Drell–Yan production at small qT, transverse parton distributions and the collinear anomaly

By T. Becher, M. Neubert. 2010

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Using methods from effective field theory, an exact all-order expression for the Drell–Yan cross section at small transverse momentum is derived directly in qT space, in which all large logarithms are resummed. The anomalous dimensions and matching coefficients necessary for resummation at NNLL order are given explicitly. The precise relation between our result and the Collins–Soper–Sterman formula is discussed, and as a by-product the previously unknown three-loop coefficient A(3) is obtained. The naive factorization of the cross section at small transverse momentum is broken by a collinear anomaly, which prevents a process-independent definition of xT-dependent parton distribution functions. A factorization theorem is derived for the product of two such functions, in which the dependence on the hard momentum transfer is separated out. The remainder factors into a product of two functions of longitudinal momentum variables and $x_{T}^{2}$, whose renormalization-group evolution is derived and solved in closed form. The matching of these functions at small xT onto standard parton distributions is calculated at $\mathcal{O}(\alpha_{s})$, while their anomalous dimensions are known to three loops.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/850ec728225b0e102772513891629e89bf9e3d92

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In Nuclear and High Energy Physics

Citations in the corpus

Introduction to Soft-Collinear Effective Theory (2014, methodology): “The restriction to positive values arises from the fact that the final state in the hard scattering, which consists of the Drell-Yan pair and soft QCD radiation, has positive energy and invariant mass.”
Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report (2017, background): “[1017,1018] for overviews of analytic resummation of color-singlet boson p⊥ spectra.”
A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory (2012, background): “It is also worth noting that our calculation of the transverse momentum distribution is distinct from the work [40].”
Heavy-quark mass effects in Higgs boson production at the LHC (2013, methodology): “A computation of the resummed pT spectrum up to next-to-next-to-leading logarithmic accuracy [16, 17, 18], matched to the O(α4 S) result valid at large pT [19, 20, 21] is implemented in the numerical program HqT [22, 23, 24].”
Parton distributions and lattice-QCD calculations: Toward 3D structure (2020, methodology): “(53) Here, yn is a free parameter appearing only in the Wilson lines of the soft function, and the Collins-Soper (CS) scale 5 In the SCET-based literature, the combination f 0 (u) i/P /S0 subnn̄ is often referred to as the beam function. is defined as ζ = (xP+e−yn)2.”