On the Computation of Form Factors in Massless QCD with Finite Master Integrals

Abstract

We present the bare one-, two-, and three-loop form factors in massless Quantum Chromodynamics as linear combinations of finite master integrals. Using symbolic integration, we compute their $\epsilon$ expansions and thereby reproduce all known results with an independent method. Remarkably, in our finite basis, only integrals with a less-than-maximal number of propagators contribute to the cusp anomalous dimensions. We report on indications of this phenomenon at four loops, including the result for a finite, irreducible, twelve-propagator form factor integral. Together with this article, we provide our automated software setup for the computation of finite master integrals.

28 pages, 3 figures, results and software in ancillary files; v2: fixed diagram in (7.1); v3: added acknowledgement

References in corpus (29)

• Higgs boson gluon-fusion production in N3LO QCD
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Quark and gluon form factors to three loops
• Higgs boson gluon-fusion production at threshold in N3LO QCD
• SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
• Resolution of singularities for multi-loop integrals
• The massless higher-loop two-point function
• Origin of the Large Perturbative Corrections to Higgs Production at Hadron Colliders
• Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra
• Threshold resummation at N${}^3$LL accuracy and soft-virtual cross sections at N${}^3$LO
• Drell-Yan Production at Threshold to Third Order in QCD
• Feynman integrals and hyperlogarithms
• Resummed Higgs cross section at N${}^3$LL
• Approximate N^3LO Higgs-boson production cross section using physical-kernel constraints
• Soft Expansion of Double-Real-Virtual Corrections to Higgs Production at N${}^3$LO
• N${}^3$LO Higgs and Drell-Yan production at threshold: the one-loop two-emission contribution
• Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• Introducing SummerTime: a package for high-precision computation of sums appearing in DRA method
• Master integrals for the four-loop Sudakov form factor
• Real-Virtual-Virtual contributions to the inclusive Higgs cross section at N3LO
• Adequate bases of phase space master integrals for $gg\to h$ at NNLO and beyond
• Two-Loop Vertices in Quantum Field Theory: Infrared and Collinear Divergent Configurations
• Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals
• Exact N${}^3$LO results for $q{q}^{\prime }\to H+X$
• HEPGAME and the Simplification of Expressions

Cited by in corpus (38)

• Integral Reduction with Kira 2.0 and Finite Field Methods
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• Collider Physics at the Precision Frontier
• A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals
• Azurite: An algebraic geometry based package for finding bases of loop integrals
• The Three-loop Quark Jet Function
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• The Four Loop QCD Rapidity Anomalous Dimension
• Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Four-loop quark form factor with quartic fundamental colour factor
• Four-loop collinear anomalous dimensions in QCD and $\mathcal{N}=4$ super Yang-Mills
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Massive vector form factors to three loops
• Di-photon amplitudes in three-loop Quantum Chromodynamics
• Quark and gluon form factors in four-loop QCD
• The Four-Loop Cusp Anomalous Dimension from the $\mathcal{N}=4$ Sudakov Form Factor
• Mixed EW-QCD two-loop amplitudes for $q\bar{q}\to {\ell }^{+}{\ell }^{-}$ and ${\gamma }_5$ scheme independence of multi-loop corrections
• The on-shell expansion: from Landau equations to the Newton polytope
• Numerical Multi-Loop Calculations via Finite Integrals and One-Mass EW-QCD Drell-Yan Master Integrals
• Quark and gluon form factors in four loop QCD: the $N_f^2$ and $N_{q\gamma }{N}_f$ contributions
• Three-loop soft function for heavy-to-light quark decays
• Evaluation of multi-loop multi-scale Feynman integrals for precision physics
• Locally finite two-loop QCD amplitudes from IR universality for electroweak production
• The Four-Loop $\mathcal{N}=4$ SYM Sudakov Form Factor
• A planar four-loop form factor and cusp anomalous dimension in QCD
• Constructing multi-loop scattering amplitudes with manifest singularity structure
• Computational challenges for multi-loop collider phenomenology
• Three-loop soft function for energetic electroweak boson production at hadron colliders
• Three-loop vertex integrals at symmetric point
• Hyperlogarithms in the theory of turbulence of infinite dimension
• Fermionic corrections to quark and gluon form factors in four-loop QCD
• Singlet and non-singlet three-loop massive form factors
• The integrand form of infrared singularities of two-loop QCD scattering amplitudes
• Higher-Order Corrections to Higgs Boson Amplitudes with Full Quark Mass Dependence in Quantum Chromodynamics