Abstract
We calculate the small-b (or large-qT) matching of transverse momentum de- pendent (TMD) distribution for linearly polarized gluons to the integrated gluon distributions at the next-to-next-to-leading order (NNLO). This is the last missing part for the complete NNLO prediction of the Higgs spectrum within TMD factorization. We discuss the numerical impact of the correction so derived to the qT -differential cross-section for Higgs boson production and to the positivity bound for linearly polarized gluon transverse momentum distribution.
Highlights
In transverse momentum dependent (TMD) factorization each TMD distribution (f1,g and h⊥1,g in this case) is an independent fundamental non-perturbative function
We discuss the numerical impact of the correction so derived to the qT -differential cross-section for Higgs boson production and to the positivity bound for linearly polarized gluon transverse momentum distribution
In the case of lpTMDPDF the main complication comes from the rich vector structure, which is reduced to scalar products by projection factor in eq (2.5), and the use of unpolarized parton states with momentum pμ = p+nμ
Summary
2.1 Definition The TMD distribution of gluons in a hadron is given by the following matrix element. The decomposition in eq (2.3) is given in d = 4 − 2 -dimensions as it was defined in [15, 17] Both f1 and h⊥1 contribute to the gluoninduced TMD processes on equal foot. At small-b the TMD operator can be matched to the collinear operators by means of operator product expansion (OPE) This relation is important because it constrains the model for TMD distributions at small values of b. In practice, for the description of the TMD distributions one typically uses a phenomenological ansatz that matches the OPE results at small-b to a non-perturbative input at large-b. It can be written in the form h⊥1,g←h(x, b) =.
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