Color suppressed contributions to the decay modes $B_{d,s} \to D_{s,d} D_{s,d} $ , $B_{d,s} \to D_{s,d} D^*_{s,d}$ , and $B_{d,s} \to D^*_{s,d} D^*_{s,d} $

Abstract

The amplitudes for decays of the typehave relatively small factorizable contributions through the annihilation mechanism. The dominant contributions to the decay amplitudes arise from chiral loop contributions and tree level amplitudes which can be obtained in terms of soft gluon emissions forming a gluon condensate. We predict that the branching ratios for the processesB. We obtain branching ratios for two D * 's in the final state of order two times bigger.

Isgur-Wise function within a modified heavy-light chiral quark model

“…As the slope of the IW function is steeper than the one used in, say, Ref. [18], the partial amplitudes for B → DD depending on the IW function, might be overestimated there. This will then have consequences for the size of the overall amplitude.…”

“…Some versions of quark models [3,4,7] gave a slope ξ ′ (1) ≃ −0.4 to −0.3, which is not in agreement with general theoretical expectations expressed in Bjorken [12] and Uraltsev [13] sum rules which together imply −ξ ′ (1) ≥ 3/4. Also, a combined fit [14] to results of experimental measurements of B → D * lν decays gives −ξ ′ (1) = 1.16 ± 0.05, and, although dispersion of experimental results is large leading to a small confidence level of this fit (≈ 1%), it seems reasonable to assume that absolute value of the slope cannot be significantly smaller than 1. In this paper we propose a modified version of the model in [7], which has a particular feature of explicit inclusion of the gluon condensate effects, enabling consistent estimation of non-factorizable amplitudes [15,16,17,18,19], and we demonstrate that this model gives a satisfactory description of the IW function slope.…”

Form factors for semileptonicDdecays

“…The LEET form factors ζ and ζ ⊥ , together with data for the D → π and D → ρ transitions, will determine the coupling constants G A and G V , which may be used in the calculation of nonfactorizable (color suppressed) nonleptonic D-meson decays, in the same manner as has previously been done for K → ππ [39,51], D → K 0K0 [52], B → DD [53,54], B → Dπ [40], and B → π 0 π 0 [41]. Then nonleptonic decay amplitudes can be written in terms of the LEET form factors ζ i , both for the factorized and the color-suppressed cases.…”

Color suppressed contribution toB¯d0→π0π0

“…The LEET form factors ζ and ζ ⊥ , together with data for the D → π and D → ρ transitions, will determine the coupling constants G A and G V , which may be used in the calculation of nonfactorizable (color suppressed) nonleptonic D-meson decays, in the same manner as has previously been done for K → ππ [39,51], D → K 0K0 [52], B → DD [53,54], B → Dπ [40], and B → π 0 π 0 [41]. Then nonleptonic decay amplitudes can be written in terms of the LEET form factors ζ i , both for the factorized and the color-suppressed cases.…”