Subleading power rapidity divergences and power corrections for q T
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Springer
Received: January 11, Revised: March 20, Accepted: April 9, Published: April 18,
2019 2019 2019 2019
Subleading power rapidity divergences and power corrections for qT
a
Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. b Berkeley Center for Theoretical Physics, University of California, Berkeley, CA 94720, U.S.A. c Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, U.S.A. d Theory Group, Deutsches Elektronen-Synchrotron (DESY), D-22607 Hamburg, Germany e Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] 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 (qT ) logarithms, logarithms involving heavy-quark or electroweak gauge boson masses, and small-x 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-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 qT spectrum for color-singlet production, for which we compute the complete qT2 /Q2 suppressed power corrections at O(αs ), 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: Effective Field Theories, Perturbative QCD, Resummation ArXiv ePrint: 1812.08189
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP04(2019)123
JHEP04(2019)123
Markus A. Ebert,a Ian Moult,b,c Iain W. Stewart,a Frank J. Tackmann,d Gherardo Vitaa and Hua Xing Zhue
Contents 1 Introduction
1 3 4 6 9 10 14
3 Power corrections for color-singlet qT spectra 3.1 Master formula for power corrections to next-to-leading power 3.1.1 General setup at NLO 3.1.2 Soft master formula for qT 3.1.3 Collinear master formula for qT 3.2 Derivation of the master formula in pure rapidity regularization 3.3 Next-to-leading power corrections at NLO 3.3.1 Gluon-fusion Higgs production 3.3.2 Drell-Yan production 3.4 Discussion 3.5 Numerical results
16 18 19 21 24 26 28 28 31 33 35
4 Conclusions
37
A NLO results for qT at leading power A.1 Soft function A.2 Beam function
39 39 40
B Higher-order plus distributions
41
C Derivation of the master formula for generic c
43
1
Introduction
Observables in qu
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