Dimensionally Regulated Pentagon Integrals

Abstract

We present methods for evaluating the Feynman parameter integrals associated with the pentagon diagram in 4-2 epsilon dimensions, along with explicit results for the integrals with all masses vanishing or with one non-vanishing external mass. The scalar pentagon integral can be expressed as a linear combination of box integrals, up to O(epsilon) corrections, a result which is the dimensionally-regulated version of a D=4 result of Melrose, and of van Neerven and Vermaseren. We obtain and solve differential equations for various dimensionally-regulated box integrals with massless internal lines, which appear in one-loop n-point calculations in QCD. We give a procedure for constructing the tensor pentagon integrals needed in gauge theory, again through O(epsilon^0).

56 pages (including figures), signs corrected in eq. (4.65)

References in corpus (2)

• One-Loop Corrections to Five-Gluon Amplitudes
• Dimensionally Regulated One-Loop Integrals

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• Multiparticle amplitudes at one-loop: an algebraic/numeric approach
• Unitarity Cuts: NLO Six-Gluon Amplitudes in QCD
• Gluon Fusion Processes at One-loop within the Standard Model and Beyond
• Rebooting quarter-BPS operators in $\mathcal{N}=4$ Super Yang-Mills
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands
• One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}\gamma$ productions at the LHC through $\mathcal{O}({\epsilon }^2)$
• Scalar one-loop 4-point integral with one massless vertex in loop regularization
• Anomalous Ward identities for on-shell amplitudes at the conformal fixed point
• Sunrise integral in non-relativistic QCD with elliptics
• NLO QCD Predictions for associated t-tbar-h production in Hadronic Collisions
• NLO QCD corrections to WW+jet production including leptonic W decays at hadron colliders
• Equivalence of Coefficients Extraction of One-loop Master Integrals
• A hitchhiker's guide to quantum field theoretic aspects of $\mathcal{N}=4$ SYM theory and its deformations
• Analytic calculation of Energy-Energy Correlation in $e^{+}{e}^{-}$ annihilation at NLO
• Disentangling singularities with non-linear mappings - a new method for NNLO
• The canonical form has got baubles
• The Intermediate Coupling Regime in the AdS/CFT Correspondence
• QCD corrections to associated t anti-t h production at hadron colliders
• Co-homology of Differential Forms and Feynman diagrams
• General One-loop Reduction in Generalized Feynman Parametrization Form
• Calculating multileg one-loop processes. The case of gg -> t bar_t+gg