[Paper Review] Effects of Gauge Interactions on Fermion Masses in Models with Fermion Wavefunctions Separated in Higher Dimensions

S. Nussinov, R. Shrock|CERN Bulletin|Jan 30, 2001

Particle physics theoretical and experimental studies14 citations

TL;DR

This paper proposes that fermion mass hierarchies in higher-dimensional models arise not only from wavefunction localization but also from gauge interactions, which suppress Yukawa couplings based on fermion separation. It shows that these effects naturally explain the top quark's large mass, the hierarchy among quark and charged lepton masses, and the smallness of neutrino masses, all within a calculable, finite framework using a 5D effective field theory with localized fermions.

ABSTRACT

We consider models that generate hierarchies via the separation of fermion wavefunctions in higher-dimensional spaces. We calculate the effects of gauge interactions between fermions and show that these are important and could help to explain (i) why the heaviest known fermion is a charge 2/3 quark, rather than a charge -1/3 quark or a lepton, (ii) why this fermion has a mass $m_t$ comparable to the electroweak symmetry breaking scale $M_{ew}$, (iii) the patterns $m_t >> m_b > m_τ$ and $m_c >> m_s > m_μ$, and (iv) the smallness of neutrino masses.

Motivation & Objective

• To explain the observed hierarchy in fermion masses, including the top quark's large mass and the pattern m_t >> m_b > m_τ and m_c >> m_s > m_μ.
• To account for the smallness of neutrino masses in a way consistent with atmospheric neutrino oscillation data.
• To show that gauge interactions in higher-dimensional models with separated fermion wavefunctions provide a calculable and finite mechanism for mass generation, avoiding divergences of standard perturbative QFT.
• To explore how gauge interactions—particularly SU(3)_c and U(1)_Y—contribute to the observed mass hierarchy, especially through repulsive Coulomb-like effects between separated fermion wavefunctions.
• To demonstrate that the observed CKM mixing patterns and the dominance of the top quark in mass scales can emerge naturally from spatial separation and gauge dynamics in extra dimensions.

Proposed method

• The model uses a 5D effective field theory (EFT) with compact extra dimensions, where fermion wavefunctions are localized at different points in the extra dimension via a kink-like scalar field Φ(y).
• Fermion masses arise from the overlap of left-handed quark and right-handed antiquark wavefunctions, suppressed by a Gaussian factor exp[−μ²(ℓ_Qi − ℓ_f^c_j)²/4], where μ⁻¹ is the localization length.
• Gauge interactions are included via standard SM gauge couplings, with the assumption that gauge and Higgs fields extend uniformly over the extra dimension, preserving universality.
• The 4D Yukawa couplings are derived by integrating over the extra dimension, yielding effective 4D couplings that depend on the spatial separation of fermion wavefunctions.
• For neutrinos, a dimension-5 operator involving Higgs and lepton doublets is used, with the Majorana mass suppressed by the Coulomb repulsion between separated left-handed neutrino wavefunctions.
• The model assumes μ⁻¹ << L and μ << Λ, ensuring the EFT is valid and the wavefunctions are well-localized, with the cutoff Λ regulating the theory.

Experimental results

Research questions

• RQ1 Why is the top quark the heaviest known fermion, and why is its mass comparable to the electroweak scale?
• RQ2 How can the observed hierarchy m_t >> m_b > m_τ and m_c >> m_s > m_μ be explained without fine-tuning?
• RQ3 Why are neutrino masses so small compared to quarks and charged leptons?
• RQ4 Can gauge interactions in higher-dimensional models provide a calculable, finite mechanism for fermion mass generation that avoids the divergences of standard perturbative QFT?
• RQ5 How do repulsive gauge interactions (e.g., SU(2) and U(1)_Y) between separated fermion wavefunctions suppress the wavefunction overlap and thus the effective Yukawa couplings?

Key findings

• The top quark's large mass arises naturally from a combination of wavefunction localization and strong SU(3)_c gauge interactions, which enhance its effective coupling relative to lighter fermions.
• The hierarchy m_t >> m_b > m_τ and m_c >> m_s > m_μ is explained by the spatial separation of wavefunctions, with the largest suppression occurring for lighter fermions due to larger separations.
• The smallness of neutrino masses is explained by the repulsive Coulomb-like interaction between separated left-handed neutrino wavefunctions, which suppresses the overlap integral in the Majorana mass term.
• The model provides a finite and calculable mechanism for fermion masses, avoiding the divergences of standard radiative corrections in 4D QFT, even when gauge interactions dominate over localization.
• The (2,3) subsector of the left-handed neutrino Majorana mass matrix naturally takes a form that leads to maximal mixing between ν_μ and ν_τ, consistent with atmospheric neutrino oscillation data.
• The model suggests that the observed fermion mass patterns and mixing angles can emerge from the relative positions of fermion wavefunctions in extra dimensions, combined with gauge dynamics, without requiring additional flavor symmetries.