What can we learn from neutrinoless double beta decay experiments?

We assess how well next-generation neutrinoless double beta decay and normal neutrino beta decay experiments can answer four fundamental questions. ~1! If neutrinoless double beta decay searches do not detect a signal, and if the spectrum is known to be inverted hierarchy, can we conclude that neutrinos are Dirac particles? ~2! If neutrinoless double beta decay searches are negative and a next-generation ordinary beta decay experiment detects the neutrino mass scale, can we conclude that neutrinos are Dirac particles? ~3! If neutrinoless double beta decay is observed with a large neutrino mass element, what is the total mass in neutrinos? ~4! If neutrinoless double beta decay is observed, but next-generation beta decay searches for a neutrino mass only set a mass upper limit, can we establish whether the mass hierarchy is normal or inverted? We base our answers on the expected performance of next-generation neutrinoless double beta decay experiments and on simulations of the accuracy of calculations of nuclear matrix elements.