Second Order Standard Model

TL;DR

This paper introduces a second order formulation of the Standard Model's fermionic Lagrangian, integrating out certain spinors, resulting in a compact, non-polynomial form that parallels the structure of General Relativity.

Contribution

It presents a novel second order Lagrangian for the Standard Model, unifying fermionic fields and Higgs interactions in a compact, non-polynomial framework.

Findings

Second order Lagrangian derived from first order form

Higgs field enters non-polynomially, akin to gravity

Proposes SU(2)xSU(4) unification in this formalism

Abstract

We rewrite the Lagrangian of the fermionic sector of the Standard Model in a novel compact form. The new Lagrangian is second order in derivatives, and is obtained from the usual first order Lagrangian by integrating out all primed (or dotted) 2-component spinors. The Higgs field enters the new Lagrangian non-polynomially, very much like the metric enters the Einstein-Hilbert Lagrangian of General Relativity. We also discuss unification in the second order formalism, and describe a natural in this framework SU(2)xSU(4) unified theory.