Nonstandard Origin of the Standard Electroweak Currents

TL;DR

This paper explores a nonstandard origin of the Standard Model electroweak currents, proposing a hypothesis involving the symplectic group $Sp(n/2)$ that leads to unique neutrino mass and anomaly properties.

Contribution

It introduces a novel gauge symmetry hypothesis with $Sp(n/2)$, explaining neutrino mass generation and anomaly cancellation differently from the Standard Model.

Findings

Only for n=6 does spontaneous violation occur with parity violation.

The see-saw mechanism yields three light and three heavy neutrinos.

Electromagnetic currents remain anomaly-free and independent of heavy mass physics.

Abstract

Implications are considered of the hypothesis that the symplectic group $Sp(n/2)$ is the spontaneously violated gauge group of n lepton flavors. Invariant Majorana masses are impossible in $Sp(n/2)$. For the local gauge symmetry $Sp(n/2)$ the dynamical spontaneous violation is only achievable for the number of flavors $n=6$ with simultaneous parity ($R,L-$symmetry) violation. The see-saw mechanism produces here three light and three heavy Dirac neutrinos. Majorana states are unavailable here. Neglecting heavy particles in the $R,L-$symmetric system of weak and electromagnetic interactions ($R,L-$independent values of isospins Tw and hypercharges $Y$ for leptons or quarks) leads to a theory with parity nonconservation and axial anomalies. Only weak left $(L)$ and full $(R+L)$ electromagnetic currents do not have anomalies and remain independent of the physics of heavy masses. These currents are the ones of the Standard Model. The absence of anomalies merely in the combination of currents forming the electromagnetic one presents essential difference with the SM case, where the both, left $T_W$ and $Y$, currents are deprived of anomalies independently.