Next-to-leading power two-loop soft functions for the Drell-Yan process at threshold

Abstract

We calculate the generalized soft functions at $\mathcal{O}({\alpha }_s^2)$ at next-to-leading power accuracy for the Drell-Yan process at threshold. The operator definitions of these objects contain explicit insertions of soft gauge and matter fields, giving rise to a dependence on additional convolution variables with respect to the leading power result. These soft functions constitute the last missing ingredient for the validation of the bare factorization theorem to NNLO accuracy. We carry out the calculations by reducing the soft squared amplitudes into a set of canonical master integrals and we employ the method of differential equations to evaluate them. We retain the exact $d$-dimensional dependence of the convolution variables at the integration boundaries in order to regulate the fixed-order convolution integrals. After combining our soft functions with the relevant collinear functions, we perform checks of the results at the cross-section level against the literature and expansion-by-regions calculations, at NNLO and partly at N${}^3$LO, finding agreement.

arXiv comment32 pages, 4 figures

References in corpus (46)

• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• Harmonic Polylogarithms
• Multiloop integrals in dimensional regularization made simple
• Asymptotic expansion of Feynman integrals near threshold
• New features of FORM
• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• Soft-collinear effective theory and heavy-to-light currents beyond leading power
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes
• HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
• Multipole-expanded soft-collinear effective theory with non-abelian gauge symmetry
• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach
• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• Factorization at Subleading Power and Irreducible Uncertainties in $\bar{B}\to X_s\gamma$ Decay
• Non-abelian factorisation for next-to-leading-power threshold logarithms
• Anomalous dimension of subleading-power N-jet operators
• Leading-logarithmic threshold resummation of the Drell-Yan process at next-to-leading power
• A Subleading Operator Basis and Matching for $gg\to H$
• First Subleading Power Resummation for Event Shapes
• A Complete Basis of Helicity Operators for Subleading Factorization
• Anomalous dimension of subleading-power $N$-jet operators II
• Threshold factorization of the Drell-Yan process at next-to-leading power
• Building Blocks for Subleading Helicity Operators
• Reparameterization Invariant Collinear Operators
• Diagrammatic resummation of leading-logarithmic threshold effects at next-to-leading power
• Leading-logarithmic threshold resummation of Higgs production in gluon fusion at next-to-leading power
• Factorization at Subleading Power, Sudakov Resummation and Endpoint Divergences in Soft-Collinear Effective Theory
• B -> chi_cJ K decays revisited
• The Soft Quark Sudakov
• Violation of the Kluberg-Stern--Zuber theorem in SCET
• Large-x resummation of off-diagonal deep-inelastic parton scattering from d-dimensional refactorization
• On next-to-leading power threshold corrections in Drell-Yan production at N${}^3$LO
• Factorization at Subleading Power and Endpoint Divergences in $h\to \gamma \gamma$ Decay: II. Renormalization and Scale Evolution
• MT: a Mathematica package to compute convolutions
• NNLO soft function for electroweak boson production at large transverse momentum
• The NNLO soft function for the pair invariant mass distribution of boosted top quarks
• Renormalization and Scale Evolution of the Soft-Quark Soft Function
• Light Quark Mediated Higgs Boson Threshold Production in the Next-to-Leading Logarithmic Approximation
• An Exclusive Soft Function for Drell-Yan at Next-to-Next-to-Leading Order
• Next-to-leading power threshold corrections for finite order and resummed colour-singlet cross sections
• Relating amplitude and PDF factorisation through Wilson-line geometries
• Power corrections in a transverse-momentum cut for vector-boson production at NNLO: the $qg$-initiated real-virtual contribution
• The next-to-next-to-leading order soft function for top quark pair production
• Analyticity, renormalization, and evolution of the soft-quark function

Cited by in corpus (1)

• Approximate NNLO QCD corrections to semi-inclusive DIS