A DETERMINATION OF THE CKM-MATRIX ELEMENT RATIO VERTICAL-BAR-V(TS)VERTICAL-BAR/VERTICAL-BAR-V(CB)VERTICAL-BAR FROM THE RARE B-DECAYS B-]K-ASTERISK+GAMMA AND B-]X(S)+GAMMA

Implications of the recent CLEO observation [1] of the rare decay mode B --> K* + gamma having a combined branching ratio BR(B --> K* + gamma) = (4.5 +/- 1.5 +/- 0.9) x 10(-5) and an improved upper limit on the inclusive branching ratio BR(B --> X(s) + gamma) < 5.4 x 10(-4) (95% C.L.) [2] are discussed in the context of the Standard Model (SM). Using the unitarity of the CKM-matrix and taking into account QCD radiative corrections in the decay rate and the inclusive photon energy spectrum we obtain an improved upper limit on the inclusive branching ratio BR(B --> X(s) + gamma) < 4.8 x 10(-4) (95% C.L.). This can be used to constrain possible non-SM contributions to the inclusive branching ratio, giving BR(B --> X(s) + gamma) (non-SM) < 3.0 x 10(-4) for m(t) greater-than-or-equal-to 108 GeV. Within the SM, we show that the resulting experimental upper limit can be interpreted as a corresponding limit on the CKM-matrix element ratio yielding \V(ts\/\V(cb)\ < 1.67, with the top quark mass assumed to weigh less than 200 GeV. We calculate the relative exclusive to inclusive branching ratio R(K*/X(s)) = GAMMA(B --> K* + gamma)/GAMMA(B --> X(s) + gamma), based on the inclusive hadronic invariant mass distribution in B --> X(s) + gamma. Estimating the K*-contribution from this distribution in the threshold region (m(K) + M(pi)) less-than-or-equal-to m(Xs) less-than-or-equal-to 0.97 GeV and using experimental measurements from the semileptonic D-decays D --> K + pi + lv(l) in the same mass interval, we obtain R (K*/X(s)) = 0.13 +/- 0.03. This enables us to put a lower bound on the ratio \V(ts)\/\V(cb\ from the 95% C.L. lower limit on the branching ratio BR(B --> K* + gamma) > 1.6 x 10(-5)[1, 2]. Combining the exclusive and inclusive decay rates, we determine 0.50 less-than-or-equal-to \V(ts)\/\V(cb\ less-than-or-equal-to 1.67 (at 95% C.L.).