W-exchange/Annihilation amplitudes in LCSR - $B_d^0 \to D_s^-K^+$ as an example
Abstract
Description
We evaluate the W-exchange diagram within the framework of light cone sum rules (LCSR), taking $B_d^0 \to D_s^-K^+$ as an example. This decay mode, though proceeding via the W-exchange diagram only and therefore expected to be highly suppressed, has the branching ratio $3.2 \times 10^{-5}$. We estimate the W-exchange amplitude within LCSR, including soft gluon corrections, to twist-3 accuracy. The calculation naturally brings out the features which suggest that such an amplitude is expected to be small in cases when both the final state mesons are light, without relying on any kind of an assumption. With minor changes, it is also possible to have a rough estimate of the exchange/annihilation type contributions to other processes like $B \to ππ,~πK, KK$. We find that though it appears as if the sum rule method yields a fair agreement with the observed value, a careful analysis of individual terms shows that the method, in its present form, is inadequate to capture the correct physical answer for the case of heavy final states.
Latex 13 pages including 2eps figures. Typos corrected, more analysis on independent terms and errors added and it is explicitly mentioned that in the present form the sum rule is inadequate for heavy final states. To appear in PLB
Latex 13 pages including 2eps figures. Typos corrected, more analysis on independent terms and errors added and it is explicitly mentioned that in the present form the sum rule is inadequate for heavy final states. To appear in PLB