Branching ratio of rare decay $B^0(B_s)\to \gamma \nu \bar{\nu}$

Abstract

The three-body decay $B^0(B_s)\to \gamma\nu \bar{\nu}$ can occur via penguin and box diagrams in the standard model (SM). These channels are useful to determine the decay constants $f_B$ ($f_{B_s}$) and $B$ ($B_s$) meson wave function. Using the B meson wave function determined in hadronic $B (B_s)$ decays, we calculate and get the branching ratio of order $10^{-9}$ and $10^{-8}$ for $B^0$ and $B_s$ decay, respectively. They agree with previous calculations.