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Plane-wave, coordinate-space, and moment techniques in the operator-product expansion: Equivalence, improved methods, and the heavy quark expansion

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Zeitschrift für Physik C Particles and Fields

Abstract

We compare plane-wave, coordinate-space and moment methods for evaluating operator-product expansion (OPE) coefficients of the light-quark and gluon condensates. Equivalence of these methods for quark condensate contributions is proven to all orders in the quark mass parameterm. The three methods are also shown to yield equivalent gluon condensate contributions to two-current correlation functions, regardless of the gauge chosen for external gluon fields in the coordinate space approach. An improved method for evaluating quarkcondensate OPE coefficients is presented for several (two-current) correlation functions. Gauge-dependent Green functions are also discussed. It is shown that contradictory expressions for the gluon-condensate contribution to the quark propagator occurring from the plane-wave and coordinate-space approaches yield identical relations between the heavy-quark and gluon condensates, as anticipated from the gauge invariance of the heavy-quark expansion.

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Author notes

  1. M. R. Ahmady

    Present address: I.C.T.P., Miramare P.O. Box 586, I-34100, Trieste, Italy

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120, Heidelberg, Germany

    E. Bagan (Alexander von Humboldt Fellow) & V. Elias

  2. Grup de Física Teòrica, Department de Física, Universitat Autònoma de Barcelona, E-08193, Bellaterra, Spain

    E. Bagan (Alexander von Humboldt Fellow)

  3. Department of Applied Mathematics, University of Western Ontario, N6A 3K7, London, Ontario, Canada

    M. R. Ahmady

  4. Department of Physics and Saskatchewan Accelerator Lab, University of Saskatchewan, S7N 0W0, Saskatoon, Saskatchewan, Canada

    T. G. Steele

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  1. E. Bagan
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  3. V. Elias
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  4. T. G. Steele
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Bagan, E., Ahmady, M.R., Elias, V. et al. Plane-wave, coordinate-space, and moment techniques in the operator-product expansion: Equivalence, improved methods, and the heavy quark expansion. Z. Phys. C - Particles and Fields 61, 157–170 (1994). https://doi.org/10.1007/BF01641898

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  • DOI: https://doi.org/10.1007/BF01641898

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