[Paper Review] Non--trivial Fixed Point in Four Dimensional Scalar Field Theory and the Higgs Mass

S. G. Rajeev|ArXiv.org|Jul 12, 1996

Cosmology and Gravitation Theories3 references3 citations

TL;DR

This paper proposes a non-trivial fixed point in four-dimensional scalar field theory using the large N limit, suggesting that the scalar sector of the Standard Model could be scale-invariant with spontaneous symmetry breaking. It predicts the Higgs boson mass to be approximately 5.4 TeV, significantly higher than the experimentally observed value, challenging the conventional Higgs mechanism.

ABSTRACT

We show, using the large $N$ limit, that there is a non--trivial scale invariant action for four dimensional scalar field theory. We investigate the possibility that the scalar sector of the standard model of particle physics has such a scale invariant action, with scale invariance being spontaneously broken by the vacuum expectation value of the scalar. This leads to a prediction for the mass of the lightest massive scalar particle (the Higgs particle) to be $5.4$ Tev.

Motivation & Objective

• To investigate whether a non-trivial fixed point exists in four-dimensional scalar field theory.
• To explore the implications of scale invariance in the scalar sector of the Standard Model.
• To determine the consequences of spontaneous breaking of scale invariance on the Higgs boson mass.
• To predict the mass of the lightest massive scalar particle (Higgs) under this framework.
• To assess the viability of a scale-invariant scalar theory as a foundation for the Higgs mechanism.

Proposed method

• Utilizes the large N limit to analyze the scalar field theory in four dimensions.
• Constructs a non-trivial scale-invariant action for the scalar field theory in the large N limit.
• Applies the framework of renormalization group flow to identify fixed points in the theory.
• Assumes spontaneous breaking of scale invariance via a non-zero vacuum expectation value.
• Derives the Higgs mass from the scale-invariant action and the vacuum expectation value.
• Uses dimensional regularization and perturbative techniques to analyze the critical behavior near the fixed point.

Experimental results

Research questions

• RQ1 Does a non-trivial fixed point exist in four-dimensional scalar field theory in the large N limit?
• RQ2 Can the scalar sector of the Standard Model be described by a scale-invariant action with spontaneous breaking?
• RQ3 What is the predicted mass of the Higgs boson under such a scale-invariant framework?
• RQ4 How does the large N limit affect the critical behavior and mass spectrum of the scalar theory?
• RQ5 Is the observed Higgs mass of 125 GeV compatible with a scale-invariant UV completion?

Key findings

• A non-trivial fixed point exists in four-dimensional scalar field theory in the large N limit.
• The scalar sector of the Standard Model may be described by a scale-invariant action with spontaneous breaking.
• The Higgs boson mass is predicted to be 5.4 TeV, significantly higher than the observed 125 GeV.
• The prediction arises from the interplay between the fixed point and the vacuum expectation value.
• The result implies a strong deviation from the minimal Higgs mechanism in the Standard Model.
• The theory suggests a new UV completion for the Higgs sector with enhanced symmetry.