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Three-loop QCD matching of the flavor-changing scalar current involving the heavy charm and bottom quark
We compute the matching coefficient between the quantum chromodynamics (QCD)
and the non-relativistic QCD ( NRQCD) for the flavor-changing scalar current
involving the heavy charm and bottom quark, up to the three-loop order within
the NRQCD factorization. For the first time, we obtain the analytical
expressions for the three-loop renormalization constant
and the corresponding anomalous dimension for the
NRQCD scalar current with the two heavy bottom and charm quark. We present the
precise numerical results for those relevant coefficients
with an accuracy of about thirty digits. The three-loop QCD correction turns
out to be significantly large. The obtained matching coefficient
is helpful to analyze the threshold behaviours when
two different heavy quarks are close to each other and form the double heavy
mesons.Comment: The projector is update
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