Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2007-01-07
Prog.Theor.Phys.118:505-520,2007
Physics
High Energy Physics
High Energy Physics - Phenomenology
18 pages, 2 figures, Version to appear in Progress of Theoretical Physics
Scientific paper
10.1143/PTP.118.505
We study the physical origins of the $O(alpha_{s})$ and $O(alpha_{s}^{2})$ corrections to the $bar{c}-s$ current in the decay $b -> c bar{c} s$ in the threshold region $delta=(M_{b}-2m_{c})/2M_{b} << 1$. We obtain the corrections which are produced by the Coulomb force between the anti-charm and strange quarks. The Coulomb corrections $C_{F} pi^{2}$ at $O(alpha_{s})$ and $-C_{F}^{2} pi^{2} ln delta$ at $O(alpha_{s}^{2})$ account for 300% and 120% of the corresponding terms in the Abelian-type perturbative corrections respectively. The differences between the Coulomb and perturbative corrections imply that other corrections which have other physical origins exist. We also check that the Wilson coefficient for the anomalous dimension of the $bar{c}-s$ current reproduces the leading and the next-to-leading logarithmic terms in the perturbative corrections.
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