Higgs mass, superconnections, and the TeV-scale left-right symmetric model

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 -1 2 6 GeV Higgs boson. 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 noncommutative geometry, and the spontaneous breaking of the gauge symmetries. The implication is that spontaneous symmetry breaking could actually be geometric/quantum gravitational in nature. The nondecoupling 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.

Spectral Noncommutative Geometry Standard Model and all that

“…With the new field the mass of the Higgs is lowered, and made compatible with the experiment, at the price of the loss of predictive power because there is a new parameter which is loosely constrained. A detailed analysis of the phenomenology is beyond the scope of this review, but we signal that it will be similar to Pati-Salam, with input coming from NCG, and we refer to [38][39][40] for a specific analysis, and to [14][15][16][17][18] for a more general view.…”

Gravity and unification: a review

“…The Higgs field gets the interpretation of the component of the gauge field along the non-commutative direction. A similar idea is used in the approach pioneered by Neeman, where the Higgs field appears as a component of a superconnection, see [34] for a review, and [35] for a recent concrete scenario along these lines.…”

“…Substituting here the solution (23) gives the pure connection linearised action (26) with very little work. Indeed, the combination that appears in (35) evaluates to…”

A Scale at 10 MeV, Gravitational Topological Vacuum, and Large Extra Dimensions

“…4 See, for instance, Refs. [95][96][97][98][99][100][101][102][103][104][105][106][107] for various geometric approaches to the Standard Model and beyond. making them interact frequently enough to be in equilibrium at T ∼ 1 MeV.…”