Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-04-21
Int.J.Mod.Phys. A13 (1998) 3929-3952
Physics
High Energy Physics
High Energy Physics - Phenomenology
26 pages, RevTeX, 10 postscript figures
Scientific paper
10.1142/S0217751X98001840
We analyze the heavy quark bound state spectrum using an order-dependent conformal mapping to re-sum the perturbative expansion for current correlators. The procedure consists of two main steps. Firstly, the Borel plane structure of the truncated perturbative expression is modified to ensure consistency with the operator product expansion. This is analogous to a resummation of infrared renormalon chains. Secondly, this perturbative expansion is conformally mapped to a new series with improved convergence properties. This approach may be shown to induce power corrections consistent with existing condensates, and the resulting expansion may be ordered in powers of an infrared-analytic effective coupling. The technique is then applied to $c\bar{c}$ and $b\bar{b}$ sum rules without any explicit introduction of vacuum condensate parameters. Ground state masses for the vector, axial--vector, and $A'$ channels are well reproduced, while results for the scalar--pseudoscalar mass splitting are less impressive.
Jones Hugh F.
Ritz Adam
Solovtsov Igor L.
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