A First Test of the Framed Standard Model against Experiment

TL;DR

This paper tests the framed standard model (FSM), which extends the standard model by incorporating frame vectors, and demonstrates its ability to fit experimental data on fermion masses and mixings with high accuracy, providing insights into CP violation and mass hierarchies.

Contribution

The paper derives the 1-loop renormalization group equations for FSM and performs the first experimental fit of its parameters to fermion mass and mixing data.

Findings

Most fitted quantities match experimental data within 0.5%

The model naturally explains the CKM phase from QCD theta-angle

It accounts for the mass hierarchy, such as m_u < m_d despite heavy top quark

Abstract

The framed standard model (FSM) is obtained from the standard model by incorporating, as field variables, the frame vectors (vielbeins) in internal symmetry space. It gives the standard Higgs boson and 3 generations of quarks and leptons as immediate consequences. It gives moreover a fermion mass matrix of the form: $m = m_T \alpha \alpha^\dagger$, where $\alpha$ is a vector in generation space independent of the fermion species and rotating with changing scale, which has already been shown to lead, generically, to up-down mixing, neutrino oscillations and mass hierarchy. In this paper, pushing the FSM further, one first derives to 1-loop order the RGE for the rotation of $\alpha$, and then applies it to fit mass and mixing data as a first test of the model. With 7 real adjustable parameters, 18 measured quantities are fitted, most (12) to within experimental error or to better than 0.5 percent, and the rest (6) not far off. (A summary of this fit can be found in Table 2 in the text.) Two notable features, both generic to FSM, not just specific to the fit, are: (i) that a theta-angle of order unity in the instanton term in QCD would translate via rotation into a Kobayashi-Maskawa phase in the CKM matrix of about the observed magnitude ($J \sim 10^{-5}$), (ii) that it would come out correctly that $m_u<m_d$, despite the fact that $m_t \gg m_b, m_c \gg m_s$. Of the 18 quantities fitted, 12 are deemed independent in the usual formulation of the standard model. In fact, the fit gives a total of 17 independent parameters of the standard model, but 5 of these have not been measured by experiment.