  Pseudo Nambu-Goldstone bosons (pNGBs) are naturally light spin-zero
particles, which can be interesting dark matter (DM) candidates. We study the
phenomenology of a pNGB theta associated with an approximate symmetry of the
neutrino seesaw sector. A small coupling of theta to the Higgs boson is induced
radiatively by the neutrino Yukawa couplings. By virtue of this Higgs portal
interaction (i) the pNGB acquires a mass m_theta proportional to the
electroweak scale, and (ii) the observed DM relic density can be generated by
the freeze-in of theta-particles with mass m_theta ~ 3 MeV. Alternatively, the
coupling of theta to heavy sterile neutrinos can account for the DM relic
density, in the 1 keV-3 MeV window. The decays of theta into light fermions are
suppressed by the seesaw scale, making such pNGB sufficiently stable to play
the role of DM.
