On the Role of Charm in Decay of B-mesons to \eta ' K

In this letter we focus on the calculation of $f_{{\eta }^{\mathrm{\prime }}}^{(c)},$ the amplitude of the $(c\bar{c})\to (gluons)\to {\eta }^{{}^{\mathrm{\prime }}}$ transition, which provides the magnitude of the contribution of the Cabbibo favored $b \to \bar c c s$elementaryprocessto$B \to \eta ’ K$decay\mathrm{.}Itisfoundthat$f_{\eta '}^{©} = - 12.3\sim -18.4 MeV$onthescaleof$m_{c}.$ This number is in strong contradiction with the estimations of Halperin, Zhitnitsky and Shuryak, Zhitnitsky but almost in agreement with phenomenological analysis of Feldman et al., Petrov and the estimations of Ali et al.