Quark Condensate Seesaw Mechanism for Neutrino Mass.

We study a mechanism of generation of Majorana neutrino mass due to spontaneous breaking of chiral symmetry (SBChS) accompanied by the formation of a quark condensate. The effect of the condensate is transmitted to the neutrino sector via Lepton-Number Violating (LNV) lepton-quark dimension-$7$ operators known in the literature as an origin of the neutrino-mass-independent mechanism of neutrinoless double-beta ($0 \nu \beta \beta$) decay. The smallness of neutrino masses is due to a large ratio between the LNV scale and the scale of the SBChS. This is a new realization of the seesaw mechanism, which we dub the Quark Condensate SeeSaw (QCSS). We show that its dominance requires a softly-broken symmetry suppressing the Weinberg operator. In the QCSS, $u$ and $d$ quarks receive their masses at (multi-)loop level and the smallness of neutrino masses is intimately related to the smallness of the $u$ and $d$ current-quark masses. We examine the predictions of the QCSS for $0 \nu \beta \beta$-decay and reveal the importance of the nuclear mater effects in this case. We find that the genuine no-fine-tuning QCSS favors the normal neutrino-mass ordering and rather narrow ranges of the neutrino masses $m_{1, 2, 3}$. We propose a realization of the QCSS with $\mathbb{Z}_4$ symmetry which predicts these features of the neutrino spectrum.