Analyticity and power corrections in hard-scattering hadronic functions

Abstract

Demanding the analyticity of hadronic observables (calculated in terms of power series of the running coupling) as a {\it whole}, we show that they are free of the Landau singularity. Employing resummation and dispersion-relation techniques, we compute in a unifying way power corrections to two different hard-scattering functions in perturbative QCD: the electromagnetic pion form factor to leading order and the inclusive cross section of the Drell-Yan process. In the second case, the leading nonperturbative power correction in $b{\Lambda }_{\mathrm{QCD}}$ gives rise to a Sudakov-like exponential factor in the impact parameter space which provides enhancement rather than suppression.

Comments: V1: 11 pages in RevTeX; 1 figure as EPS file; V2: typos in Eqs. (5) and (24) corrected; V3: Phys. Lett. B. 504 (2001) 225; V4: The following equations have been corrected: (2), (5), (14), (15), (21), (22), (27), (32), (33), (34); one equation added: new (28). Figure corrected. Conclusions unchanged