Joint two-dimensional resummation in q T and 0-jettiness at NNLL

Autor: Gillian Lustermans, Johannes K. L. Michel, Frank J. Tackmann, Wouter J. Waalewijn
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Journal of High Energy Physics, Vol 2019, Iss 3, Pp 1-59 (2019)
Druh dokumentu: article
ISSN: 1029-8479
DOI: 10.1007/JHEP03(2019)124
Popis: Abstract We consider Drell-Yan production pp → Z/γ ∗ → ℓ + ℓ − with the simultaneous measurement of the Z-boson transverse momentum q T and 0-jettiness T 0 $$ {\mathcal{T}}_0 $$ . Since both observables resolve the initial-state QCD radiation, the double-differential cross section in q T and T 0 $$ {\mathcal{T}}_0 $$ contains Sudakov double logarithms of both q T /Q and T 0 / Q $$ {\mathcal{T}}_0/Q $$ , where Q ∼ m Z is the dilepton invariant mass. We simultaneously resum the logarithms in q T and T 0 $$ {\mathcal{T}}_0 $$ to next-to-next-to-leading logarithmic order (NNLL) matched to next-to-leading fixed order (NLO). Our results provide the first genuinely two-dimensional analytic Sudakov resummation for initial-state radiation. Integrating the resummed double-differential spectrum with an appropriate scale choice over either T 0 $$ {\mathcal{T}}_0 $$ or q T recovers the corresponding single-differential resummation for the remaining variable. We discuss in detail the required effective field theory setups and their combination using two-dimensional resummation profile scales. We also introduce a new method to perform the q T resummation where the underlying resummation is carried out in impact-parameter space, but is consistently turned off depending on the momentum-space target value for q T . Our methods apply at any order and for any color-singlet production process, such that our results can be systematically extended when the relevant perturbative ingredients become available.
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