Electroweak gauge-boson production at small q _T : Infrared safety from the collinear anomaly

Abstract

Using methods from effective field theory, we develop a novel, systematic framework for the calculation of the cross sections for electroweak gauge-boson production at small and very small transverse momentum q _T , in which large logarithms of the scale ratio M _V /q _T are resummed to all orders. These cross sections receive logarithmically enhanced corrections from two sources: the running of the hard matching coefficient and the collinear factorization anomaly. The anomaly leads to the dynamical generation of a non-perturbative scale ${q_* } \sim {M_V}{e^{ - {\text{const}}/{\alpha_s}\left( {{M_V}} \right)}}$, which protects the processes from receiving large long-distance hadronic contributions. Expanding the cross sections in either α _s or q _T generates strongly divergent series, which must be resummed. As a by-product, we obtain an explicit non-perturbative expression for the intercept of the cross sections at q _T  = 0, including the normalization and first-order α _s (q _∗ ) correction. We perform a detailed numerical comparison of our predictions with the available data on the transverse-momentum distribution in Z-boson production at the Tevatron and LHC.