Longitudinal structure function at small x: The effect of next-to-leading-order QCD corrections and heavy-flavor thresholds

The longitudinal structure function FL at small x is a very direct probe of the gluon distribution. Studies have shown that measurements at the DESY ep collider HERA can distinguish various possible theoretical small-x behaviors. Phenomenological analyses to date have used leading-order expressions for the structure function. We use the recent O(αs2) calculation of Kazakov et al. to extend the analysis to next-to-leading order. We also investigate the effect of the b-quark threshold on the longitudinal structure function. We show that both these effects are numerically under control, and therefore do not change the conclusion that there is indeed a very direct connection between FL and the gluon