Three loop QCD corrections to heavy quark form factors

Abstract

Higher order calculations in perturbative Quantum Field Theories often produce coupled linear systems of differential equations which factorize to first order. Here we present an algorithm to solve such systems in terms of iterated integrals over an alphabet the structure of which is implied by the coefficient matrix of the given system. We apply this method to calculate the master integrals in the color-planar and complete light quark contributions to the three-loop massive form factors.

9 pages; To appear in the proceedings of ACAT 2019, 10th - 15th March 2019, Saas Fee, Switzerland;

References in corpus (57)

• Harmonic Polylogarithms
• Multiloop integrals in dimensional regularization made simple
• New features of FORM
• Five-Loop Running of the QCD coupling constant
• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• Numerical evaluation of multiple polylogarithms
• The five-loop beta function of Yang-Mills theory with fermions
• The Multiple Zeta Value Data Mine
• FIESTA 4: optimized Feynman integral calculations with GPU support
• The elliptic dilogarithm for the sunset graph
• The Multithreaded version of FORM
• Quark mass relations to four-loop order
• Analytic treatment of the two loop equal mass sunrise graph
• Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• Infrared singularities of QCD amplitudes with massive partons
• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• The massless higher-loop two-point function
• Two-loop QCD Corrections to the Heavy Quark Form Factors: the Vector Contributions
• Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
• The three loop on-shell renormalization of QCD and QED
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism
• The singular behavior of massive QCD amplitudes
• A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics
• FIESTA 2: parallelizeable multiloop numerical calculations
• The kite integral to all orders in terms of elliptic polylogarithms
• Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra
• $\overline{\mathrm{MS}}$-on-shell quark mass relation up to four loops in QCD and a general SU$(N)$ gauge group
• Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
• Computer Algebra Algorithms for Special Functions in Particle Physics
• The three-loop cusp anomalous dimension in QCD
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• Two-Loop QCD Corrections to the Heavy Quark Form Factors: Anomaly Contributions
• Iterated Binomial Sums and their Associated Iterated Integrals
• Relation between the pole and the minimally subtracted mass in dimensional regularization and dimensional reduction to three-loop order
• Automated Solution of First Order Factorizable Systems of Differential Equations in One Variable
• Two-Loop QCD Corrections to the Heavy Quark Form Factors: Axial Vector Contributions
• Three-Loop Chromomagnetic Interaction in HQET
• Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms
• The QCD form factor of heavy quarks at NNLO
• The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory
• The Heavy Quark Form Factors at Two Loops
• Numerical Implementation of Harmonic Polylogarithms to Weight w = 8
• Heavy Quark Form Factors at Three Loops in the Planar Limit
• Massive three-loop form factor in the planar limit
• Four-loop wave function renormalization in QCD and QED
• Analytic results for planar three-loop integrals for massive form factors
• Three-loop massive form factors: complete light-fermion and large-$N_c$ corrections for vector, axial-vector, scalar and pseudo-scalar currents
• High energy behaviour of form factors
• The asymptotic behavior of the heavy quark form factors at higher order
• Three-loop massive form factors: complete light-fermion corrections for the vector current
• "Sixth root of unity" and Feynman diagrams: hypergeometric function approach point of view
• Recent Symbolic Summation Methods to Solve Coupled Systems of Differential and Difference Equations
• Computing the Inverse Mellin Transform of Holonomic Sequences using Kovacic's Algorithm
• A toolbox to solve coupled systems of differential and difference equations
• From modular forms to differential equations for Feynman integrals