Title: Neutrino Masses in the Mirror Twin Higgs with Spontaneous $\mathbb{Z}_2$ Breaking

Abstract: We introduce a mirror twin Higgs model with spontaneous $\mathbb{Z}_2$ symmetry breaking that ameliorates the constraints in twin Higgs cosmology and, at the same time, generates the Standard Model neutrino masses. The model features an $SU(2)$ triplet with hypercharge $1$ alongside its twin counterpart. Spontaneous breaking of both $\mathbb{Z}_2$ and electroweak symmetry occurs in the scalar sector. The Standard Model neutrinos acquire small masses through the type-II seesaw mechanism. In contrast, their twin counterparts acquire large masses, effectively addressing the dark radiation problem in mirror twin Higgs scenarios. We study the impact of the model on the $N_{\rm eff.}$ constraints, as well as on collider phenomenology.