polarized gluons to the Higgs boson qT -spectrum

Scale evolution of gluon TMDPDFs