Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2011-05-04
JHEP 1106:091,2011
Physics
High Energy Physics
High Energy Physics - Phenomenology
18 pages, 4 figures; v2: minor corrections, reference added, matches journal version
Scientific paper
10.1007/JHEP06(2011)091
We evaluate the Schechter-Valle (Black Box) theorem quantitatively by considering the most general Lorentz invariant Lagrangian consisting of point-like operators for neutrinoless double beta decay. It is well known that the Black Box operators induce Majorana neutrino masses at four-loop level. This warrants the statement that an observation of neutrinoless double beta decay guarantees the Majorana nature of neutrinos. We calculate these radiatively generated masses and find that they are many orders of magnitude smaller than the observed neutrino masses and splittings. Thus, some lepton number violating New Physics (which may at tree-level not be related to neutrino masses) may induce Black Box operators which can explain an observed rate of neutrinoless double beta decay. Although these operators guarantee finite Majorana neutrino masses, the smallness of the Black Box contributions implies that other neutrino mass terms (Dirac or Majorana) must exist. If neutrino masses have a significant Majorana contribution then this will become the dominant part of the Black Box operator. However, neutrinos might also be predominantly Dirac particles, while other lepton number violating New Physics dominates neutrinoless double beta decay. Translating an observed rate of neutrinoless double beta decay into neutrino masses would then be completely misleading. Although the principal statement of the Schechter-Valle theorem remains valid, we conclude that the Black Box diagram itself generates radiatively only mass terms which are many orders of magnitude too small to explain neutrino masses. Therefore, other operators must give the leading contributions to neutrino masses, which could be of Dirac or Majorana nature.
Duerr Michael
Lindner Manfred
Merle Alexander
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