Family Gauge Boson Production at the LHC

TL;DR

This paper investigates the production of family gauge bosons at the LHC within a specific $U(3)$ family gauge model, analyzing cross sections and potential to confirm or rule out the model through experimental measurements.

Contribution

It introduces a $U(3)$ family gauge model with twisted family number assignment and calculates production cross sections at LHC energies, linking measurements to model validation.

Findings

Calculated cross sections for $A_1^{ ext{1}}$ production at 14 TeV and 100 TeV.

Discussed how dielectron production can determine quark mixing matrices.

Provided predictions to confirm or exclude the model based on LHC data.

Abstract

Family gauge boson production at the LHC is investigated according to a $U(3)$ family gauge model with twisted family number assignment. In the model we study, a family gauge boson with the lowest mass, $A_1^{\ 1}$, interacts only with the first generation leptons and the third generation quarks. (The family numbers are assigned, for example, as $(e_1, e_2, e_3)= (e^-, \mu^-, \tau^-)$ and $(d_1, d_2, d_3)=(b, d, s) $[or $(d_1, d_2, d_3)=(b, s, d)$]). In the model, the family gauge coupling constant is fixed by relating to the electroweak gauge coupling constant. Thus measurements of production cross sections and branching ratios of $A_1^{\ 1}$ clearly confirm or rule out the model. We calculate the cross sections of inclusive $A_1^{\ 1}$ production and $b \bar{b} \, (t \bar{t})$ associated $A_1^{\ 1}$ production at $\sqrt{s} = 14~\text{TeV}$ and $100~\text{TeV}$. With the dielectron production cross section, we discuss the determination of diagonalizing matrix of quark mass matrix, $U_{u}$ and $U_{d}$, respectively.