[Paper Review] Towards a Maximal Mass Model

V. G. Kadyshevsky, M. D. Mateev+2 more|arXiv (Cornell University)|Aug 30, 2007

Quantum and Classical Electrodynamics21 citations

TL;DR

This paper proposes the Maximal Mass Model, a generalization of the Standard Model that introduces a fundamental upper limit $ M $ on particle masses via de Sitter geometry in 4-momentum space. By formulating quantum fields on de Sitter p-space, all particles satisfy a 5D Klein-Gordon or Dirac equation with mass $ M $, leading to new geometric chirality, exotic fermions, and novel Higgs-mediated interactions, with potential implications for dark matter and high-energy physics beyond the SM.

ABSTRACT

We investigate the possibility to construct a generalization of the Standard Model, which we call the Maximal Mass Model because it contains a limiting mass $M$ for its fundamental constituents. The parameter $M$ is considered as a new universal physical constant of Nature and therefore is called the fundamental mass. It is introduced in a purely geometrical way, like the velocity of light as a maximal velocity in the special relativity. If one chooses the Euclidean formulation of quantum field theory, the adequate realization of the limiting mass hypothesis is reduced to the choice of the de Sitter geometry as the geometry of the 4-momentum space. All fields, defined in de Sitter p-space in configurational space obey five dimensional Klein-Gordon type equation with fundamental mass $M$ as a mass parameter. The role of dynamical field variables is played by the Cauchy initial conditions given at $x_5 = 0$, guarantying the locality and gauge invariance principles. The corresponding to the geometrical requirements formulation of the theory of scalar, vector and spinor fields is considered in some detail. On a simple example it is demonstrated that the spontaneously symmetry breaking mechanism leads to renormalization of the fundamental mass $M$. A new geometrical concept of the chirality of the fermion fields is introduced. It would be responsible for new measurable effects at high energies $E \geq M$. Interaction terms of a new type, due to the existence of the Higgs boson are revealed. The most intriguing prediction of the new approach is the possible existence of exotic fermions with no analogues in the SM, which may be candidate for dark matter constituents.

Motivation & Objective

• To generalize the Standard Model by introducing a universal maximal mass $ M $ as a new fundamental constant of nature.
• To reformulate quantum field theory using de Sitter geometry in 4-momentum space to enforce the mass limit $ m \leq M $.
• To preserve locality, gauge invariance, and renormalizability while redefining chirality and field dynamics via Cauchy initial conditions on $ x_5 = 0 $.
• To explore the implications of the mass cutoff for spontaneous symmetry breaking, Higgs mechanism, and the emergence of new particles.
• To investigate whether the observed parity violation in weak interactions could stem from the de Sitter structure of momentum space.

Proposed method

• Realize the maximal mass hypothesis geometrically by adopting de Sitter space as the 4-momentum space, replacing Minkowski space.
• Define all fields (scalar, vector, spinor) as solutions to 5D Klein-Gordon or Dirac equations in de Sitter p-space with mass parameter $ M $.
• Implement dynamics through Cauchy initial data on the hypersurface $ x_5 = 0 $, ensuring locality and gauge invariance.
• Introduce a new geometric chirality concept via $ \gamma^5 $-dependent mass terms in the Dirac action, differing from the SM’s chiral projection.
• Couple fermions to the Higgs doublet using covariant derivatives and Higgs insertion, leading to new interaction terms absent in the SM.
• Use the Higgs mechanism to dynamically generate masses and study renormalization of $ M $, showing $ M $ can be shifted by symmetry breaking.

Experimental results

Research questions

• RQ1 How can a fundamental upper bound on particle mass $ M $ be consistently incorporated into local quantum field theory without breaking gauge invariance or locality?
• RQ2 What is the geometric origin of chirality in fermion fields under the maximal mass hypothesis, and how does it differ from the SM’s definition?
• RQ3 What novel interaction terms arise from the coupling of fermions to the Higgs field in the new model, and how do they differ from the SM’s Yukawa interactions?
• RQ4 Can the spontaneous symmetry breaking mechanism in this model lead to a renormalization of the fundamental mass $ M $, and if so, how?
• RQ5 Do the new field equations in de Sitter momentum space predict the existence of exotic fermions with no SM analogues, and could they be dark matter candidates?

Key findings

• The Maximal Mass Model realizes the mass limit $ m \leq M $ through de Sitter geometry in 4-momentum space, with $ M $ as a new universal physical constant.
• All fields—scalar, vector, and spinor—obey a 5D Klein-Gordon or Dirac equation with $ M $ as the mass parameter, ensuring the mass cutoff by construction.
• The model introduces a new geometric chirality defined via $ \gamma^5 $-dependent mass terms, which differs fundamentally from the SM’s chiral projection and may explain parity violation.
• Spontaneous symmetry breaking via the Higgs mechanism leads to a renormalization of the fundamental mass $ M $, indicating $ M $ is not necessarily fixed by the Lagrangian.
• New interaction terms emerge between fermions and the Higgs boson due to the modified chirality and field dynamics, which are absent in the Standard Model.
• The model predicts the existence of exotic fermions—stable, massive, and with no SM counterparts—that could serve as dark matter candidates, especially at energies $ E \geq M $.