Flavor versus mass eigenstates in neutrino asymmetries: implications for cosmology

TL;DR

The paper demonstrates that lepton-number asymmetries in neutrinos are not invariant under flavor mixing and, due to oscillations, are best analyzed in the mass-eigenstate basis where $\mathbf{L}_{\rm m}$ is related to $\mathbf{L}_{\rm f}$ by the PMNS matrix. It provides analytic relations and numerical quantum-kinetic simulations showing that $\mathbf{L}_{\rm m}$ can differ from $\mathbf{L}_{\rm f}$ and that $\Delta N_{\rm eff}$ must account for contributions from flavor-mixed states. Through eight-parameter cosmological fits with Planck/Keck and Riess supernova data (and with/without tensor modes), the study finds no robust evidence for nonzero neutrino lepton asymmetries and sets bounds around $|\xi|<0.77$, while inflationary constraints tighten with polarization data. A key implication is that cosmological constraints on lepton asymmetries should be interpreted in the mass basis to avoid ambiguous mappings to muon- and tau-neutrino asymmetries.

Abstract

We show that, if they exist, lepton number asymmetries ($L_α$) of neutrino flavors should be distinguished from the ones ($L_i$) of mass eigenstates, since Big Bang Nucleosynthesis (BBN) bounds on the flavor eigenstates cannot be directly applied to the mass eigenstates. Similarly, Cosmic Microwave Background (CMB) constraints on mass eigenstates do not directly constrain flavor asymmetries. Due to the difference of mass and flavor eigenstates, the cosmological constraint on the asymmetries of neutrino flavors can be much stronger than conventional expectation, but not uniquely determined unless at least the asymmetry of the heaviest neutrino is well constrained. Cosmological constraint on $L_i$ for a specific case is presented as an illustration.

Figures (4)

• Figure 1: Evolutions of $\mathbf{L}_{\rm f}$ for $\theta=(\theta_{12},\theta_{13},\theta_{23})$ with $\theta_{ij}$ being the mixing angles in PMNS matrix, and $(\xi_e,\xi_\mu,\xi_\tau) = (-1.0,1.6,0.3)$. Left/Right: Diagonal/off-diagonal entries.
• Figure 2: Comparisons of lepton number asymmetries of both mass-eigenstates ($L_i ; \ i=1,2,3$) and flavor-eigenstates ($L_\alpha ; \ \alpha = e,\mu,\tau$) for $\theta =(\theta_{12},\theta_{13},\theta_{23})$. Solid/dashed lines are the asymmetries of flavor/mass eigenstates. Left and right panels are showing two examples of $\mathbf{L}_{\rm m}$ leading to $L_e \approx 0$ satisfying BBN constraint. Left: $\mathbf{L}_{\rm m} = {\rm diag}(L_1,L_2,L_3)=(-t_{12}^2 L_0, L_0, 0)$. Right: $\mathbf{L}_{\rm m} = {\rm diag}(-(t_{12}^2+t_{13}^2/c_{12}^2) L_0, L_0, L_0)$.
• Figure 3: Constraints on $H_0$ and $\xi$ for the eight-parameter $\Lambda$CDM+$\xi$ case. Filled contours show the 68% (dark red) and 95% (light red) constraints from Planck+BICEP/Keck alone. Dashed contours show the corresponding constraints with the addition of the Riess et al. supernova data. The constraint on $H_0$ from the supernova data alone, $H_0 = 73.24 \pm 1.74$Riess:2016jrr is shown by the filled regions, with $1\sigma$ limits in lavender, and $2\sigma$ limits in grey.
• Figure 4: CMB constraints on lepton number asymmetries for the nine-parameter model including tensor perturbations. Contours are 68% and 95% uncertainties from CMB-only (red-shaded regions), and CMB+supernovae (dashed lines). Left: Constraint as a function of $\xi$ and $H_0$. The filled region is the Riess et al. constraint on $H_0$ from supernovae. Right: Constraint on the spectral index $n_S$ and tensor-to-scalar ratio $r$, plotted with the predictions of representative choices of inflationary scalar-field potential. Dotted contours for $\Lambda$CDM+$r$, with fixed $\xi = 0$. This can be compared to Fig. 1 of Tram, et al.Tram:2016rcw.