Classical running of neutrino masses from six dimensions

We discuss a six dimensional mass generation for the neutrinos. Active neutrinos live on a three-brane and interact via a brane localized mass term with a bulk sixdimensional standard model singlet (sterile) Weyl fermion, the two dimensions being transverse to the three-brane. We derive the physical neutrino mass spectrum and show that the active neutrino mass and Kaluza–Klein masses have a logarithmic cutoff divergence related to the zero-size limit of the three-brane in the transverse space. This translates into a renormalisation group running of the neutrino masses above the Kaluza–Klein compactification scale coming from classical effects, without any new non-singlet particles in the spectrum. For compact radii in the eV–MeV range, relevant for neutrino physics, this scenario predicts running neutrino masses which could affect, in particular, neutrinoless double beta decay experiments. Unité mixte du CNRS et de l’EP, UMR 7644. Unité mixte du CNRS, UMR 8627. Unité de recherche associ au CNRS, URA 2306.