Family Gauge Boson Mass Estimated from $K^+ \rightarrow π^+ ν\barν$

It is emphasized that a rare decay $K^+ \rightarrow π^+ ν\barν$ becomes promising in a future search for a new particle, because the theoretical treatment is well established and the value of the branching ratio $Br(K^+ \rightarrow π^+ ν\barν)$ is sensitive to a search for a new particle with a TeV scale mass. As an example, according to a U(3) family gauge boson model which predicts the lowest family gauge boson with a few TeV mass $M_{11}$, the branching ratio $Br(K^+ \rightarrow π^+ ν\barν)$ is discussed. If we can obtain, in future, a slightly lower value $Br^{obs} \sim 0.9 \times 10^{-10}$ compared with the present observed value $Br^{obs}=(1.7\pm 1.1)\times 10^{-10}$, we can conclude $M_{11} \sim$ a few TeV.

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