Origin of the $k_T$ smearing in direct photon production

We show that the Sudakov factor from the resummation of double logarithms $\ln(s/k_T^2)$ contained in the distribution functions is responsible for the $k_T$ smearing mechanism employed in the next-to-leading-order QCD ($\alpha\alpha_s^2$) calculations of direct photon production. $s$ is the center-of-mass energy, and $k_T$ the transverse momentum carried by a parton in a colliding hadron. This factor exhibits the appropriate $s$-dependent Gaussian width in $k_T$, such that our predictions are in good agreement with experimental data.