Two-loop QCD corrections to the heavy quark form factors: the vector contributions

Abstract

We present closed analytic expressions of the electromagnetic vertex form factors for heavy quarks at the two-loop level in QCD for arbitrary momentum transfer. The calculation is carried out in dimensional regularization. The electric and magnetic form factors are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.

Heavy quark form factors at two loops

“…In Refs. [20,21,23], another convention has been used and other terms are absorbed as well. In higher orders in ε, this leads to different expressions and also influences, beyond NLO, the evolution of the strong coupling constant α s .…”

“…[12][13][14][15][16][17][18][19]. A series of papers followed obtaining the two-loop QCD corrections for the vector form factor [20], the axial-vector form factor [21], the anomaly contributions [22] and the scalar and pseudoscalar form factors [23]. An independent cross-check of the vector form factor has been performed in [24] with the addition of the OðεÞ contribution, where ε ¼ ð4 − DÞ=2 and D is the spacetime dimension.…”

Electroweak production of top-quark pairs ine+e−annihilation at NNLO in QCD: The vector current contributions

“…The two-loop heavy quark form factor was first obtained in refs. [29][30][31] and then confirmed some time later by an independent calculation [32]. In fact, for quite some time, the only outstanding problem was to construct an efficient framework for the combination of the ingredients described above into an infrared-safe Monte Carlo event generator.…”

“…Also the authors of ref. [29] include a factor Γ(1 + ǫ) exp(ǫγ E ) in the coupling renormalization, where Γ(z) is Euler's Gamma function, and γ E = 0.577216 . .…”

Probing the top-quark width through ratios of resonance contributions of e + e − → W + W − b b ¯ $$ {\mathrm{e}}^{+}{\mathrm{e}}^{-}\to {\mathrm{W}}^{+}{\mathrm{W}}^{-}\mathrm{b}\overline{\mathrm{b}} $$

“…On-shell top-quark pair-production in the continuum is now known at next-to-next-to-leading order (NNLO) in QCD [11][12][13][14][15][16][17][18][19][20][21]. Relaxing the assumption of stable top quarks, top-pair production and decay in e + e − collisions has been studied in the narrow-width approximation in ref.…”