Two-Loop QCD Corrections to the Heavy Quark Form Factors: Anomaly Contributions

TL;DR

This work computes the two-loop QCD triangle (anomalous) contributions to heavy-quark axial-vector and pseudoscalar form factors, covering both flavor-singlet and flavor-non-singlet currents across four mass configurations.Using dimensional regularization with a gamma5 prescription, the authors derive closed analytic expressions for the form factors, renormalize the currents, and verify chiral Ward identities, including the ABJ anomaly contribution through a finite renormalization of the singlet current.The results are expressed in terms of master integrals and one-dimensional harmonic polylogarithms, with explicit spacelike and timelike (above threshold) results, and are complemented by threshold and asymptotic expansions to assess convergence and applicability.The findings enable a fully differential description of heavy-quark electroproduction at order ${α_s^2}$ and provide robust benchmarks for forward-backward asymmetries and related observables in current and future collider experiments.

Abstract

We present closed analytic expressions for the order $α_s^2$ triangle diagram contributions to the matrix elements of the singlet and non-singlet axial vector currents between the vacuum and a quark-antiquark state. We have calculated these vertex functions for arbitrary momentum transfer and for four different sets of internal and external quark masses. We show that both the singlet and non-singlet vertex functions satisfy the correct chiral Ward identities. Using the exact expressions for the finite axial vector form factors, we check the quality and the convergence of expansions at production threshold and for asymptotic energies.

Figures (4)

• Figure 1: Triangle diagram (type B) contributions to the various axial vector and pseudoscalar vertex functions considered in this paper. The double and single straight line triangles in (a) and (b) denote massive and massless quarks, respectively. The external $q, \, \bar{q}$ quarks are either massive or massless. The dashed line denotes either an axial vector or a pseudoscalar vertex. The crossed diagrams are not drawn.
• Figure 2: One-loop anomalous vertex function $F_q$.
• Figure 3: The real and imaginary parts of $C_F T_R {\cal G}_{1,2}(s,m,m)$ as functions of the rescaled c.m. energy and their threshold and asymptotic expansions.
• Figure 5: The real and imaginary parts of $C_F T_R {\cal G}_{1}(s,m,0)$ as functions of the rescaled c.m. energy and their threshold and asymptotic expansions.