Recoil and Power Corrections in High-x_T Direct-Photon Production
George Sterman, Werner Vogelsang
TL;DR
The paper develops a self-consistent joint resummation framework for high-x_T direct-photon production that unifies threshold and transverse-momentum resummation while avoiding kinematic singularities. It disentangles perturbative recoil from nonperturbative power corrections, providing NNLL recoil terms and a parametric nonperturbative exponent tied to moments of the running coupling. The approach yields a resummed cross section that matches fixed-order results and reduces sensitivity to recoil at large x_T, with energy-dependent power corrections that diminish at collider energies. Phenomenological results indicate that nonperturbative effects are small at RHIC and Tevatron energies but can become relevant near the x_T → 1 edge, illustrating the practical impact of energy conservation in joint resummation.
Abstract
We study a class of nonperturbative corrections to single-inclusive photon cross sections at measured transverse momentum p_T, in the large-x_T limit. We develop an extension of the joint (threshold and transverse momentum) resummation formalism, appropriate for large x_T, in which there are no kinematic singularities associated with recoil, and for which matching to fixed order and to threshold resummation at next-to-leading logarithm (NLL) is straightforward. Beyond NLL, we find contributions that can be attributed to recoil from initial state radiation. Associated power corrections occur as inverse powers of p_T^2 and are identified from the infrared structure of integrals over the running coupling. They have significant energy dependence and decrease from typical fixed-target to collider energies. Energy conservation, which is incorporated into joint resummation, moderates the effects of perturbative recoil and power corrections for large x_T.