[Paper Review] Study of $T'$ Flavor Symmetry

Paul H. Frampton, Shinya Matsuzaki|ArXiv.org|Dec 10, 2007

Gamma-ray bursts and supernovae3 citations

TL;DR

This paper proposes an extension of the Standard Model gauge group by adding a global flavor symmetry $T'$, along with additional $Z_2$ factors, to achieve approximate tribimaximal neutrino mixing and derive novel relations between quark and lepton mixing parameters. The model predicts new mass bounds from flavor-changing neutral currents and provides a group-theory-based alternative to grand unification for connecting quark and lepton mixing patterns.

ABSTRACT

A systematic study of the flavor group $T^{'}$ is presented in terms of a specific model which extends the standard model symmetry to $[SU(3) imes SU(2) imes U(1)]_{(local)} imes [T^{'} imes Z_2 imes Z_2^{'} imes Z_2^{''}]_{(global)}$. In the model, approximate tribimaximal mixing occurs in the neutrino sector. There is also one new formula relating a quark mixing parameter to quark masses. Most exciting are new formulas relating lepton and quark mixing parameters of the type usually associated with grand unification but here relying only on the group structure of $T^{'}$. Flavor-changing neutral currents in the model lead to lower bounds on scalar masses.

Motivation & Objective

• To construct a flavor symmetry model that explains the observed tribimaximal mixing in neutrinos within a unified framework.
• To derive new analytical relations between quark and lepton mixing parameters without relying on grand unification.
• To establish constraints on scalar masses using flavor-changing neutral current processes.
• To explore the implications of the global symmetry group $T' \times Z_2 \times Z_2' \times Z_2''$ on fermion mixing patterns.

Proposed method

• Extend the Standard Model gauge group to $[SU(3) \times SU(2) \times U(1)]_{\text{local}} \times [T' \times Z_2 \times Z_2' \times Z_2'']_{\text{global}}$.
• Implement a specific Higgs sector that breaks the global flavor symmetry to produce mass matrices consistent with tribimaximal mixing in the neutrino sector.
• Derive a new formula connecting quark mixing parameters to quark masses using the $T'$ group structure.
• Use the group structure of $T'$ to relate lepton and quark mixing parameters in a way analogous to grand unification but without unification.
• Analyze flavor-changing neutral currents to derive lower bounds on scalar masses.

Experimental results

Research questions

• RQ1 How can the $T'$ flavor group be embedded in a global symmetry extension of the Standard Model to reproduce tribimaximal neutrino mixing?
• RQ2 What new analytical relations between quark and lepton mixing parameters emerge from the $T'$ group structure?
• RQ3 Can the model reproduce observed quark and lepton mixing patterns without invoking grand unification?
• RQ4 What are the phenomenological constraints on scalar masses from flavor-changing neutral current processes in this model?

Key findings

• The model realizes approximate tribimaximal mixing in the neutrino sector through the structure of the $T'$ flavor group.
• A new formula is derived that relates a quark mixing parameter directly to quark masses, independent of the Cabibbo-Kobayashi-Maskawa matrix.
• Novel relations are established between lepton and quark mixing parameters, resembling those in grand unified theories but based solely on the $T'$ group structure.
• Flavor-changing neutral current processes impose lower bounds on the masses of scalar particles in the model.