Unparticle-Higgs Mixing: MSW Resonances, See-saw Mechanism and Spinodal Instabilities

Motivated by slow-roll inflationary cosmology we study a scalar unparticle weakly coupled to a Higgs field in the broken symmetry phase. The mixing between the unparticle and the Higgs field results in a seesaw type matrix and the mixing angles feature a Mikheyev-Smirnov-Wolfenstein (MSW) effect as a consequence of the unparticle field being noncanonical. We find two (MSW) resonances for small and large spacelike momenta. The unparticlelike mode features a nearly flat potential with spinodal instabilities and a large expectation value. An effective potential for the unparticlelike field is generated from the Higgs potential, but with couplings suppressed by a large power of the small seesaw ratio. The dispersion relation for the Higgs-like mode features an imaginary part even at "tree level" as a consequence of the fact that the unparticle field describes a multiparticle continuum. Mixed unparticle-Higgs propagators reveal the possibility of oscillations, albeit with short coherence lengths. The results are generalized to the case in which the unparticle features a mass gap, in which case a low energy MSW resonance may occur for lightlike momenta depending on the scales. Unparticle-Higgs mixing leads to an effective unparticle potential of the new-inflation form. Slow-roll variables are suppressed by seesaw ratios and the anomalous dimensions and favor a red spectrum of scalar perturbations consistent with cosmic microwave background data.