Alternative technique for Standard Model estimation of the rare kaon decay branchings left. {BR(K to pi nu bar nu )} right|_{SM}

We estimate $BR(K to pi nu bar nu )$ in the context of the Standard Model by fitting for λ _t≡V _tdV _ts ^* of the “kaon unitarity triangle” relation. To find the vertex of this triangle, we fit data from |? _K|, the CP-violating parameter describing K mixing, and a _ψ,K , the CP-violating asymmetry in B _d ⁰ → J/ψK ⁰ decays, and obtain the values $left. {BR(K to pi nu bar nu )} right|_{SM} = (7.07 pm 1.03) times 10^{ - 11} $ and $left. {BR(K_L^0 to pi ^0 nu bar nu )} right|_{SM} = (2.60 pm 0.52) times 10^{ - 11} $ . Our estimate is independent of the CKM matrix element V _cb and of the ratio of B-mixing frequencies ${{Delta m_{B_s } } mathord{left/ {vphantom {{Delta m_{B_s } } {Delta m_{B_d } }}} right. kern-0em} {Delta m_{B_d } }}$ . We also use the constraint estimation of λ _t with additional data from $Delta m_{B_d } $ and |V _ub|. This combined analysis slightly increases the precision of the rate estimation of $K^ + to pi ^ + nu bar nu $ and $K_L^0 to pi ^0 nu bar nu $ (by ?10 and ?20%, respectively). The measured value of $BR(K^ + to pi ^ + nu bar nu )$ can be compared both to this estimate and to predictions made from ${{Delta m_{B_s } } mathord{left/ {vphantom {{Delta m_{B_s } } {Delta m_{B_d } }}} right. kern-0em} {Delta m_{B_d } }}$ .