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

Abstract

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 |ɛ 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 $${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-\nulldelimiterspace} {\Delta m_{B_d } }}$$ . 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 $${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-\nulldelimiterspace} {\Delta m_{B_d } }}$$ .