Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions

Abstract

We calculate the four-loop massless QCD corrections with three closed quark lines to quark and gluon form factors. We apply a novel integration by parts algorithm based on modular arithmetic and compute all relevant master integrals for arbitrary values of the space-time dimension. This is the first calculation of a gluon form factor at this perturbative order in QCD.

arXiv comment4 pages

References in corpus (28)

• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• FORM version 4.0
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• FIRE5: a C++ implementation of Feynman Integral REduction
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Group theory factors for Feynman diagrams
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Calculation of the quark and gluon form factors to three loops in QCD
• A novel approach to integration by parts reduction
• HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
• Quark and gluon form factors to three loops
• FIESTA 4: optimized Feynman integral calculations with GPU support
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• Towards a Basis for Planar Two-Loop Integrals
• High-precision calculation of multi-loop Feynman integrals by difference equations
• Two-loop Integrand Decomposition into Master Integrals and Surface Terms
• Integration-by-parts reductions from unitarity cuts and algebraic geometry
• The Quark Form Factor at Higher Orders
• Color-kinematic Duality for Form Factors
• A quasi-finite basis for multi-loop Feynman integrals
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• On the Computation of Form Factors in Massless QCD with Finite Master Integrals
• Master Integrals for Massless Three-Loop Form Factors: One-Loop and Two-Loop Insertions
• Master integrals for the four-loop Sudakov form factor
• Finding Linear Dependencies in Integration-By-Parts Equations: A Monte Carlo Approach
• First Forcer results on deep-inelastic scattering and related quantities
• The diamond rule for multi-loop Feynman diagrams
• Calculating four-loop massless propagators with Forcer

Cited by in corpus (50)

• Kira - A Feynman Integral Reduction Program
• FIRE6: Feynman Integral REduction with Modular Arithmetic
• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• Reconstructing Rational Functions with $\text{FireFly}$
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• On quartic colour factors in splitting functions and the gluon cusp anomalous dimension
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Collider Physics at the Precision Frontier
• Interpolation of Dense and Sparse Rational Functions and other Improvements in $\text{FireFly}$
• Four-loop photon quark form factor and cusp anomalous dimension in the large-$N_c$ limit of QCD
• Azurite: An algebraic geometry based package for finding bases of loop integrals
• Matter dependence of the four-loop cusp anomalous dimension
• MultivariateApart: Generalized Partial Fractions
• The Four Loop QCD Rapidity Anomalous Dimension
• Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory
• Four-loop quark form factor with quartic fundamental colour factor
• Three-loop gluon scattering in QCD and the gluon Regge trajectory
• The $n_f^2$ contributions to fermionic four-loop form factors
• Four-loop collinear anomalous dimensions in QCD and $\mathcal{N}=4$ super Yang-Mills
• Di-photon amplitudes in three-loop Quantum Chromodynamics
• Quark and gluon form factors in four-loop QCD
• Two-loop leading colour QCD corrections to $q\bar{q}\to \gamma \gamma g$ and $qg\to \gamma \gamma q$
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• The Four-Loop Cusp Anomalous Dimension from the $\mathcal{N}=4$ Sudakov Form Factor
• Two-loop five-point massless QCD amplitudes within the IBP approach
• Three-loop helicity amplitudes for diphoton production in gluon fusion
• On next to soft corrections to Drell-Yan and Higgs Boson productions
• Differential equations on unitarity cut surfaces
• Three-loop helicity amplitudes for quark-gluon scattering in QCD
• A Numerical Routine for the Crossed Vertex Diagram with a Massive-Particle Loop
• Soft-gluon effective coupling and cusp anomalous dimension
• Extracting analytical one-loop amplitudes from numerical evaluations
• Quark and gluon form factors in four loop QCD: the $N_f^2$ and $N_{q\gamma }{N}_f$ contributions
• Lecture Notes on Multi-loop Integral Reduction and Applied Algebraic Geometry
• On next to soft threshold corrections to DIS and SIA processes
• Three-loop massive form factors: complete light-fermion corrections for the vector current
• Rapidity distribution at soft-virtual and beyond for n-colorless particles to N${}^4$LO in QCD
• The Four-Loop $\mathcal{N}=4$ SYM Sudakov Form Factor
• Going beyond Soft plus Virtual
• QCD calculations for the LHC: status and prospects
• Three-loop helicity amplitudes for photon+jet production
• Double-Real-Virtual and Double-Virtual-Real Corrections to the Three-Loop Thrust Soft Function
• DREAM, a program for arbitrary-precision computation of dimensional recurrence relations solutions, and its applications
• Fermionic corrections to quark and gluon form factors in four-loop QCD
• The nonplanar cusp and collinear anomalous dimension at four loops in $\mathcal{N}=4$ SYM theory
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• Three-loop helicity amplitudes for four-quark scattering in massless QCD
• Massive Two-Loop Heavy Particle Diagrams
• Singlet and non-singlet three-loop massive form factors
• On-shell Methods for Form Factors in N=4 SYM and Their Applications