Neutrinoless double β decay with small neutrino masses Águila Giménez, Francisco Del Aparici, Alberto Bhattacharya, S. Santamaria, Arcadi Wudka, Jose Neutrinoless Double β Double beta Neutrino mass Proceedings of the Corfu Summer Institute 2012 "School and Workshops on Elementary Particle Physicsand Gravity", September 8-27, 2012, Corfu (Greece). PoS(Cofu2012)028. If the only contribution to neutrinoless double beta decay (0vββ) are neutrino masses its discovery may be very difficult, especially if neutrinos present a normal hierarchy spectrum. However, this is not the only possibility; 0nbb can in general produce electrons of either chirality, in contrast with the neutrino induced 0vββ which predicts two left-handed electrons. Using an effective Lagrangian approach we classify the lepton number violating (LNV) effective operators with two leptons of either chirality but no quarks, ordered according to the magnitude of their contribution to 0vββ. We point out that, for each of the three chirality assignments, eLeL;eLeR and eReR , there is only one LNV operator of the corresponding type to lowest order, and these have dimensions 5, 7 and 9, respectively. Neutrino masses are always induced by these extra operators but can be delayed to one (dimension 7) or two loops (dimension 9). Under the assumption that 0nbb is dominated by the operators of dimension 7 or 9 we find that the scale of new physics should be relatively low (< 30 TeV). We also list the SM additions generating these operators upon integration of the heavy modes, and discuss simple realistic examples of renormalizable theories for each case. The phenomenology of a model giving rise to the dimension 9 operator has been analyzed with some detail: if 0vββ is going to be seen in the next round of experiments, the doubly charged scalars of the model could be seen at the LHC and lepton flavour violating (LFV) rates could be at the reach of foreseen experiments. Moreover neutrino masses, which arise at two loops, display a very particular structure and are strongly constrained, in fact, sin2 ϴ13 > 0,008, when μ --> eee is required to lie below its present experimental limit. 2014-02-26T13:52:41Z 2014-02-26T13:52:41Z 2012 journal article Águila, F.; et al. Neutrinoless double β decay with small neutrino masses. Proceedings of Science: 028 (2012). [http://hdl.handle.net/10481/30578] 1824-8039 http://hdl.handle.net/10481/30578 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ open access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Scuola Internazionale Superiore di Studi Avanzati (SISSA)