Family Gauge Boson Mass Estimated from $K^+ \rightarrow \pi^+ \nu \bar{\nu}$

TL;DR

This paper discusses how the rare decay $K^+ ightarrow \pi^+ u ar{ u}$ can be used to estimate the mass of a family gauge boson predicted by a U(3) model, with potential to reveal TeV scale new physics.

Contribution

It proposes a method to estimate the family gauge boson mass from future measurements of the $K^+ ightarrow \pi^+ u ar{ u}$ decay branching ratio within a specific theoretical framework.

Findings

Future lower measurements of the branching ratio could imply a family gauge boson mass of a few TeV.

The decay process is sensitive to new particles at the TeV scale.

Theoretical predictions align with potential experimental observations for estimating new particle masses.

Abstract

It is emphasized that a rare decay $K^+ \rightarrow \pi^+ \nu \bar{\nu}$ becomes promising in a future search for a new particle, because the theoretical treatment is well established and the value of the branching ratio $Br(K^+ \rightarrow \pi^+ \nu \bar{\nu})$ 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 $Br(K^+ \rightarrow \pi^+ \nu \bar{\nu})$ 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.