Rapidity renormalized TMD soft and beam functions at two loops

Abstract

We compute the transverse momentum dependent (TMD) soft function for the production of a color-neutral final state at the LHC within the rapidity renormalization group (RRG) framework to next-to-next-to-leading order (NNLO). We use this result to extract the universal renormalized TMD beam functions (aka TMDPDFs) in the same scheme and at the same order from known results in another scheme. We derive recurrence relations for the logarithmic structure of the soft and beam functions, which we use to cross check our calculation. We also explicitly confirm the non-Abelian exponentiation of the TMD soft function in the RRG framework at two loops. Our results provide the ingredients for resummed predictions of pT-differential cross sections at NNLL' in the RRG formalism. The RRG provides a systematic framework to resum large (rapidity) logarithms through (R)RG evolution and to assess the associated perturbative uncertainties.

37 pages, 3 figures; v2: journal version; v3: typos in eq.(6.19) corrected

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Cited by in corpus (62)

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• Subleading Power Rapidity Divergences and Power Corrections for $q_T$
• Towards Quasi-Transverse Momentum Dependent PDFs Computable on the Lattice
• Resummation of Transverse Momentum Distributions in Distribution Space
• Simplicity from Recoil: The Three-Loop Soft Function and Factorization for the Energy-Energy Correlation
• Transverse momentum dependent PDFs at N${}^3$LO
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• Higgs $p_T$ Spectrum and Total Cross Section with Fiducial Cuts at Third Resummed and Fixed Order in QCD
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• TMD Soft Function from Large-Momentum Effective Theory
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• Neutralino/chargino pair production at NLO+NLL with resummation-improved PDFs for LHC Run II
• A Toolbox for $q_T$ and $0$-Jettiness Subtractions at N${}^3$LO
• Fiducial Higgs and Drell-Yan distributions at N${}^3$LL${}^{\prime }$+NNLO with RadISH
• The Energy-Energy Correlation in the back-to-back limit at N${}^3$LO and N${}^3$LL${}^{\prime }$
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• Factorization connecting continuum and lattice TMDs
• Two-loop anomalous dimensions of generic dijet soft functions
• Energy-energy correlators in Deep Inelastic Scattering
• Factorization and Resummation for Massive Quark Effects in Exclusive Drell-Yan
• Associated production of a $W$ boson and massive bottom quarks at next-to-next-to-leading order in QCD
• Joint Two-Dimensional Resummation in $q_T$ and $0$-Jettiness at NNLL
• Generic dijet soft functions at two-loop order: correlated emissions
• Joint transverse momentum and threshold resummation beyond NLL
• Renormalization and Matching for the Collins-Soper Kernel from Lattice QCD
• Power corrections and renormalons in Transverse Momentum Distributions
• Transverse-Energy-Energy Correlations in Deep Inelastic Scattering
• Challenges with Large Transverse Momentum in Semi-Inclusive Deeply Inelastic Scattering
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• Matching NNLO to parton shower using N${}^3$LL colour-singlet transverse momentum resummation in GENEVA
• Threshold resummation for computing large-$x$ parton distribution through large-momentum effective theory
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• Precision boson-jet azimuthal decorrelation at hadron colliders
• Soft factors for double parton scattering at NNLO
• One-loop Matching for Spin-Dependent Quasi-TMDs
• Gauge-invariant TMD factorization for Drell-Yan hadronic tensor at small x
• Collinear expansion for color singlet cross sections
• One-loop matching for gluon lattice TMDs
• Drell-Yan Transverse-Momentum Spectra at N${}^3$LL${}^{\prime }$ and Approximate N${}^4$LL with SCETlib
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• A fast and accurate method for perturbative resummation of transverse momentum-dependent observables
• The Fully-Differential Gluon Beam Function at NNLO
• Structure of rapidity divergences in soft factors
• Conformal invariance of TMD rapidity evolution
• Combining nonperturbative transverse momentum dependence with TMD evolution
• QCD evolution of the gluon Sivers function in heavy flavor dijet production at the Electron-Ion Collider
• Soft Functions for Generic Jet Algorithms and Observables at Hadron Colliders
• Impact of Jet Veto Resummation on Slepton Searches
• The NNLO quark beam function for jet-veto resummation
• Two-loop bottom mass effects on the Higgs transverse momentum spectrum in top-induced gluon fusion
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• NNLO electron structure functions (PDFs) from SCET
• $q_T$-slicing with multiple jets
• Transverse momentum dependent distribution functions in the threshold limit
• Fully differential Higgs boson pair production at N${}^3$LO with top quark mass effects