Subleading power rapidity divergences and power corrections for qT

• DOI: 10.1007/jhep04(2019)123
• Publication Date: 2019-04-22T08:03:02Z
• Authors: Markus A. Ebert; Ian Moult; Iain W. Stewart; Frank J. Tackmann; Gherardo Vita; Hua Xing Zhu
• Keywords: Nuclear Theory; FOS: Physical sciences; parton: distribution function; QC770-798; transverse momentum; 530; 01 natural sciences; Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph); Nuclear and particle physics. Atomic energy. Radioactivity; Perturbative QCD; 0103 physical sciences; heavy quark; structure; info:eu-repo/classification/ddc/530; electroweak interaction; Effective Field Theories; suppression; High Energy Physics - Phenomenology; rapidity; resummation; soft collinear effective theory; gauge boson: mass; Resummation

AbstractA number of important observables exhibit logarithms in their perturbative description that are induced by emissions at widely separated rapidities. These include transverse-momentum (qT) logarithms, logarithms involving heavy-quark or electroweak gauge boson masses, and small-xlogarithms. In this paper, we initiate the study of rapidity logarithms, and the associated rapidity divergences, at subleading order in the power expansion. This is accomplished using the soft collinear effective theory (SCET). We discuss the structure of subleading-power rapidity divergences and how to consistently regulate them. We introduce a new pure rapidity regulator and a corresponding$$ \overline{\mathrm{MS}} $$MS¯-like scheme, which handles rapidity divergences while maintaining the homogeneity of the power expansion. We find that power-law rapidity divergences appear at subleading power, which give rise to derivatives of parton distribution functions. As a concrete example, we consider theqTspectrum for color-singlet production, for which we compute the completeqT2/Q2suppressed power corrections at$$ \mathcal{O}\left({\alpha}_s\right) $$Oαs, including both logarithmic and nonlogarithmic terms. Our results also represent an important first step towards carrying out a resummation of subleading-power rapidity logarithms.