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Transverse Momentum Dependent (Un)polarized Gluon Distributions in Higgs Production

We combine soft and collinear matrix elements to define transverse momentum dependent parton distributions (TMDs) for gluons, free from rapidity divergences. We establish a factorization theorem at next-to-leading order for the Higgs boson transverse momentum ($q_T$) spectrum, and use it to derive evolution equations for gluon TMDs. The evolution for all gluon TMDs is driven by a universal kernel, i.e. the same for all polarizations. In the region of intermediate $q_T$ we match the unpolarized, helicity and linearly polarized gluon distributions onto PDFs. We calculate the resummed Higgs transverse momentum distribution at NNLL, including the contribution of the linearly polarized gluons, and investigate the impact of non-perturbative models for the transverse distribution of gluons inside the proton.