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The NNLO soft function for the pair invariant mass distribution of boosted top quarks

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Abstract

At high values of the pair invariant mass the differential cross section for top-quark pair production at hadron colliders factorizes into soft, hard, and fragmentation functions. In this paper we calculate the next-to-next-to-leading-order (NNLO) corrections to the soft function appearing in this factorization formula, thus providing the final piece needed to evaluate at NNLO the differential cross section in the virtual plus soft approximation in the large invariant-mass limit. Technically, this amounts to evaluating the vacuum expectation value of a soft Wilson loop operator built out of light-like Wilson lines for each of the four partons participating in the hard scattering process, with a certain constraint on the total energy of the soft radiation. Our result turns out to be surprisingly simple, because in the sum of all graphs the three and four parton contributions multiply color structures whose coefficients are governed by the non-abelian exponentiation theorem.

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Authors and Affiliations

  1. New York City College of Technology, 300 Jay Street, Brooklyn, NY, 11201, U.S.A.

    Andrea Ferroglia

  2. Institut für Physik (THEP), Johannes Gutenberg-Universität, D-55099, Mainz, Germany

    Ben D. Pecjak

  3. Institute for Theoretical Physics, University of Zürich, CH-8057, Zürich, Switzerland

    Li Lin Yang

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  1. Andrea Ferroglia
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  2. Ben D. Pecjak
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  3. Li Lin Yang
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Correspondence to Andrea Ferroglia.

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ArXiv ePrint: 1207.4798

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Ferroglia, A., Pecjak, B.D. & Yang, L.L. The NNLO soft function for the pair invariant mass distribution of boosted top quarks. J. High Energ. Phys. 2012, 180 (2012). https://doi.org/10.1007/JHEP10(2012)180

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