Neutrino Masses with Enhanced $B-L$ Symmetry

Abstract

Assuming all three known neutrinos are Dirac fermions, $U(1)_{B-L}$ can be an exact symmetry. We show that, if the condition of charge quantization is relaxed, the anomaly-free $B-L$ charges of two out of three right-handed neutrinos can be enhanced by arbitrarily large factors, while all other fermions retain their canonical charges. We call this setup as `enhanced $B-L$ symmetry' and promote it to be local. As long as this enhanced $B-L$ gauge symmetry remains unbroken, neutrinos stay chiral and massless at low energies. Nonzero neutrino masses then require sub-eV-scale symmetry breaking order parameters, which we associate with gravity-induced neutrino condensate. If the enhancement is large and the $B-L$ gauge boson $A'$ is lighter than the heaviest neutrino, then the neutrino decay into $A'$ directly constrains the gauge coupling, which can be significantly stronger than the baryon-based fifth-force tests. Through kinetic mixing with the photon, $A'$ can also mediate neutrino-electron and coherent neutrino-nucleus scatterings, leading to possible signatures in neutrino observatories and dark matter detectors.

Figures (1)

• Figure 1: Constraints on the $B-L$ gauge coupling strength $g_{B-L}$, enhanced by $\epsilon^{-1}=10^{15}$ (left panel) and $\epsilon^{-1}=10^{30}$ (right panel), as a function of $m_{A'}$. The gray regions are excluded by the high-precision tests on the fifth force. The green region denotes bounds from the neutrino lifetime. The red dashed line shows the current limit from $\nu-e$ elastic scattering, evaluated with the benchmark value $\chi P_{L\to R}^{1/2}=10^{-15}$.