We consider the possibility that the quark condensate formed by QCD confinement generates Majorana
neutrino masses
mν via dimension seven operators. No degrees of freedom beyond the Standard Model are necessary, below the electroweak scale. Obtaining experimentally acceptable
neutrino masses requires the new physics scale
ΛTeV, providing a new motivation for weak-scale discoveries at the LHC. We implement this mechanism using a
Z3 symmetry which leads to a massless up quark above the QCD chiral condensate scale. We use non-
helicity-suppressed light meson rare decay data to constrain
Λ. Experimental constraints place a mild hierarchy on the flavor structure of dimension seven operators and the resulting
neutrino mass matrix.