A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory

By Jui-yu Chiu, A. Jain, D. Neill, I. Rothstein. 2012

385 citations recorded by the source corpus.

A bstractMany observables in QCD rely upon the resummation of perturbation theory to retain predictive power. Resummation follows after one factorizes the cross section into the relevant modes. The class of observables which are sensitive to soft recoil effects are particularly challenging to factorize and resum since they involve rapidity logarithms. Such observables include: transverse momentum distributions at pT much less then the high energy scattering scale, jet broadening, exclusive hadroproduction and decay, as well as the Sudakov form factor. In this paper we will present a formalism which allows one to factorize and resum the perturbative series for such observables in a systematic fashion through the notion of a “rapidity renormalization group”. That is, a Collin-Soper like equation is realized as a renormalization group equation, but has a more universal applicability to observables beyond the traditional transverse momentum dependent parton distribution functions (TMDPDFs) and the Sudakov form factor. This formalism has the feature that it allows one to track the (non-standard) scheme dependence which is inherent in any sce- nario where one performs a resummation of rapidity divergences. We present a pedagogical introduction to the formalism by applying it to the well-known massive Sudakov form fac- tor. The formalism is then used to study observables of current interest. A factorization theorem for the transverse momentum distribution of Higgs production is presented along with the result for the resummed cross section at NLL. Our formalism allows one to define gauge invariant TMDPDFs which are independent of both the hard scattering amplitude and the soft function, i.e. they are universal. We present details of the factorization and re- summation of the jet broadening cross section including a renormalization in p⊥ space. We furthermore show how to regulate and renormalize exclusive processes which are plagued by endpoint singularities in such a way as to allow for a consistent resummation.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5f0fbb5668e2c129ec6b2f850c574facf84e0acf

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Citations in the corpus

Parton distributions and lattice-QCD calculations: Toward 3D structure (2020, methodology): “5 All these functions are plagued by additional so-called rapidity divergences (Becher and Neubert, 2011; Chiu et al., 2012; Collins, 2008; Collins and Soper, 1981; Collins and Tkachov, 1992; Echevarria et al., 2012), which are regulated by τ .”
Jet shapes with the broadening axis (2014, methodology): “Our result is in contrast to the usual case of τ (β) about the thrust axis, where there is a factorization theorem for 1 < β < ∞ that expands any recoil contributions as power suppressed [21, 39], and a different factorization theorem that accounts for recoil at β = 1 [25, 26].”
Jet substructure at the Large Hadron Collider: A review of recent advances in theory and machine learning (2017, background): “Recently, groups have calculated the broadening observable in e+e− collisions and fully included the effects of recoil [203, 204, 205, 206].”
Soft and collinear factorization and transverse momentum dependent parton distribution functions (2012, methodology): “quantities stand for their values evaluated in impact parameter space and the superscript (0) stands for pure collinear contributions. 2Explicit examples can be found in eq. (64) of [12], and also in [5] where the zero-bin contributions vanish beyond tree-level while the soft function does not. – 3 ”
Calculation of the transverse parton distribution functions at next-to-next-to-leading order (2014, methodology): “This procedure has various names in the literature: Collins-Soper equation in the pioneering works [16–21], rapidity renormalization group in [24, 26], and refactorization in [22, 27].”
Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order (2016, methodology): “Such a strategy has been recently used in [20], following the “Rapidity Renormalization Group” introduced in [13, 25], which is built in order to cancel the rapidity divergences through renormalization factors from the beam and soft factors independently.”
An effective field theory for forward scattering and factorization violation (2016, methodology): “[57, 58], and discuss the structure of zero-bin subtractions [59] in the presence of Glauber modes.”
Introduction to Soft-Collinear Effective Theory (2014, methodology): “An alternative way to achieve this resummation is the rapidity RG [12, 14].”