The complete singlet contribution to the massless quark form factor at three loops in QCD

Abstract

It is well known that the effect of top quark loop corrections in the axial part of quark form factors (FF) does not decouple in the large top mass or low energy limit due to the presence of the axial-anomaly type diagrams. The top-loop induced singlet-type contribution should be included in addition to the purely massless result for quark FFs when applied to physics in the low energy region, both for the non-decoupling mass logarithms and for an appropriate renormalization scale dependence. In this work, we have numerically computed the so-called singlet contribution to quark FFs with the exact top quark mass dependence over the full kinematic range. We discuss in detail the renormalization formulae of the individual subsets of the singlet contribution to an axial quark FF with a particular flavor, as well as the renormalization group equations that govern their individual scale dependence. Finally we have extracted the 3-loop Wilson coefficient in the low energy effective Lagrangian, renormalized in a non-$\overline{\mathrm{MS}}$ scheme and constructed to encode the leading large mass approximation of our exact results for singlet quark FFs. We have also examined the accuracy of the approximation in the low energy region.

arXiv commentA typo in the coefficient of the C_F^2 in the third line of eq.(6.6) is fixed

References in corpus (46)

• Harmonic Polylogarithms
• Multiloop integrals in dimensional regularization made simple
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Differential Equations for Feynman Graph Amplitudes
• The renormalization of the axial anomaly in dimensional regularization
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Infrared singularities of scattering amplitudes in perturbative QCD
• Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering
• Calculation of the quark and gluon form factors to three loops in QCD
• Quark and gluon form factors to three loops
• The Quark Form Factor at Higher Orders
• 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 Drell-Yan cross section to third order in the strong coupling constant
• Facts of life with gamma(5)
• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• The Large Quark Mass Expansion of Gamma (Z^0 -> hadrons) and Gamma(tau^- -> nu_tau + hadrons) in the Order alpha_s^3
• Analytic Results for Massless Three-Loop Form Factors
• Complete QCD Corrections to Hadronic $Z$--Decays in Order ${\alpha }_s^4$
• Two-Loop QCD Corrections to the Heavy Quark Form Factors: Anomaly Contributions
• 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
• Effective QCD Interactions of CP-odd Higgs Bosons at Three Loops
• Charged Current Drell-Yan Production at N3LO
• Two-Loop QCD Corrections to the Heavy Quark Form Factors: Axial Vector Contributions
• 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
• Decays of Scalar and Pseudoscalar Higgs Bosons into Fermions: Two-loop QCD Corrections to the Higgs-Quark-Antiquark Amplitude
• The $Hb\bar{b}$ form factor to three loops in QCD
• The alpha_s^3 correction to Gamma (Z^0 -> hadrons)
• The ${\alpha }_s^3$ Corrections to the Effective Neutral Current and to the Z Decay Rate in the Heavy Top Quark Limit
• A prescription for projectors to compute helicity amplitudes in D dimensions
• Exact quark-mass dependence of the Higgs-gluon form factor at three loops in QCD
• The Heavy Fermion Contributions to the Massive Three Loop Form Factors
• Pseudo-scalar Form Factors at Three Loops in QCD
• The $q_T$ and $\Delta \varphi$ spectra in W and Z production at the LHC at N${}^3$LL'+N${}^2$LO
• Heavy Quark Form Factors at Three Loops in the Planar Limit
• Massive three-loop form factor in the planar limit
• Three-loop massive form factors: complete light-fermion and large-$N_c$ corrections for vector, axial-vector, scalar and pseudo-scalar currents
• Polarised Amplitudes and Soft-Virtual Cross Sections for $b\bar{b}\to ZH$ at NNLO in QCD
• Three-loop massive form factors: complete light-fermion corrections for the vector current
• Renormalization of the flavor-singlet axial-vector current and its anomaly in dimensional regularization
• Polarized $q\bar{q}\to Z+$Higgs amplitudes at two loops in QCD: the interplay between vector and axial vector form factors and a pitfall in applying a non-anticommuting ${\gamma }_5$
• Fermion Traces Without Evanescence
• The three-loop singlet contribution to the massless axial-vector quark form factor

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