Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors

Abstract

In this letter we continue the calculation of master integrals for massless three-loop form factors by giving analytical results for those integrals which are relevant for the fermionic contributions proportional to N_F^2, N_F*N, and N_F/N. Working in dimensional regularisation, we express one of the integrals in a closed form which is exact to all orders in epsilon, containing Gamma-functions and hypergeometric functions of unit argument. In all other cases we derive multiple Mellin-Barnes representations from which the coefficients of the Laurent expansion in epsilon are extracted in an analytical form. To obtain the finite part of the three-loop quark and gluon form factors, all coefficients through transcendentality six in the Riemann zeta-function have to be included.

12 pages, 1 figure. References added and updated. Appendix on evaluation of Mellin-Barnes integrals added. Version to appear in PLB

References in corpus (34)

• Differential Equations for Two-Loop Four-Point Functions
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• An automatized algorithm to compute infrared divergent multi-loop integrals
• Harmonic sums, Mellin transforms and Integrals
• Automatized analytic continuation of Mellin-Barnes integrals
• HPL, a Mathematica implementation of the harmonic polylogarithms
• The third-order QCD corrections to deep-inelastic scattering by photon exchange
• Multi-loop Amplitudes and Resummation
• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• Automatic Integral Reduction for Higher Order Perturbative Calculations
• HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
• Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• Three-Loop Results for Quark and Gluon Form Factors
• Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses
• Numerical evaluation of multi-loop integrals by sector decomposition
• Virtual corrections to gg -> H to two loops in the heavy top limit
• The Quark Form Factor at Higher Orders
• Two-Loop Quark and Gluon Form Factors in Dimensional Regularisation
• Infrared Structure of $e^{+}{e}^{-}\to 2$ jets at NNLO
• Two-loop QCD Corrections to the Heavy Quark Form Factors: the Vector Contributions
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• Extension of HPL to complex arguments
• Infrared structure of e+e- --> 3 jets at NNLO
• Two-loop corrections to Higgs boson production
• Two-Loop QCD Corrections to the Heavy Quark Form Factors: Anomaly Contributions
• Two-Loop QCD Corrections to the Heavy Quark Form Factors: Axial Vector Contributions
• A practical criterion of irreducibility of multi--loop Feynman integrals
• Numerical evaluation of loop integrals
• Analytic resummation for the quark form factor in QCD
• Master Integrals for Massless Three-Loop Form Factors: One-Loop and Two-Loop Insertions
• Calculation of Massless Feynman Integrals using Harmonic Sums

Cited by in corpus (41)

• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• Calculation of the quark and gluon form factors to three loops in QCD
• Quark and gluon form factors to three loops
• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• Sector Decomposition
• On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
• The Drell-Yan cross section to third order in the strong coupling constant
• SecDec: A general program for sector decomposition
• FIESTA 2: parallelizeable multiloop numerical calculations
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Collider Physics at the Precision Frontier
• Evaluating single-scale and/or non-planar diagrams by differential equations
• Analytic Results for Massless Three-Loop Form Factors
• Charged Current Drell-Yan Production at N3LO
• The three-loop form factor in N=4 super Yang-Mills
• Higgs production in bottom-quark fusion to third order in the strong coupling
• The quark and gluon form factors to three loops in QCD through to O(eps^2)
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• Three-loop master integrals for ladder-box diagrams with one massive leg
• Two-Loop Master Integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering
• A geometric method of sector decomposition
• Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
• On the Computation of Form Factors in Massless QCD with Finite Master Integrals
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Higgs production in bottom quark fusion: Matching the 4- and 5-flavour schemes to third order in the strong coupling
• The $Hb\bar{b}$ form factor to three loops in QCD
• Pseudo-scalar Form Factors at Three Loops in QCD
• A Numerical Routine for the Crossed Vertex Diagram with a Massive-Particle Loop
• Konishi Form Factor at Three Loop in $\mathcal{N}=4$ SYM
• Dimensional recurrence relations: an easy way to evaluate higher orders of expansion in $\epsilon$
• Hepp and Speer Sectors within Modern Strategies of Sector Decomposition
• Mixed QCD-electroweak corrections to Higgs production via gluon fusion in the small mass approximation
• Planar master integrals for four-loop form factors
• Cutting massless four-loop propagators
• Three loop form factors of a massive spin-2 particle with nonuniversal coupling
• Spin-2 Form Factors at Three Loop in QCD
• Methods for the Reduction of Three-Loop QCD Form Factors
• Hypergeometric functions with rational arguments
• Z-Sum Approach to Loop Integrals using Taylor Expansion
• Higher-Order Corrections to Higgs Boson Amplitudes with Full Quark Mass Dependence in Quantum Chromodynamics