Mass Generation, the Cosmological Constant Problem, Conformal Symmetry, and the Higgs Boson

Abstract

In 2013 the Nobel Prize in Physics was awarded to Francois Englert and Peter Higgs for their work in 1964 along with the late Robert Brout on the mass generation mechanism (the Higgs mechanism) in local gauge theories. This mechanism requires the existence of a massive scalar particle, the Higgs boson, and in 2012 the Higgs boson was finally discovered at the Large Hadron Collider after being sought for almost half a century. In this article we review the work that led to the discovery of the Higgs boson and discuss its implications. We approach the topic from the perspective of a dynamically generated Higgs boson that is a fermion-antifermion bound state rather than an elementary field that appears in an input Lagrangian. In particular, we emphasize the connection with the Barden-Cooper-Schrieffer theory of superconductivity. We identify the double-well Higgs potential not as a fundamental potential but as a mean-field effective Lagrangian with a dynamical Higgs boson being generated through a residual interaction that accompanies the mean-field Lagrangian. We discuss what we believe to be the key challenge raised by the discovery of the Higgs boson, namely determining whether it is elementary or composite, and through study of a conformal invariant field theory model as realized with critical scaling and anomalous dimensions, suggest that the width of the Higgs boson might serve as a suitable diagnostic for discriminating between an elementary Higgs boson and a composite one. We show that the contribution to the cosmological constant due to a composite Higgs boson is more tractable and under control than the contribution due to an elementary Higgs boson, and is potentially completely under control if there is an underlying conformal symmetry not just in a critical scaling matter sector, but equally in the gravity sector to which the matter sector couples.

84 pages, 21 figures. Updated, includes discussion of renormalizability of four-fermion interaction. Review article, prepared for Progress in Particle and Nuclear Physics

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• Lorentz invariance and the zero-point stress-energy tensor
• Conformal Symmetry in Field Theory and in Quantum Gravity
• Unitarity of loop diagrams for the ghost-like $1/(k^2-M_1^2)-1/(k^2-M_2^2)$ propagator
• Exploring non-singular black holes in gravitational perturbations
• Ultraviolet-complete quantum field theories with fractional operators
• Dynamical Majorana Neutrino Masses and Axions II: Inclusion of Axial Background and Anomaly Terms
• Ghost Problems from Pauli-Villars to Fourth-Order Quantum Gravity and their Resolution
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• Linear potentials in galaxy halos by Asymmetric Wormholes
• Introduction to Quantization of Conformal Gravity
• Cosmological perturbations in conformal gravity II
• Is dark matter fact or fantasy? -- clues from the data
• Exact solution to perturbative conformal cosmology in the recombination era
• Conformally-rescaled Schwarzschild metrics do not predict flat galaxy rotation curves
• Three-dimensional and four-dimensional scalar, vector, tensor cosmological fluctuations and the cosmological decomposition theorem
• Dark side of Weyl gravity
• Critique of the use of geodesics in astrophysics and cosmology
• The Pauli sum rules imply BSM physics
• Anomalous Dimensions and the Renormalizability of the Four-Fermion Interaction
• Exact solution to perturbative conformal cosmology from recombination until the current era
• Is the Cosmological Constant Problem Properly Posed?
• Cosmological Fluctuations on the Light Cone
• Structure of conformal gravity in the presence of a scale breaking scalar field
• How to understand the Structure of Beta Functions in Six-derivative Quantum Gravity?
• Imprint of galactic rotation curves and metric fluctuations on the recombination era anisotropy
• Test of conformal gravity as an alternative to dark matter from the observations of elliptical galaxies
• Cosmic Strings in Conformal Gravity
• Probing the conformal invariance around the nonsingular static spherical black holes with waves
• Infrared behavior of Weyl Gravity
• Running of the Number of Degrees of Freedom in Quantum Conformal Gravity
• A New Property of the Electromagnetic/Yang-Mills-Conformal Gravity System in Spherical Symmetry
• Hawking radiation from nonrotating singularity-free black holes in conformal gravity
• Nonconformally Ricci-flat instantons in Conformal Gravity with and without nonlinear matter fields
• Statistical Strong Lensing as a Test of Conformal Gravity