Borel resummation of soft gluon radiation and higher twists

Abstract

We show that the well-known divergence of the perturbative expansion of resummed results for processes such as deep-inelastic scattering and Drell-Yan in the soft limit can be treated by Borel resummation. The divergence in the Borel inversion can be removed by the inclusion of suitable higher twist terms. This provides us with an alternative to the standard 'minimal prescription' for the asymptotic summation of the perturbative expansion, and it gives us some handle on the role of higher twist corrections in the soft resummation region.

Figures (3)

• Figure 1: Dependence of the truncated Borel integral $R_{\rm B}$ eq. (\ref{['pbreg']}) on the cutoff $C$ for $\alpha_s(Q^2)=0.25$ and three values of $x$: below, at and above the Landau pole.
• Figure 2: Position of the leading--order Landau pole eq. (\ref{['polepos']}) as a function of $\alpha_s(Q^2)$.
• Figure 3: Various determination of the $x$--space resummed result for $\alpha_s(Q^2)=0.25$. LLx denotes the leading $\ln(1-x)$ result of eq. (\ref{['PLL']}), while B, MP and pert denote three different determinations of the divergent leading $\ln N$ series eq. (\ref{['PasymptLL']}), respectively through Borel summation eq. (\ref{['pbreg']}) with $C=1$, the minimal prescription eq. (\ref{['PMP']}) and the asymptotic truncation of the perturbative expansion at $K_0$ eq. (\ref{['astrunc']}). The large--$x$ (constant) leading order result eq. (\ref{['lo']}) is also shown for comparison.