English

Subleading Power Rapidity Divergences and Power Corrections for $q_T$

High Energy Physics - Phenomenology 2019-04-24 v3 Nuclear Theory

Abstract

A number of important observables exhibit logarithms in their perturbative description that are induced by emissions at widely separated rapidities. These include transverse-momentum (qTq_T) logarithms, logarithms involving heavy-quark or electroweak gauge boson masses, and small-xx logarithms. 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 MS\overline{\rm 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 the qTq_T spectrum for color-singlet production, for which we compute the complete qT2/Q2q_T^2/Q^2 suppressed power corrections at O(αs)\mathcal{O}(\alpha_s), including both logarithmic and nonlogarithmic terms. Our results also represent an important first step towards carrying out a resummation of subleading-power rapidity logarithms.

Keywords

Cite

@article{arxiv.1812.08189,
  title  = {Subleading Power Rapidity Divergences and Power Corrections for $q_T$},
  author = {Markus A. Ebert and Ian Moult and Iain W. Stewart and Frank J. Tackmann and Gherardo Vita and Hua Xing Zhu},
  journal= {arXiv preprint arXiv:1812.08189},
  year   = {2019}
}

Comments

40 pages + appendices, 3 figures; v2: TMD collaboration included in acknowledgement; v3: minor changes, journal version