Singlet and non-singlet three-loop massive form factors

Abstract

We consider Quantum Chromodynamics with external vector, axial-vector, scalar and pseudo-scalar currents and compute three-loop corrections to the corresponding vertex function taking into account massive quarks. We consider all non-singlet contributions as well as those singlet contributions where the external current couples to a massive quark loop. We apply a semi-numerical method which is based on expansions around singular and regular kinematical points. They are matched at intermediate values of the squared partonic center-of-mass energy $s$ which allows to cover the whole kinematic range for negative and positive values of $s$. Our method permits a systematic increase of the precision by varying the expansion depth and the choice of the intermediate matching points. In our current set-up we have at least seven significant digits for the finite contribution of all form factors. We present our results as a combination of series expansions and interpolation functions which allows for a straightforward use in practical applications.

arXiv comment73 pages, 15 figures

References in corpus (78)

• Asymptotic expansion of Feynman integrals near threshold
• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• FORM version 4.0
• The renormalization of the axial anomaly in dimensional regularization
• The three loop relation between the \bar {MS} and the pole quark masses
• The analytical value of the electron (g-2) at order alpha^3 in QED
• Harmonic sums, Mellin transforms and Integrals
• Kira - A Feynman Integral Reduction Program
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Integral Reduction with Kira 2.0 and Finite Field Methods
• The Multiple Zeta Value Data Mine
• 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
• Three-Loop Polarization Function and $\mathcal{O}({\alpha }_s^2)$ Corrections to the Production of Heavy Quarks
• A Systematic and Efficient Method to Compute Multi-loop Master Integrals
• QCD Corrections to the $e^{+}{e}^{-}$ Cross Section and the $Z$ Boson Decay Rate
• Reconstructing Rational Functions with $\text{FireFly}$
• Two-loop QCD Corrections to the Heavy Quark Form Factors: the Vector Contributions
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• The three loop on-shell renormalization of QCD and QED
• The singular behavior of massive QCD amplitudes
• Expansion by regions: revealing potential and Glauber regions automatically
• Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions
• $\overline{\mathrm{MS}}$-on-shell quark mass relation up to four loops in QCD and a general SU$(N)$ gauge group
• Reconstruction of heavy quark current correlators at O(α_s^3)
• Interpolation of Dense and Sparse Rational Functions and other Improvements in $\text{FireFly}$
• The three-loop cusp anomalous dimension in QCD
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops
• Low energy moments of heavy quark current correlators at four loops
• Two-Loop QCD Corrections to the Heavy Quark Form Factors: Anomaly Contributions
• Heavy Quark Pair Production near Threshold with Potential Non-Relativistic QCD
• Four-loop photon quark form factor and cusp anomalous dimension in the large-$N_c$ limit of QCD
• Solving differential equations for Feynman integrals by expansions near singular points
• 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
• The quark and gluon form factors to three loops in QCD through to O(eps^2)
• Heavy Quark Vacuum Polarization Function at O(alpha_s^2) and O(alpha_s^3)
• How to choose master integrals
• QED vertex form factors at two loops
• 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
• ep-Finite Basis of Master Integrals for the Integration-By-Parts Method
• High-Energy Limit of QCD beyond Sudakov Approximation
• NNLO fermionic corrections to the charm quark mass dependent matrix elements in B -> X_s gamma
• The QCD form factor of heavy quarks at NNLO
• Four-loop quark form factor with quartic fundamental colour factor
• 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
• 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
• Decays of Scalar and Pseudoscalar Higgs Bosons into Fermions: Two-loop QCD Corrections to the Higgs-Quark-Antiquark Amplitude
• Massive vector form factors to three loops
• High-Energy Limit of Mass-Suppressed Amplitudes in Gauge Theories
• Quark and gluon form factors in four-loop QCD
• Two-Loop Form Factors in QED
• Introducing SummerTime: a package for high-precision computation of sums appearing in DRA method
• The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory
• The Heavy Quark Form Factors at Two Loops
• The Heavy Fermion Contributions to the Massive Three Loop Form Factors
• Evaluating `elliptic' master integrals at special kinematic values: using differential equations and their solutions via expansions near singular points
• 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
• A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $\overline{\mathrm{MS}}$-pole quark mass relation
• Three-loop massive form factors: complete light-fermion and large-$N_c$ corrections for vector, axial-vector, scalar and pseudo-scalar currents
• Quark and gluon form factors in four loop QCD: the $N_f^2$ and $N_{q\gamma }{N}_f$ contributions
• High energy behaviour of form factors
• Three-loop quark form factor at high energy: the leading mass corrections
• Analytic Calculation of Two Loop Corrections to Heavy Quark Pair Production Vertices Induced by Light Quarks
• Three-loop massive form factors: complete light-fermion corrections for the vector current
• Higgs Boson Production and Quark Scattering Amplitudes at High Energy through the Next-to-Next-to-Leading Power in Quark Mass
• The complete singlet contribution to the massless quark form factor at three loops in QCD
• Three-loop QCD corrections and b-quark decays
• Heavy quark form factors in the large ${\beta }_0$ limit

Cited by in corpus (6)

• 50 Years of Quantum Chromodynamics
• Muon-electron scattering at NNLO
• Heavy-quark pair production at lepton colliders at NNNLO in QCD
• Radiative corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^{+}{e}^{-}$ collisions
• Three-loop QCD matching of the flavor-changing scalar current involving the heavy charm and bottom quark
• Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L