Neutrino Masses and Mixings from String Theory Instantons

TL;DR

This work shows that string theory instantons, particularly in models with a massive $U(1)_{B-L}$, can naturally generate neutrino masses and mixings through flavour-factorised structures for both the Weinberg operator and right-handed Majorana masses. A hierarchy among neutrino masses arises from the exponential suppression of different instantons, while the flavour vectors $c_a^{(r)}$ and $d_a^{(r)}$ gate the mixing patterns, enabling normal or inverted hierarchies and even tri-bimaximal mixing for symmetric alignments. The analysis covers both Weinberg-operator–driven masses and see-saw scenarios, highlighting that substantial leptonic mixing is a generic outcome and that TBM can be realized under specific flavour alignments. These results bridge string-compactification data with low-energy neutrino phenomenology, offering testable links between instanton parameters and oscillation observables and informing string model-building choices related to $U(1)_{B-L}$ and instanton sectors.

Abstract

We study possible patterns of neutrino masses and mixings in string models in which Majorana neutrino masses are generated by a certain class of string theory instantons recently considered in the literature. These instantons may generate either directly the dim=5 Weinberg operator or right-handed neutrino Majorana masses, both with a certain flavour-factorised form. A hierarchy of neutrino masses naturally appears from the exponentially suppressed contributions of different instantons. The flavour structure is controlled by string amplitudes involving neutrino fields and charged instanton zero modes. For some simple choices for these amplitudes one finds neutrino mixing patterns consistent with experimental results. In particular, we find that a tri-bimaximal mixing pattern is obtained for simple symmetric values of the string correlators.

Figures (2)

• Figure 1: World-sheet disk amplitude inducing a cubic coupling on the D2-brane instanton action. The cubic coupling involves the right-handed neutrinos lying at the intersection of the $c$ and $d$ D6-branes, and the instanton fermion zero modes $\alpha$ and $\gamma$ from the D2-D6 intersections.
• Figure 2: World-sheet disk amplitude inducing a quartic coupling on the D2-brane instanton action. The coupling involves the Higgs ${\overline H}$ and left-handed leptons $L^a$ lying at the intersection of the $b$, $c$ and $d$ D6-branes, and the instanton fermion zero modes $\beta$ and $\delta$ from the D2-D6 intersections.