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 mathrm{non}hbox{-} 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.
Highlights
JHEP12(2021)095 to the vector quark form factors (FF) [8, 9, 31, 32].1 The three-loop singlet contribution to the axial part of quark FFs in purely massless QCD was determined only very recently in ref. [42]
In the absence of the top-loop contribution, the purely massless contribution to the axial FFs contains an explicit logarithmic renormalization scale dependence beyond that expected from the running of the MS renormalized αs, which is related to the non-vanishing anomalous dimension of the singlet axial current
With all necessary ingredients ready, we present our numerical results for the finite remainders of singlet quark FFs with exact top mass dependence over the full kinematic range from the low-energy limit s/m2t → 0 to the high-energy limit s/m2t → ∞
Summary
The Lorentz-invariant coefficients F V and F V are, respectively, the vector and axial FF of the massless quark q, which are functions of s = (p1 + p2)2 = 2 p1 · p2 as well as the top mass mt (when the top quark loop contributes) The normalization is such that the tree-level values of these FFs read (in 4 dimensions): F V,0 = 1 , F A,0 = 1. The non-singlet QCD corrections have the Z boson coupled directly to the open fermion line of the external quark q, which starts from the tree level. It depends only on the electroweak coupling of the external quark q. It is known to be power suppressed in the low energy limit
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