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In-medium operator product expansion for heavy-light-quark pseudoscalar mesons

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Abstract

The operator product expansion (OPE) for heavy-light-quark pseudoscalar mesons (D -mesons and B -mesons) in medium is determined, both for a moving meson with respect to the surrounding medium as well as for a meson at rest. First of all, the OPE is given in terms of normal-ordered operators up to mass dimension 5, and the mass of the heavy quark and the mass of the light quark are kept finite. The Wilson coefficients of such an expansion are infrared (IR) divergent in the limit of a vanishing light-quark mass. A consistent separation of scales necessitates an OPE in terms of non-normal-ordered operators, which implies operator mixing, where the IR-divergences are absorbed into the operators. It is shown that the Wilson coefficients of such an expansion are IR-stable, and the limit of a vanishing light-quark mass is perfomed. Details of the major steps for the calculation of the Wilson coefficients are presented. By a comparison with previous results obtained by other theoretical groups we have found serious disagreements.

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Authors and Affiliations

  1. Institut für Planetare Geodäsie, Lohrmann-Observatorium, TU Dresden, D-01062, Dresden, Germany

    Sven Zschocke

  2. Dept. of Physics and Technology, University of Bergen, Allegaten 55, N-5007, Bergen, Norway

    Sven Zschocke

  3. Helmholtz-Zentrum Dresden-Rossendorf, PF 510119, D-01314, Dresden, Germany

    Thomas Hilger & Burkhard Kämpfer

  4. Institut für Theoretische Physik, TU Dresden, D-01062, Dresden, Germany

    Thomas Hilger & Burkhard Kämpfer

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  1. Sven Zschocke
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  2. Thomas Hilger
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  3. Burkhard Kämpfer
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Communicated by J. Bijnens

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Zschocke, S., Hilger, T. & Kämpfer, B. In-medium operator product expansion for heavy-light-quark pseudoscalar mesons. Eur. Phys. J. A 47, 151 (2011). https://doi.org/10.1140/epja/i2011-11151-y

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