The QCD form factor of heavy quarks at NNLO

Abstract

We present an analytical calculation of the two-loop QCD corrections to the electromagnetic form factor of heavy quarks. The two-loop contributions to the form factor are reduced to linear combinations of master integrals, which are computed through higher orders in the parameter of dimensional regularization epsilon=(4-D)/2. Our result includes all terms of order epsilon at two loops and extends the previous literature. We apply the exponentiation of the heavy-quark form factor to derive new improved three-loop expansions in the high-energy limit. We also discuss the implications for predictions of massive n-parton amplitudes based on massless results in the limit, where the quark mass is small compared to all kinematical invariants.

latex, 37 pages, 4 figures

References in corpus (55)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Harmonic Polylogarithms
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Differential Equations for Feynman Graph Amplitudes
• 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
• Automatized analytic continuation of Mellin-Barnes integrals
• Decoupling Relations to O(alpha_s^3) and their Connection to Low-Energy Theorems
• HPL, a Mathematica implementation of the harmonic polylogarithms
• Multi-loop Amplitudes and Resummation
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Automatic Integral Reduction for Higher Order Perturbative Calculations
• NLO Production and Decay of Quarkonium
• QCD Decoupling at Four Loops
• Four-Loop Decoupling Relations for the Strong Coupling
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• Three-Loop Results for Quark and Gluon Form Factors
• Massive Feynman diagrams and inverse binomial sums
• One-loop Singular Behaviour of QCD and SUSY QCD Amplitudes with Massive Partons
• High-precision calculation of multi-loop Feynman integrals by difference equations
• Universal structure of subleading infrared poles in gauge theory amplitudes
• Two-loop QCD corrections to the heavy quark pair production cross section in e+e- annihilation near the threshold
• The Quark Form Factor at Higher Orders
• Resolution of singularities for multi-loop integrals
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• Two-loop QCD Corrections to the Heavy Quark Form Factors: the Vector Contributions
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• The three loop on-shell renormalization of QCD and QED
• The singular behavior of massive QCD amplitudes
• The Large Quark Mass Expansion of Gamma (Z^0 -> hadrons) and Gamma(tau^- -> nu_tau + hadrons) in the Order alpha_s^3
• Two-loop QED corrections to Bhabha scattering
• Heavy-quark production in gluon fusion at two loops in QCD
• Heavy-quark production in massless quark scattering at two loops in QCD
• Top-quark pair production near threshold at LHC
• Bound-state Effects on Top Quark Production at Hadron Colliders
• Two-Loop Photonic Corrections to Massive Bhabha Scattering
• Two-Loop QCD Corrections to the Heavy Quark Form Factors: Anomaly Contributions
• Next-to-Next-to-Leading Logarithms in Four-Fermion Electroweak Processes at High Energy
• Perturbative Heavy Quark Fragmentation Function through O(alpha_s^2)
• Heavy Quark Pair Production near Threshold with Potential Non-Relativistic QCD
• Two-Loop Corrections to Bhabha Scattering
• Master integrals for massive two-loop Bhabha scattering in QED
• Two-Loop QCD Corrections to the Heavy Quark Form Factors: Axial Vector Contributions
• Two-loop self-energy master integrals on shell
• ON-SHELL2: FORM based package for the calculation of two-loop self-energy single scale Feynman diagrams occurring in the Standard Model
• Virtual Hadronic and Leptonic Contributions to Bhabha Scattering
• Two-Loop Heavy-Flavor Contribution to Bhabha Scattering
• Second order contributions to elastic large-angle Bhabha scattering
• Vertex diagrams for the QED form factors at the 2-loop level
• Calculation of the Two-Loop Heavy-Flavor Contribution to Bhabha Scattering
• Virtual Hadronic and Heavy-Fermion O(alpha^2) Corrections to Bhabha Scattering
• Fermionic and Scalar Corrections for the Abelian Form Factor at Two Loops
• Two-loop QED hadronic corrections to Bhabha scattering
• A complete set of scalar master integrals for massive 2-loop Bhabha scattering: where we are

Cited by in corpus (36)

• Threshold Resummation for Top-Pair Hadroproduction to Next-to-Next-to-Leading Log
• Factorization Structure of Gauge Theory Amplitudes and Application to Hard Scattering Processes at the LHC
• Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
• The cusp anomalous dimension at three loops and beyond
• Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel
• The singular behavior of one-loop massive QCD amplitudes with one external soft gluon
• Massive vector form factors to three loops
• Computation of the Soft Anomalous Dimension Matrix in Coordinate Space
• The Heavy Quark Form Factors at Two Loops
• Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations
• Top-quark forward-backward asymmetry in e+e- annihilation at NNLO in QCD
• Heavy Quark Form Factors at Three Loops in the Planar Limit
• Massive three-loop form factor in the planar limit
• Electroweak prodution of top-quark pairs in e+e- annihilation at NNLO in QCD: the vector contributions
• The real radiation antenna function for $S\to Q\bar{Q}q\bar{q}$ at NNLO QCD
• The two-loop soft function for heavy quark pair production at future linear colliders
• Analytic results for planar three-loop integrals for massive form factors
• Higgs decay into massive b-quarks at NNLO QCD in the nested soft-collinear subtraction scheme
• Three-loop massive form factors: complete light-fermion and large-$N_c$ corrections for vector, axial-vector, scalar and pseudo-scalar currents
• Towards muon-electron scattering at NNLO
• High energy behaviour of form factors
• The LBK theorem to all orders
• The asymptotic behavior of the heavy quark form factors at higher order
• Massive three-loop form factors: anomaly contribution
• Calculation of two-loop QCD corrections for hadronic single top-quark production in the t channel
• Efficient Evaluation of Massive Mellin--Barnes Integrals
• Three-loop massive form factors: complete light-fermion corrections for the vector current
• Hard Matching for Boosted Tops at Two Loops
• Probing the top-quark width through ratios of resonance contributions of $e^{+}{e}^{-}\to W^{+}{W}^{-}b\bar{b}$
• Top-quark pair production at next-to-next-to-leading order QCD in electron positron collisions
• The real-virtual antenna functions for $S\to Q\bar{Q}X$ at NNLO QCD
• Transverse Momentum-Dependent Heavy-Quark Fragmentation at Next-to-Leading Order
• Two-loop Vertices with Vacuum Polarization Insertion
• Multiple soft-photon emission at next-to-leading power to all orders
• Singlet and non-singlet three-loop massive form factors
• Three loop QCD corrections to heavy quark form factors