Master Integrals for Massless Three-Loop Form Factors: One-Loop and Two-Loop Insertions

Abstract

The three-loop form factors in massless QCD can be expressed as a linear combination of master integrals. Besides a number of master integrals which factorise into products of one-loop and two-loop integrals, one finds 16 genuine three-loop integrals. Of these, six have the form of a bubble insertion inside a one-loop or two-loop vertex integral. We compute all master integrals with these insertion topologies.

12 pages, 1 figure

References in corpus (1)

• Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses

Cited by in corpus (39)

• Calculation of the quark and gluon form factors to three loops in QCD
• Quark and gluon form factors to three loops
• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
• 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
• Evaluating single-scale and/or non-planar diagrams by differential equations
• Analytic Results for Massless Three-Loop Form Factors
• On hyperlogarithms and Feynman integrals with divergences and many scales
• On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems
• 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)
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• 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
• Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
• Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors
• 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
• All order epsilon-expansion of Gauss hypergeometric functions with integer and half/integer values of parameters
• 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
• Master integrals for the four-loop Sudakov form factor
• 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
• Planar master integrals for four-loop form factors
• 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
• Higher-Order Corrections to Higgs Boson Amplitudes with Full Quark Mass Dependence in Quantum Chromodynamics