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Neutrino spectral density at electroweak scale temperature

Motivated by the scenario of resonant leptogenesis in which lepton number creation in the electroweak-scale is relevant, we investigate the spectral properties and possible collective nature of the standard model neutrinos at electroweak scale temperature (T). We adopt the R_xi gauge fixing, which includes the unitary gauge as a limiting case, and allows us to study the broken as well as the restored phases of the gauge symmetry in a unified way. We show that the spectral density of the neutrino has a three-peak structure in the low-momentum region due to the scattering with the thermally excited particles (i.e., Landau damping) when T becomes comparable to the weak-boson masses in the plasma. The three peaks are identified with a novel ultrasoft mode, the usual quasiparticle, and antiplasmino modes. Varying the gauge-fixing parameter, we show that the three-peak structure appears independently of the gauge fixing and thus has a physical significance. We discuss possible implications of the neutrino spectral density obtained in the present work on particle cosmology, in particular in the context of resonant leptogenesis.