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Fully-unintegrated parton distribution and fragmentation functions at perturbative k⊥

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Abstract

We define and study the properties of generalized beam functions (BFs) and fragmenting jet functions (FJFs), which are fully-unintegrated parton distribution functions (PDFs) and fragmentation functions (FFs) for perturbative k ⊥. We calculate at one loop the coefficients for matching them onto standard PDFs and FFs, correcting previous results for the BFs in the literature. Technical subtleties when measuring transverse momentum in dimensional regularization are clarified, and this enables us to renormalize in momentum space. Generalized BFs describe the distribution in the full four-momentum k μ of a colliding parton taken out of an initial-state hadron, and therefore characterize the collinear initial-state radiation. We illustrate their importance through a factorization theorem for pp → ℓ+ℓ− + 0 jets, where the transverse momentum of the lepton pair is measured. Generalized FJFs are relevant for the analysis of semi-inclusive processes where the full momentum of a hadron, fragmenting from a jet with constrained invariant mass, is measured. Their significance is shown for the example of e + e − → dijet + h, where the perpendicular momentum of the fragmenting hadron with respect to the thrust axis is measured.

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Authors and Affiliations

  1. Department of Physics, Carnegie Mellon University, Pittsburgh, PA, 15213, U.S.A

    Ambar Jain

  2. Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, CH-3012, Bern, Switzerland

    Massimiliano Procura

  3. Department of Physics, University of California at San Diego, La Jolla, CA, 92093, U.S.A

    Wouter J. Waalewijn

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  1. Ambar Jain
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  2. Massimiliano Procura
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  3. Wouter J. Waalewijn
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Correspondence to Massimiliano Procura.

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Jain, A., Procura, M. & Waalewijn, W.J. Fully-unintegrated parton distribution and fragmentation functions at perturbative k⊥ . J. High Energ. Phys. 2012, 132 (2012). https://doi.org/10.1007/JHEP04(2012)132

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