Lepton-number violation and right-handed neutrinos in Higgsless effective theories

Following previous work, we identify a symmetry ${S}_{\mathrm{nat}}$ that generalizes the concept of custodial symmetry, keeping under control deviations from the standard model (SM). To realize ${S}_{\mathrm{nat}}$ linearly, the space of gauge fields has to be extended. Covariant constraints formulated in terms of spurions reduce ${S}_{\mathrm{nat}}$ back to $\mathrm{SU}(2{)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{Y}$. This allows for a covariant introduction of explicit ${S}_{\mathrm{nat}}$-breaking parameters. We assume that ${S}_{\mathrm{nat}}$ is at play in a theory of electroweak symmetry-breaking without a light Higgs particle. We describe some consequences of this assumption, using a nondecoupling effective theory in which the loop expansion procedure is based on both momentum and spurion power-counting, as in chiral perturbation theory. A hierarchy of lepton-number violating effects follows. Leading corrections to the SM are nonoblique. The effective theory includes stable light right-handed neutrinos, with an unbroken ${\mathbb{Z}}_{2}$ symmetry forbidding neutrino Dirac masses. ${\ensuremath{\nu}}_{R}$ contribution to dark matter places bounds on their masses.