Neutrinos Vis-a-vis the Six-Dimensional Standard Model

TL;DR

This work embeds the six-dimensional standard model with two universal extra dimensions into a seven-dimensional warped framework, where three gauge-singlet right-handed neutrinos propagate in the bulk. Neutrino masses are generated as Dirac masses through a dimension-seven operator, with an exponential suppression from the right-handed neutrino wavefunctions localized away from the standard-model brane, naturally yielding a small mass scale. The light-neutrino spectrum displays $m_{ u_1}, m_{ u_2} \sim O(\epsilon)\, m_{ u_3}$ and large mixing angles, in particular accommodating the large-mixing-angle MSW solution for solar oscillations and near-maximal atmospheric mixing, while LSND is not explained. Gravitational anomaly analysis shows the model remains consistent, and the mechanism extends to a broader class of higher-dimensional theories that forbid Majorana masses, linking neutrino phenomenology to the geometry and warping of extra dimensions.

Abstract

We examine the origin of neutrino masses and oscillations in the context of the six-dimensional standard model. The space-time symmetries of this model explain proton stability and forbid Majorana neutrino masses. The consistency of the six-dimensional theory requires three right-handed neutrinos, and therefore Dirac neutrino masses are allowed. We employ the idea that the smallness of these masses is due to the propagation of the right-handed neutrinos in a seventh, warped dimension. We argue that this class of theories is free of gravitational anomalies. Although an exponential hierarchy arises between the neutrino masses and the electroweak scale, we find that the mass hierarchy among the three neutrino masses is limited by higher-dimension operators. All current neutrino oscillation data, except for the LSND result, are naturally accommodated by our model. In the case of the solar neutrinos, the model leads to the large mixing angle, MSW solution. The mechanism employed, involving three right-handed neutrinos coupled to a scalar in an extra dimension, may explain the features of the neutrino spectrum in a more general class of theories that forbid Majorana masses.

Figures (2)

• Figure 1: Scalar profile when $M_{\varphi}/k=10$, $\pi r_{c} M_{\varphi}=70$. The plateau is at $f \approx M_\varphi/\sqrt{\lambda_\varphi}$. The points $z_{1}$ and $z_{2}$ define the boundaries between regions I, II and III. In the main text we consider the case where $z_{1}/z_{2} \ll 1$.
• Figure 2: The flow diagram when $M_{\varphi}/3k=4$.