Neutrino Majorana Masses from String Theory Instanton Effects

Abstract

Finding a plausible origin for right-handed neutrino Majorana masses in semirealistic compactifications of string theory remains one of the most difficult problems in string phenomenology. We argue that right-handed neutrino Majorana masses are induced by non-perturbative instanton effects in certain classes of string compactifications in which the $U(1{)}_{B-L}$ gauge boson has a Stückelberg mass. The induced operators are of the form $e^{-U}{\nu }_R{\nu }_R$ where $U$ is a closed string modulus whose imaginary part transforms appropriately under $B-L$. This mass term may be quite large since this is not a gauge instanton and $ReU$ is not directly related to SM gauge couplings. Thus the size of the induced right-handed neutrino masses could be a few orders of magnitude below the string scale, as phenomenologically required. It is also argued that this origin for neutrino masses would predict the existence of R-parity in SUSY versions of the SM. Finally we comment on other phenomenological applications of similar instanton effects, like the generation of a $\mu$-term, or of Yukawa couplings forbidden in perturbation theory.

Comments: 40 pages, 4 figures (v2: added references, small corrections)(v3: minor corrections)