Abstract
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.
Highlights
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)
The derivation of the factorization theorem for the Higgsboson qT -spectrum is done by applying the following set of consecutive matchings between effective theories [1]: QCD(n f = 6) → QCD(n f = 5) → SCETqT → SCETΛQCD
We integrate out the mass of the Higgs boson, mH, obtaining a factorization theorem which holds for qT mH
Summary
The effective QCD operator is matched onto the SCET-qT one by The cross-section at leading order can be written as dσ σ0(μ) μ)H (m2H , μ) m2H τs dy d2q⊥ (2π)2 [1] by performing an explicit NLO perturbative calculation, the collinear and soft matrix elements defined above contain un-cancelled rapidity divergences and are ill-defined They need to be properly combined to obtain well-defined hadronic quantities. Where the twiddle refers to impact parameter space (IPS) This factorized cross-section is valid for qT mH. Extending that decomposition to well-defined TMDPDFs, as given in Eq (13), we have
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