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 six-dimensional 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.