Subleading Power Rapidity Divergences and Power Corrections for $q_T$

Abstract

A number of important observables exhibit logarithms in their perturbative description that are induced by emissions at widely separated rapidities. These include transverse-momentum ($q_T$) logarithms, logarithms involving heavy-quark or electroweak gauge boson masses, and small-$x$ logarithms. In this paper, we initiate the study of rapidity logarithms, and the associated rapidity divergences, at subleading order in the power expansion. This is accomplished using the soft collinear effective theory (SCET). We discuss the structure of subleading-power rapidity divergences and how to consistently regulate them. We introduce a new pure rapidity regulator and a corresponding $\overline{\mathrm{MS}}$-like scheme, which handles rapidity divergences while maintaining the homogeneity of the power expansion. We find that power-law rapidity divergences appear at subleading power, which give rise to derivatives of parton distribution functions. As a concrete example, we consider the $q_T$ spectrum for color-singlet production, for which we compute the complete $q_T^2/Q^2$ suppressed power corrections at $\mathcal{O}({\alpha }_s)$, including both logarithmic and nonlogarithmic terms. Our results also represent an important first step towards carrying out a resummation of subleading-power rapidity logarithms.

arXiv comment40 pages + appendices, 3 figures; v2: TMD collaboration included in acknowledgement; v3: minor changes, journal version

References in corpus (107)

• Operator expansion for high-energy scattering
• An effective field theory for collinear and soft gluons: heavy to light decays
• Parton distributions from high-precision collider data
• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• Soft-Collinear Factorization in Effective Field Theory
• The Wilson renormalization group for low x physics: towards the high density regime
• An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Invariant Operators in Collinear Effective Theory
• The Renormalization Group Equation for the Color Glass Condensate
• The Intrinsic Glue Distribution at Very Small x
• Soft-collinear effective theory and heavy-to-light currents beyond leading power
• QCD Factorization for Semi-Inclusive Deep-Inelastic Scattering at Low Transverse Momentum
• Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC
• A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory
• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Factorization Theorem For Drell-Yan At Low q_T And Transverse-Momentum Distributions On-The-Light-Cone
• The Rapidity Renormalization Group
• Multipole-expanded soft-collinear effective theory with non-abelian gauge symmetry
• Universality of non-leading logarithmic contributions in transverse-momentum distributions
• Bootstrapping rapidity anomalous dimension for transverse-momentum resummation
• Factorization of heavy-to-light form factors in soft-collinear effective theory
• Factorization and Endpoint Singularities in Heavy-to-Light decays
• Higgs and Z-boson production with a jet veto
• Jet Shapes with the Broadening Axis
• Revisiting parton evolution and the large-x limit
• Vector boson production at hadron colliders: hard-collinear coefficients at the NNLO
• Calculation of the transverse parton distribution functions at next-to-next-to-leading order
• Sudakov Form Factors
• QCD transverse-momentum resummation in gluon fusion processes
• Resummation of double logarithms in electroweak high energy processes
• Jet p_T Resummation in Higgs Production at NNLL'+NNLO
• Path integral approach to eikonal and next-to-eikonal exponentiation
• Reparameterization Invariance for Collinear Operators
• The structure of large logarithmic corrections at small transverse momentum in hadronic collisions
• Sudakov Effects in Electroweak Corrections
• Soft-/rapidity- anomalous dimensions correspondence
• Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach
• Analytic Regularization in Soft-Collinear Effective Theory
• Summing up Subleading Sudakov Logarithms
• Fiducial distributions in Higgs and Drell-Yan production at N${}^3$LL+NNLO
• An Effective Field Theory for Forward Scattering and Factorization Violation
• Subleading Power Corrections for N-Jettiness Subtractions
• The Universal Transverse Momentum Dependent Soft Function at NNLO
• On the QCD analysis of Jet Broadening
• A QCD Analysis of Double Parton Scattering: Color Correlations, Interference Effects and Evolution
• Momentum-space resummation for transverse observables and the Higgs $p_{\perp }$ at N${}^3$LL+NNLO
• Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case
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• The method of regions and next-to-soft corrections in Drell-Yan production
• Higgs boson production at the LHC using the $q_T$ subtraction formalism at N${}^3$LO QCD
• Factorization at Subleading Power and Irreducible Uncertainties in $\bar{B}\to X_s\gamma$ Decay
• Recoil and Threshold Corrections in Short-distance Cross Sections
• Factorization Structure of Gauge Theory Amplitudes and Application to Hard Scattering Processes at the LHC
• On next-to-eikonal corrections to threshold resummation for the Drell-Yan and DIS cross sections
• Power Corrections in the N-jettiness Subtraction Scheme
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• A Complete Basis for Power Suppressed Collinear-Ultrasoft Operators
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• Resummation of Double-Differential Cross Sections and Fully-Unintegrated Parton Distribution Functions
• NNLL Resummation for Jet Broadening
• Rapidity renormalized TMD soft and beam functions at two loops
• Precise QCD Description of the Higgs Boson Transverse Momentum Spectrum
• Strong Phases and Factorization for Color Suppressed Decays
• Leading-logarithmic threshold resummation of the Drell-Yan process at next-to-leading power
• On Power Suppressed Operators and Gauge Invariance in SCET
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• Higher-twist corrections to gluon TMD factorization
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• Factorization and Resummation for Massive Quark Effects in Exclusive Drell-Yan
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• Breakdown of Dimensional Regularization in the Sudakov Problem
• Renormalization of Subleading Dijet Operators in Soft-Collinear Effective Theory
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• Shape Function Effects in B -> X_c l ν_l
• From Underlying Event Sensitive To Insensitive: Factorization and Resummation

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