Hf. Jones et al., CONFORMAL MAPPING, POWER CORRECTIONS, AND THE QCD BOUND-STATE-SPECTRUM, International journal of modern physics A, 13(22), 1998, pp. 3929-3952
We analyze the heavy quark bound state spectrum using an order-depende
nt conformal mapping to re-sum the perturbative expansion for current
correlators. The procedure consists of two main steps. Firstly, the Bo
rel plane structure of the truncated perturbative expression is modifi
ed to ensure consistency with the operator product expansion. This is
analogous to a resummation of infrared renormalon chains. Secondly, th
is perturbative expansion is conformally mapped to a new series with i
mproved convergence properties. This approach may be shown to induce p
ower corrections consistent with existing condensates, and the resulti
ng expansion may be ordered in powers of an infrared-analytic effectiv
e coupling. The technique is then applied to c (c) over bar and b (b)
over bar sum rules without any explicit introduction of vacuum condens
ate parameters. Ground state masses for the vector, axial-vector and A
' channels are well reproduced, while results for the scalar-pseudosca
lar mass splitting are less impressive.