Combining $Q_T$ and small-$x$ resummations

Abstract

We analyze transverse momentum ($Q_T$) resummation of a colorless final state, e.g. Higgs production in gluon fusion or the production of a lepton pair via the Drell-Yan mechanism, in the limit where the invariant mass of the final state is much less then the center-of-mass energy, i.e. $Q^2\ll s$. We show how the traditional resummation of logarithms of $Q_T/Q$ can be supplemented with the resummation of the leading logarithmic contributions at small $x=Q^2/s$ and we compute the necessary ingredients to perform such joint resummation.