The Higgs Mass, Superconnections and the TeV-scale Left-Right Symmetric Model

TL;DR

This paper explores a superconnection formalism for the Standard Model and its extension to a left-right symmetric model, predicting the Higgs mass and linking spontaneous symmetry breaking to modified spacetime geometry, with implications for TeV-scale physics and future experiments.

Contribution

It extends the superconnection formalism from su(2/1) to su(2/2), accommodating a realistic Higgs mass and connecting gauge symmetry breaking to non-commutative geometry and quantum gravity.

Findings

Superconnection formalism predicts a ~170 GeV Higgs in SM, which is inconsistent with experiment.

Extending to su(2/2) yields a Higgs mass of ~126 GeV, aligning with observations.

The model suggests a deep link between geometry, quantum gravity, and symmetry breaking.

Abstract

We discuss the physical implications of formulating the Standard Model (SM) in terms of the superconnection formalism involving the superalgebra su(2/1). In particular, we discuss the prediction of the Higgs mass according to the formalism and point out that it is ~170 GeV, in clear disagreement with experiment. To remedy this problem, we extend the formalism to the superalgebra su(2/2), which extends the SM to the left-right symmetric model (LRSM) and accommodates a ~126 GeV Higgs. Both the SM in the su(2/1) case and the LRSM in the su(2/2) case are argued to emerge at ~4 TeV from an underlying theory in which the spacetime geometry is modified by the addition of a discrete extra dimension. The formulation of the exterior derivative in this model space suggests a deep connection between the modified geometry, which can be described in the language of non-commutative geometry (NCG), and the spontaneous breaking of the gauge symmetries. The implication is that spontaneous symmetry breaking could actually be geometric/quantum gravitational in nature. The non-decoupling phenomenon seen in the Higgs sector can then be reinterpreted in a new light as due to the mixing of low energy (SM) physics and high energy physics associated with quantum gravity, such as string theory. The phenomenology of a TeV scale LRSM is also discussed, and we argue that some exciting discoveries may await us at the LHC, and other near-future experiments.