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.

73 pages, 15 figures

References in corpus (22)

• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Quark and gluon form factors to three loops
• Expansion by regions: revealing potential and Glauber regions automatically
• Reconstruction of heavy quark current correlators at O(α_s^3)
• The three-loop cusp anomalous dimension in QCD
• Low energy moments of heavy quark current correlators at four loops
• Heavy Quark Pair Production near Threshold with Potential Non-Relativistic QCD
• Three-Loop Chromomagnetic Interaction in HQET
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• High-Energy Limit of QCD beyond Sudakov Approximation
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• 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
• The $n_f^2$ contributions to fermionic four-loop form factors
• Four-loop quark form factor with quartic fundamental colour factor
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• Massive vector form factors to three loops
• Massive three-loop form factor in the planar limit
• A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $\overline{\mathrm{MS}}$-pole quark mass relation
• Quark and gluon form factors in four loop QCD: the $N_f^2$ and $N_{q\gamma }{N}_f$ contributions
• Three-loop quark form factor at high energy: the leading mass corrections
• Heavy quark form factors in the large ${\beta }_0$ limit