O(α_s^2) Corrections to Top Quark Production at $e^+e^-$ Colliders

Abstract

In this article we evaluate mass corrections up to $O((m^2/q^2)^6)$ to the three-loop polarization function induced by an axial-vector current. Special emphasis is put on the evaluation of the singlet diagram which is absent in the vector case. As a physical application $O(α_s^2)$ corrections to the production of top quarks at future $e^+e^-$ colliders is considered. It is demonstrated that for center of mass energies $\sqrt{s} >~ 500$ GeV the inclusion of the first seven terms into the cross section leads to a reliable description.

Figures (4)

• Figure 1: Diagrams contributing to $\Pi_S^{a}$. In the triangle loops either a top or bottom quark may be present.
• Figure 2: $R^{(2),a}_i$, $i={\it A, NA, l, F, S, Sb}$ as functions of $x = 2M_t/\sqrt{s}$ at $\mu^2 = M_t^2$. Successively higher order terms in $(M_t^2/s)^n$: Dotted: $n=0$; dashed: $n=1,\ldots,5$; solid: $n=6$. Narrow dots: exact result ($R_l^{(2),a}$, $R_{Sb}^{(2),a}$) or semi-analytical results ($R_A^{(2),a}$, $R_{NA}^{(2),a}$).
• Figure 3: Normalized cross section $R_t$ as a function of the center of mass energy $\sqrt{s}$, together with the pure vector and axial-vector contributions: $R_t = R_t^{\rm vector}+R_t^{\rm axial-vector}$. Dotted: Born approximation; dashed: ${\cal O}(\alpha_s)$, solid: ${\cal O}(\alpha_s^2)$. The scale $\mu^2=s$ has been adopted.
• Figure 4: Two-loop vector and axial-vector contributions $R^{(2),v}$, $R^{(2),a} + C_F T R^{(2),a}_S$. The scale $\mu^2=s$ has been adopted and $M_t=175$ GeV has been chosen.