Fermions on an Interval: Quark and Lepton Masses without a Higgs

TL;DR

The paper develops a principled framework for fermions living on a finite extra-dimensional interval, deriving boundary conditions from the variational principle and linking them to physical brane dynamics. By analyzing both flat and warped (RS) geometries, it shows how higgsless electroweak symmetry breaking can coexist with realistic quark and lepton masses through bulk fermions, brane-localized masses, and boundary mixings, while preserving custodial symmetry. The work provides explicit KK decompositions, mass spectra, and illustrative parameter choices that yield SM-like masses for all generations and characteristic TeV-scale KK excitations, highlighting a viable path for Higgsless models. It also clarifies the physical interpretation of various boundary conditions and how localized operators on branes map to these BCs, extending the toolbox for model-building in extra dimensions. The results have important implications for unitarization mechanisms, electroweak precision tests, and flavor structure in higgsless scenarios.

Abstract

We consider fermions on an extra dimensional interval. We find the boundary conditions at the ends of the interval that are consistent with the variational principle, and explain which ones arise in various physical circumstances. We apply these results to higgsless models of electroweak symmetry breaking, where electroweak symmetry is not broken by a scalar vacuum expectation value, but rather by the boundary conditions of the gauge fields. We show that it is possible to find a set of boundary conditions for bulk fermions that would give a realistic fermion mass spectrum without the presence of a Higgs scalar, and present some sample fermion mass spectra for the standard model quarks and leptons as well as their resonances.

Figures (3)

• Figure 1: (a) Contour plot of the value of $M_D$ needed to obtain $m_{c}=1.2$ GeV forvarying values of $c_L$ and $c_R$. The regions starting with the darkest moving toward the lighter ones correspond to $M_D=0.1,0.3,0.6,1,1.5,2,2.5,3,3.5,4,4.5$ TeV. (b) Contour plot of the value of the lightest KK mass for the second generation quarks assuming that $M_D$ is chosen such that $m_{c}=1.2$ GeV, for varying values of $c_L$ and $c_R$. The regions starting with the darkest moving toward the lighter ones correspond to $M_{KK}=0.1,0.3,0.5,0.7,0.9,1.1$ TeV
• Figure 2: Contour plot of the value of $M_D$ needed to obtain $m_{top}=175$ GeV for varying values of $c_L$ and $c_R$. The regions starting with the darkest moving toward the lighter ones correspond to $M_D=1,1.5,2,\ldots ,6,6.5$ TeV.
• Figure 3: (a) Contour plot of the value of $M_R$ needed to obtain $m_{\mu}=100$ MeV and $m_{\nu_\mu}= 2\cdot 10^{-3}$ eV for varying values of $M_D$ and $M/f$. The regions starting with the darkest moving toward the lighter ones correspond to $M_R = 4,6,8,10,13,16,19,22\cdot 10^{14}$ GeV. (b) Contour plot of the mass of the first KK excitation of the muon neutrino, keeping fixed $m_{\mu}=100$ MeV and $m_{\nu_\mu}= 2\cdot 10^{-3}$ eV and varying $M_D$ and $M/f$. The regions starting with the darkest moving toward the lighter ones correspond to $m^{KK}_{\nu_{\mu}} = 300,400,500,600,700$ GeV.