Renormalization Group Improved Heavy Quark Production in Polarized \gamma \gamma Collisions

TL;DR

This paper improves predictions for heavy quark production in polarized gamma-gamma collisions by incorporating the running of the strong coupling, reducing scale uncertainties and enhancing theoretical stability.

Contribution

It introduces the inclusion of leading and next-to-leading order running coupling effects into all-order double logarithmic calculations for better accuracy.

Findings

Significant reduction in scale uncertainty of the cross section.

Effective scale for the non-Sudakov form factor is approximately 6 m_q^2.

Restoration of positivity and stability at the four-loop level.

Abstract

The experimental determination of the partial width $\Gamma (H \longrightarrow \gamma \gamma)$ of an intermediate mass Higgs is among the most important measurements at a future photon photon collider. Recently it was shown that large non-Sudakov as well as Sudakov double logarithmic (DL) corrections can be summed to all orders in the background process $\gamma \gamma (J_z=0) \longrightarrow q \bar{q}$. It was found that positivity and stability of the cross section was only restored at the four-loop level. One remaining large source of uncertainty stems from the fact that the scale of the strong coupling is unspecified within the double logarithmic approximation. In this paper we include the leading and next-to-leading order running coupling to all orders. We thus remove the inherent scale uncertainty of both the exact one-loop and all-orders DL result without encountering any Landau-pole singularities. The effect is significant and, for the non-Sudakov form factor, is found to correspond to an effective scale of roughly $\alpha_s(9m_q^2)$.