High-energy neutrino conversion and the lepton asymmetry in the universe

TL;DR

The paper investigates how a CP-asymmetric relic neutrino background can modify high-energy neutrino oscillations as they traverse the Universe. It develops a formalism for matter-induced phases and resonant conversion in both active-active and active-sterile channels, showing that substantial deviations from vacuum oscillations are possible when η ≳ 1 and neutrinos originate at high redshift. Applications to diffuse fluxes from GRBs, AGN, and heavy relic decays reveal energy- and epoch-dependent signatures in flavor ratios, with potential deviations up to tens of percent. The work proposes observable consequences in flavor composition and event ratios in future detectors, arguing that such measurements would probe large lepton asymmetries and refine our understanding of cosmological neutrino backgrounds.

Abstract

We study matter effects on oscillations of high-energy neutrinos in the Universe. Substantial effect can be produced by scattering of the neutrinos from cosmological sources ($z\gta 1$) on the relic neutrino background, provided that the latter has large CP-asymmetry: $η\equiv (n_ν-n_{\barν})/n_γ\gta 1$, where $n_ν$, $n_{\barν}$ and $n_γ$ are the concentrations of neutrinos, antineutrinos and photons. We consider in details the dynamics of conversion in the expanding neutrino background. Applications are given to the diffuse fluxes of neutrinos from GRBs, AGN, and the decay of super-heavy relics. We find that the vacuum oscillation probability can be modified by $\sim (10-20)%$ and in extreme cases allowed by present bounds on $η$ the effect can reach $\sim 100%$. Signatures of matter effects would consist (i) for both active-active and active-sterile conversion, in a deviation of the numbers of events produced in a detector by neutrinos of different flavours, $N_α~(α=e,μ,τ)$, and of their ratios from the values given by vacuum oscillations; such deviations can reach $\sim 5-15%$, (ii) for active-sterile conversion, in a characteristic energy dependence of the ratios $N_{e}/N_μ,N_{e}/N_τ,N_μ/N_τ$. Searches for these matter effects will probe large CP and lepton asymmetries in the universe.

Figures (16)

• Figure 1: The length scales $l_v$, $l_c$ and $l_H$ as functions of the temperature $T$ of the electromagnetic radiation in the universe. The three thick solid lines represent the vacuum oscillation length $l_v$ and correspond, from the upper to the lower, to $\Delta m^2=10^{-11},10^{-7},10^{-3}~{\rm eV^2}$ respectively. The narrow solid line and the dashed line represent the coherence length, $l_c$, for the $\nu_e-\nu_\mu$ and the $\nu_\mu-\nu_\tau$ channels respectively. We have taken $\eta_\mu\simeq 1$, $\eta_e \simeq \eta_\tau\simeq 0$. The dotted line represents the inverse expansion rate of the universe, $l_H$.
• Figure 2: The survival probability $1-P(\nu_\alpha\rightarrow \nu_\beta)$ as a function of the ratio $E_0/\Delta m^2$ for various values of $F \eta$. We have taken $\sin^2 2\theta=0.5$ and production epoch $z=3$.
• Figure 3: The minimum width, resonance and adiabaticity conditions in the $z$-$F\eta$ plane for $\nu_\alpha-\nu_s$ conversion. The solid lines are iso-contours of adiabaticity, i.e. of the quantity $\chi_R/\tan^2 2\theta$ (numbers on the curves). The dashed lines are iso-contours of resonance, i.e. of the ratio $E_0/(\Delta m^2 \cos 2\theta)$; the values are given on the curves in units of $10^{30}~{\rm eV^{-1}}$. The minimum width condition is satisfied in the shadowed region.
• Figure 4: The $\nu_\alpha - \nu_s$ conversion probability $P(t)$ as a function of time. We have taken $\sin^2 2\theta=0.5$ and three different choices of $E_0/\Delta m^2$ (in units of $10^{30}~{\rm eV^{-1}}$), production epoch $z$ and $F \eta$. The time $t$ is given in units of the age of the universe, $t_0$.
• Figure 5: The $\nu_\alpha - \nu_s$ conversion probability $P(t)$ as a function of time in the regime of good adiabaticity (see fig. \ref{['fig:fig1']}). We have taken production epochs $z$ earlier, simultaneous and later than the resonance epoch $z_R$. Here $\sin^2 2\theta=0.5$, $F \eta=14$ and $E_0/\Delta m^2 =1.8\cdot 10^{28}~{\rm eV^{-1}}$. The time $t$ is given in units of the age of the universe, $t_0$.