Angular integrals in d dimensions

Abstract

We discuss the evaluation of certain d dimensional angular integrals which arise in perturbative field theory calculations. We find that the angular integral with n denominators can be computed in terms of a certain special function, the so-called H-function of several variables. We also present several illustrative examples of the general result and briefly consider some applications.

30 pages, discussion slightly extended by mentioning the existence of contiguous relations for H-functions, new references added

References in corpus (8)

• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams
• Analytic integration of real-virtual counterterms in NNLO jet cross sections I
• A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the iterated singly-unresolved subtraction terms
• Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case
• Analytic integration of real-virtual counterterms in NNLO jet cross sections II
• A new subtraction scheme for computing QCD jet cross sections at next-to-leading order accuracy

Cited by in corpus (30)

• Soft triple-real radiation for Higgs production at N3LO
• QED Corrections in $\bar{B}\to \bar{K}{\ell }^{+}{\ell }^{-}$ at the Double-Differential Level
• Soft Expansion of Double-Real-Virtual Corrections to Higgs Production at N${}^3$LO
• On next-to-leading power threshold corrections in Drell-Yan production at N${}^3$LO
• Zero-jettiness resummation for top-quark pair production at the LHC
• A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the doubly unresolved subtraction terms
• Higgs-differential cross section at NNLO in dimensional regularisation
• Integration of collinear-type doubly unresolved counterterms in NNLO jet cross sections
• Real-virtual corrections to Higgs boson pair production at NNLO: three closed top quark loops
• A new approach to QCD final-state evolution in processes with massive partons
• The soft function for color octet production at threshold
• New ideas for handling of loop and angular integrals in D-dimensions in QCD
• Soft-parton contributions to heavy-quark production at low transverse momentum
• NNLO zero-jettiness beam and soft functions to higher orders in the dimensional-regularization parameter $\epsilon$
• Efficient Evaluation of Massive Mellin--Barnes Integrals
• Double-real contribution to the quark beam function at N${}^3$LO QCD
• Fully exclusive heavy quark-antiquark pair production from a colourless initial state at NNLO in QCD
• Collinear functions for QCD resummations
• Analytic continuations of the Horn $H_1$ and $H_5$ functions
• Expansion by regions meets angular integrals
• Asymptotic behavior of angular integrals in the massless limit
• Analytic NNLO transverse-momentum-dependent soft function for heavy quark pair hadroproduction at threshold
• Analytic double-soft integrated subtraction terms for two massive emitters in a back-to-back kinematics
• Angular integrals with three denominators via IBP, mass reduction, dimensional shift, and differential equations
• On multi-propagator angular integrals
• Dihadron Angular Correlations in the $e^{+}{e}^{-}$ Collision
• Integral of the double-emission eikonal function for a massive and a massless emitter at an arbitrary angle
• Momentum expansions in finite-density perturbative calculations
• CoLoRFulNNLO for hadron collisions: integrating the iterated single unresolved subtraction terms
• Soft Integrals and Soft Anomalous Dimensions at N${}^3$LO and Beyond