Towards Deriving Higgs Lagrangian from Gauge Theories

TL;DR

This paper proposes a novel approach to derive the Higgs Lagrangian from gauge theories by extending them supersymmetrically and analyzing the emergence of the Higgs field as a composite auxiliary field, including its dynamics and potential issues.

Contribution

It introduces a supersymmetric extension of gauge theories to identify the composite Higgs field and explores the emergence of its kinetic term through non-perturbative supersymmetry breaking mechanisms.

Findings

Kinetic term for the composite Higgs field emerges at one-loop level.

The Higgs potential remains unbounded due to the chosen Kähler potential.

Spontaneous chiral symmetry breaking gives mass to composite fermions.

Abstract

A new method of deriving the Higgs Lagrangian from vector-like gauge theories is explored. After performing a supersymmetric extension of gauge theories we identify the auxiliary field associated with the "meson" superfield, in the low energy effective theory, as the composite Higgs field. The auxiliary field, at tree level, has a "negative squared mass". By computing the one-loop effective action in the low energy effective theory, we show that a kinetic term for the auxiliary field emerges when an explicit non-perturbative mechanism for supersymmetry breaking is introduced. We find that, due to the naive choice of the Kaehler potential, the Higgs potential remains unbounded from the below. A possible scenario for solving this problem is presented. It is also shown that once chiral symmetry is spontaneously broken via a non-zero vacuum expectation value of the Higgs field, the low energy composite fermion field acquires a mass and decouples, while in the supersymmetric limit it was kept massless by the 't Hooft anomaly matching conditions.