Apart from the abundance of matter (both visible and dark) and energy (dark) in the cosmos, the observation of neutrino oscillations has provided our first direct evidence for physics beyond the standard model. A consequence of this observation is that neutrinos have mass, and oscillation experiments imply that none of these masses is larger than about 1 eV. This scale is considerably smaller than the mass of the lightest charged lepton, and presents us with a puzzle: Why are neutrino masses non-zero but so tiny?

The most popular proposed answer to this question is a theoretical construction called the "see-saw" mechanism. The see-saw mechanism posits that the neutrinos seen in oscillation experiments are actually mixtures of two primordial neutrino species: a very light neutrino and a very heavy Majorana neutrino. Unlike all other known fermions, Majorana neutrinos are their own antiparticles. According to the see-saw mechanism, then, the neutrinos we see in experiments should be their own antiparticles.

The most powerful experimental test of this idea is to search for the neutrinoless double beta-decay of atomic nuclei. Double beta decay is a process where two neutrons in the nucleus simultaneously decay into protons. The version of the double beta decay where two neutrinos are emitted was first observed in laboratory in 1986. It is the rarest process in nature so far observed. If the neutrino is a Majorana particle, the emitted neutrino is absorbed by another nucleon and a neutrinoless double beta decay can occur. Several searches for the neutrinoless decay are being pursued throughout the world, including the CUORE experiment in which UW-Madison experimentalists are participating.

The observation of neutrinoless double beta-decay would imply that neutrinos are Majorana particles, giving strong support to the see-saw idea. However a positive signal does not necessarily imply the existence of a light Majorana neutrino. Other mechanisms such as heavy neutrinos, right-handed gauge bosons or exchange of supersymmetric particles coming at a mass scale of ~ 1 TeV may contribute as much as a light Majorana neutrino. Theoretical challenges in understanding neutrinoless double beta decay include calculation of the appropriate nuclear matrix elements and elucidating physics beyond the standard model which may be responsible for it. NPAC theorists are addressing both of these challenges, using a variety of methods in many-body nuclear theory, effective field theory, and elementary particle theory.

In addition to addressing these theoretical challenges for neutrinoless double beta-decay, we are also studying the implications of the small, but non-zero, neutrino masses for other neutrino properties and interactions. For example, the scale of neutrino mass generally implies that neutrinos would have very small magnetic moments if they are ordinary Dirac particles, and small - but possibly observable - magnetic moments if they are Majorana fermions. Thus, the observation of a neutrino magnetic moment could point to the neutrino being its own antiparticle. NPAC theorists are currently analyzing the implications of neutrino mass for the interactions of neutrinos with other particles.