The quark beam function at NNLL
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Author(s)
Tackmann, Frank
Waalewijn, Wouter Jonathan
Stewart, Iain W
Date Issued
September 2010
Journal
Journal of High Energy Physics
Publisher
Springer / SISSA
Citation
Stewart, Iain W., Frank J. Tackmann, and Wouter J. Waalewijn. “The quark beam function at NNLL.” Journal of High Energy Physics 2010.9 (2010) : n. pag. Copyright © 2010, SISSA, Trieste, Italy
Version
Author's final manuscript
Abstract
In hard collisions at a hadron collider the most appropriate description of the
initial state depends on what is measured in the final state. Parton distribution functions
(PDFs) evolved to the hard collision scale Q are appropriate for inclusive observables, but
not for measurements with a specific number of hard jets, leptons, and photons. Here the
incoming protons are probed and lose their identity to an incoming jet at a scale μB ≪ Q [mu subscript beta << Q],
and the initial state is described by universal beam functions. We discuss the field-theoretic
treatment of beam functions, and show that the beam function has the same RG evolution
as the jet function to all orders in perturbation theory. In contrast to PDF evolution, the
beam function evolution does not mix quarks and gluons and changes the virtuality of the
colliding parton at fixed momentum fraction. At μB [mu subscript beta], the incoming jet can be described
perturbatively, and we give a detailed derivation of the one-loop matching of the quark
beam function onto quark and gluon PDFs. We compute the associated NLO Wilson
coefficients and explicitly verify the cancellation of IR singularities. As an application,
we give an expression for the next-to-next-to-leading logarithmic order (NNLL) resummed
Drell-Yan beam thrust cross section.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Laboratory for Nuclear Science
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DOI of Published Version
https://doi.org/10.1007/JHEP09(2010)005
