Phenomenology of Harmless Family Gauge Bosons to $K^0$-$\bar{K}^0$ Mixing

TL;DR

This paper proposes a U(3) family gauge boson model where certain mass relations make these bosons harmless to meson mixing constraints, allowing for potentially observable effects at TeV scales.

Contribution

It introduces a specific mass relation in a U(3) family gauge boson model that avoids constraints from meson mixing, enabling lower energy scale predictions.

Findings

Gauge bosons are harmless to meson mixings under specific mass relations.

Inverted mass hierarchy allows for TeV-scale family gauge bosons.

Potential for observable signatures at collider energies.

Abstract

When we try to consider family gauge bosons with a lower energy scale, a major obstacle is constraints from the observed $P^0$-$\bar{P}^0$ mixings ($P^0=K^0, D^0, B^0,B^0_s$). Against such a conventional view, we point out that, in a U(3) family gauge boson model, the bosons are harmless to any $P^0$-$\bar{P}^0$ mixings independently of explicit values of the family mixings, if masses $M_{ij}$ of the gauge bosons $A_i^{\ j}$ ($i,j$ are family indexes) satisfy a relation $2/M_{ij}^2=1/M_{ii}^2 +1/M_{jj}^2$. If such the case can be realized together with an inverted mass hierarchy $M_{33}^2 \ll M_{22}^2 \ll M_{11}^2$, we can consider family gauge bosons with a considerably lower scale, so that we can expect rich signs for family gauge bosons in a TeV scale.