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arXiv · hep-ph/9908362

Two-loop renormalization of the effective field theory of a static quark

D. J. Broadhurst·A. G. Grozin
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Abstract

We give a recurrence relation for two-loop integrals encountered in the effective field theory of an infinitely heavy quark, Q, interacting with gluons and Nl massless quarks, q, from which we obtain exact two-loop results, in any dimension and covariant gauge, for the propagator of Q and the vertex function of the heavy-light current J = Q Gamma q, at zero q momentum. The anomalous dimension of the Q field agrees with the recent result of Broadhurst, Gray and Schilcher. The anomalous dimension of the current is gamma_J = d log Z_J / d log mu = - alpha_s/pi (1 + (127 + 56 zeta(2) - 10 Nl)/72) alpha_s/pi + O(alpha_s^2)) which gives the new two-loop correction to the result of Voloshin and Shifman.

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D. J. Broadhurst, A. G. Grozin. 1999-08-16. Two-loop renormalization of the effective field theory of a static quark. https://doi.org/10.1016/0370-2693(91)90532-u

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