The $n_f^2$ contributions to fermionic four-loop form factors

Abstract

We compute the four-loop contributions to the photon quark and Higgs quark form factors involving two closed fermion loops. We present analytical results for all non-planar master integrals of the two non-planar integral families which enter our calculation.

arXiv comment26 pages

References in corpus (44)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Harmonic Polylogarithms
• Multiloop integrals in dimensional regularization made simple
• The three-loop QCD $\beta$-function and anomalous dimensions
• The 4-loop quark mass anomalous dimension and the invariant quark mass
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• FORM version 4.0
• Algorithm FIRE -- Feynman Integral REduction
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• FIRE5: a C++ implementation of Feynman Integral REduction
• HPL, a Mathematica implementation of the harmonic polylogarithms
• Quark Mass Anomalous Dimension to alpha_s**4
• Multi-loop Amplitudes and Resummation
• Complete Corrections of O(αα_s) to the Decay of the Z Boson into Bottom Quarks
• Calculation of the quark and gluon form factors to three loops in QCD
• Quark and gluon form factors to three loops
• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• Three-Loop Results for Quark and Gluon Form Factors
• Reducing differential equations for multiloop master integrals
• Infrared Factorization, Wilson Lines and the Heavy Quark Limit
• Two-Loop Quark and Gluon Form Factors in Dimensional Regularisation
• FIRE4, LiteRed and accompanying tools to solve integration by parts relations
• Power corrections and renormalons in Drell-Yan production
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form
• Next-to-next-to-leading logarithmic threshold resummation for deep-inelastic scattering and the Drell-Yan process
• Anomalous Dimension of Non-Singlet Wilson Operators at O(1/N_f) in Deep Inelastic Scattering
• Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve
• $\overline{\mathrm{MS}}$-on-shell quark mass relation up to four loops in QCD and a general SU$(N)$ gauge group
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• epsilon: A tool to find a canonical basis of master integrals
• The fully differential decay rate of a Higgs boson to bottom-quarks at NNLO in QCD
• Transforming differential equations of multi-loop Feynman integrals into canonical form
• Four-loop photon quark form factor and cusp anomalous dimension in the large-$N_c$ limit of QCD
• 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
• Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• Higher Orders in A(α_s)/[1-x]_+ of Non-Singlet Partonic Splitting Functions
• The $Hb\bar{b}$ form factor to three loops in QCD
• Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals
• A planar four-loop form factor and cusp anomalous dimension in QCD
• Fuchsia and master integrals for splitting functions from differential equations in QCD

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• FIRE6: Feynman Integral REduction with Modular Arithmetic
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• On quartic colour factors in splitting functions and the gluon cusp anomalous dimension
• Collider Physics at the Precision Frontier
• Matter dependence of the four-loop cusp anomalous dimension
• The Four Loop QCD Rapidity Anomalous Dimension
• Infrared Singularities of Scattering Amplitudes and N${}^3$LL Resummation for $n$-Jet Processes
• Four-Loop Nonplanar Cusp Anomalous Dimension in 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
• Soft corrections to inclusive deep-inelastic scattering at four loops and beyond
• Quark and gluon form factors in four-loop QCD
• Approximate four-loop QCD corrections to the Higgs-boson production cross section
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Two-loop five-point massless QCD amplitudes within the IBP approach
• Resummed prediction for Higgs boson production through $b\bar{b}$ annihilation at N${}^3$LL
• The Four-Loop Cusp Anomalous Dimension from the $\mathcal{N}=4$ Sudakov Form Factor
• A Numerical Routine for the Crossed Vertex Diagram with a Massive-Particle Loop
• Soft-gluon effective coupling and cusp anomalous dimension
• Quark and gluon form factors in four loop QCD: the $N_f^2$ and $N_{q\gamma }{N}_f$ contributions
• Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
• 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
• Rapidity distribution at soft-virtual and beyond for n-colorless particles to N${}^4$LO in QCD
• The complete singlet contribution to the massless quark form factor at three loops in QCD
• Beam functions for $N$-jettiness at N${}^3$LO in perturbative QCD
• The Four-Loop $\mathcal{N}=4$ SYM Sudakov Form Factor
• Resummed inclusive cross-section in Randall-Sundrum model at NNLO+NNLL
• Infrared singularities of multi-leg QCD amplitudes with a massive parton at three loops
• QCD calculations for the LHC: status and prospects
• Precision QCD phenomenology of exotic spin-2 search at the LHC
• 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
• Rational Function Simplification for Integration-by-Parts Reduction and Beyond
• Singlet and non-singlet three-loop massive form factors
• On-shell Methods for Form Factors in N=4 SYM and Their Applications