A fast and accurate method for perturbative resummation of transverse momentum-dependent observables

Abstract

We propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the $q_T$ spectra of gauge bosons (${\gamma }^{\ast }$, Higgs) in $pp$ collisions in the regime of low (but perturbative) transverse momentum $q_T$ as a specific example. First we introduce a scheme to choose the factorization scale for virtuality in momentum space instead of in impact parameter space, allowing us to avoid integrating over (or cutting off) a Landau pole in the inverse Fourier transform of the latter to the former. The factorization scale for rapidity is still chosen as a function of impact parameter $b$, but in such a way designed to obtain a Gaussian form (in $\ln b$) for the exponentiated rapidity evolution kernel, guaranteeing convergence of the $b$ integral. We then apply this scheme to obtain the $q_T$ spectra for Drell-Yan and Higgs production at NNLL accuracy. In addition, using this scheme we are able to obtain a fast semi-analytic formula for the perturbative resummed cross sections in momentum space: analytic in its dependence on all physical variables at each order of logarithmic accuracy, up to a numerical expansion for the pure mathematical Bessel function in the inverse Fourier transform that needs to be performed just once for all observables and kinematics, to any desired accuracy.

60 pages + Appendices, 16 Figures v.2, Accepted in JHEP, discussion added on low-qT limit, other minor clarifications made and typos corrected

References in corpus (21)

• Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO
• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• How bright is the proton? A precise determination of the photon parton distribution function
• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• Treating the b quark distribution function with reliable uncertainties
• The Photon Content of the Proton
• Top mass effects in Higgs production at next-to-next-to-leading order QCD: virtual corrections
• Production of Drell--Yan lepton pairs in hadron collisions: transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy
• QCD transverse-momentum resummation in gluon fusion processes
• Soft-/rapidity- anomalous dimensions correspondence
• Resummation of Threshold Logarithms in Effective Field Theory For DIS, Drell-Yan and Higgs Production
• Origin of the Large Perturbative Corrections to Higgs Production at Hadron Colliders
• Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel
• Virtual three-loop corrections to Higgs boson production in gluon fusion for finite top quark mass
• Electroweak Corrections in High Energy Processes using Effective Field Theory
• Resummation of Transverse Momentum Distributions in Distribution Space
• Fragmentation in Jets at NNLO
• Non-perturbative QCD effects in $q_T$ spectra of Drell-Yan and $Z$-boson production
• Transverse Momentum Distributions from Effective Field Theory with Numerical Results
• The Fully-Differential Quark Beam Function at NNLO
• Vector boson production in joint resummation

Cited by in corpus (10)

• Fiducial distributions in Higgs and Drell-Yan production at N${}^3$LL+NNLO
• Simplicity from Recoil: The Three-Loop Soft Function and Factorization for the Energy-Energy Correlation
• Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N${}^3$LL
• Fiducial Higgs and Drell-Yan distributions at N${}^3$LL${}^{\prime }$+NNLO with RadISH
• Resummation of Boson-Jet Correlation at Hadron Colliders
• The $q_T$ and $\Delta \varphi$ spectra in W and Z production at the LHC at N${}^3$LL'+N${}^2$LO
• Event-Based Transverse Momentum Resummation
• Higher-Order Sudakov Resummation in Coupled Gauge Theories
• Projected transverse momentum resummation in top-antitop pair production at LHC
• Efficient Fourier Transforms for Transverse Momentum Dependent Distributions