[Paper Review] Mass Issues in Fundamental Interactions

Jean‐Marc Gérard|ArXiv.org|Nov 4, 2008

Noncommutative and Quantum Gravity Theories7 references3 citations

TL;DR

This paper explores the role of mass in fundamental interactions through non-abelian gauge theories and effective field models, linking mass generation to time-reversal violation and baryon asymmetry. It proposes that Yukawa couplings and QCD θ-term dynamics may explain fermion masses and the neutron electric dipole moment, with key predictions around 10⁻³⁰ e·cm.

ABSTRACT

Driven by the mass problem, we raise some issues of the fundamental interactions in terms of non trivial commutation relations implemented within toy theories.

Motivation & Objective

• To investigate how mass generation in strong and electroweak interactions arises from spontaneous symmetry breaking and confinement.
• To examine the connection between time-reversal violation and the origin of matter-antimatter asymmetry in the universe.
• To assess whether the neutron electric dipole moment (EDM) can serve as a probe of new physics beyond the Standard Model.
• To explore the geometric and dynamical role of mass in unifying gravity with other fundamental forces through effective field theories.
• To evaluate the implications of non-universal mass ratios in gravitational bound states for the Einstein equivalence principle.

Proposed method

• Uses a scalar-tensor toy model of gravity to simplify the geometric interpretation of non-abelian gauge invariance and equivalence principle.
• Applies effective chiral Lagrangians for QCD with two light flavors to analyze nucleon mass splitting and its implications for neutron EDM.
• Analyzes the QCD θ-term and CP-violating quark mass determinant as sources of T-violation, with transformation properties under C and P.
• Evaluates the interplay between the QCD θ-term and the CKM phase as dual sources of T-violation in the Standard Model.
• Estimates the neutron EDM using the relation between the quark mass spectrum and the CP-violating parameter J, assuming both sources have comparable magnitude.
• Considers the Higgs mechanism as a potential source of T-violation via Yukawa couplings, suggesting a possible fifth fundamental interaction.

Experimental results

Research questions

• RQ1 Can the observed proton-neutron mass splitting in QCD imply a non-zero neutron electric dipole moment due to T-violating interactions?
• RQ2 To what extent can the QCD θ-term and the CKM phase jointly account for the observed baryon asymmetry of the universe?
• RQ3 What is the predicted size of the neutron electric dipole moment if the QCD θ-term and quark mass determinant are of comparable magnitude?
• RQ4 How does the breakdown of gauge invariance in strong and weak interactions correlate with the emergence of time-reversal violation?
• RQ5 Can the Higgs boson’s Yukawa couplings be interpreted as a geometric or dynamical mechanism analogous to gravity, suggesting a deeper unification?

Key findings

• The neutron electric dipole moment is predicted to be approximately 10⁻³⁰ e·cm if the QCD θ-term and the CKM phase are of comparable magnitude.
• The magnitude of the QCD CP-violating parameter θ is estimated to be around 10⁻¹⁴ if the two independent sources of T-violation are of similar strength.
• The observed baryon asymmetry of the universe, (n_B - n_bar)/n_γ ≈ 6.1 × 10⁻¹⁰, requires a source of T-violation that the Standard Model may not fully supply.
• The Higgs mechanism, through Yukawa couplings, provides a potential source of T-violation that could be elevated to a fundamental interaction if the Higgs is elementary.
• The compactness factor s ≈ 10⁻²⁶ for a typical Earth-like body implies that current Eötvös-type experiments cannot detect deviations in gravitational binding energy’s contribution to inertial and gravitational mass.
• The paper concludes that a direct observation of the neutron EDM or non-baryonic dark matter could resolve fundamental issues related to the cosmological constant and CP violation in QCD.