Observables sensitive to absolute neutrino masses: Constraints and correlations from world neutrino data

TL;DR

The paper addresses how to constrain the absolute neutrino mass scale by jointly analyzing three observables: $m_eta$, $m_{etaeta}$, and $Σ$, within the standard 3ν mixing and cosmology. It develops a global, data-driven framework that combines neutrino oscillation data with laboratory bounds from Tritium β-decay and 0νββ searches, and cosmological measurements including CMB, LSS, and Lyα, to map the allowed regions in the ($m_eta$, $m_{etaeta}$, $Σ$) space for normal and inverted hierarchies. A key finding is that cosmological upper bounds on $Σ$ generally dominate, but the 0νββ results can induce tension depending on the dataset and assumptions, especially when Lyα is included. The work provides a visualization-based approach to anticipate how future measurements of any of the three observables will sharpen or resolve the mass hierarchy and Majorana phases.

Abstract

In the context of three-flavor neutrino mixing, we present a thorough study of the phenomenological constraints applicable to three observables sensitive to absolute neutrino masses: The effective neutrino mass in Tritium beta decay (m_beta); the effective Majorana neutrino mass in neutrinoless double beta decay (m_2beta); and the sum of neutrino masses in cosmology (Sigma). We discuss the correlations among these variables which arise from the combination of all the available neutrino oscillation data, in both normal and inverse neutrino mass hierarchy. We set upper limits on m_beta by combining updated results from the Mainz and Troitsk experiments. We also consider the latest results on m_2beta from the Heidelberg-Moscow experiment, both with and without the lower bound claimed by such experiment. We derive upper limits on Sigma from an updated combination of data from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite and the 2 degrees Fields (2dF) Galaxy Redshifts Survey, with and without Lyman-alpha forest data from the Sloan Digital Sky Survey (SDSS), in models with a non-zero running of the spectral index of primordial inflationary perturbations. The results are discussed in terms of two-dimensional projections of the globally allowed region in the (m_beta,m_2beta,Sigma) parameter space, which neatly show the relative impact of each data set. In particular, the (in)compatibility between Sigma and m_2beta constraints is highlighted for various combinations of data. We also briefly discuss how future neutrino data (both oscillatory and non-oscillatory) can further probe the currently allowed regions.

Figures (7)

• Figure 1: Bounds on the $3\nu$ mass-mixing neutrino parameters $(\delta m^2,\Delta m^2,\sin^2\theta_{12},\sin^2\theta_{13})$ from our analysis of current neutrino oscillation data. The solid curves represent projections of the $\Delta\chi^2_\mathrm{osc}$ fit function. The intercepts of the curves with the horizontal dotted lines at $\Delta\chi^2=n^2$ define the $n$-$\sigma$ limits on each parameter. There is no statistically significant lower limit for $\sin^2\theta_{13}$.
• Figure 2: Upper bounds on the sum of neutrino masses $\Sigma$ from our $3\nu$ analysis of cosmological data, given in terms of the $\Delta\chi^2_\Sigma$ function. The solid and dashed curves refer to the combination of CMB and LSS data (CMB+2dF and CMB+SDSS, respectively). The two CMB+LSS fits provide comparable results and, for definiteness, the CMB+2df one is adopted. In addition, we consider also the case where the recent Ly$\alpha$ data from the SDSS are included, providing significantly stronger constraints on $\Sigma$ (dotted curve). See the text for details.
• Figure 3: Global $3\nu$ analysis in the $(m_{\beta},m_{\beta\beta},\Sigma)$ parameter space, using oscillation data only. The three panels show the two-dimensional projections of the volume allowed at $\Delta\chi^2_\mathrm{osc}=4$ ($2\sigma$ on each parameter) for both normal hierarchy (thick solid curves) and inverted hierarchy (thin solid curves), respectively. The emerging correlations between parameters are discussed in the text.
• Figure 4: Global $3\nu$ analysis in the $(m_{\beta},m_{\beta\beta},\Sigma)$ parameter space, using oscillation data plus laboratory data and cosmological data. With respect to Fig. 3, this figure implements also upper limits (shown as dashed lines at $2\sigma$ level) on $m_\beta$ from Mainz+Troitsk data, on $m_{\beta\beta}$ from $0\nu2\beta$ data, and on $\Sigma$ from CMB+2dF data. In combination with oscillation parameter bounds, the cosmological upper limit on $\Sigma$ dominates over the laboratory upper limits on $m_\beta$ and $m_{\beta\beta}$.
• Figure 5: Global $3\nu$ analysis in the $(m_{\beta},m_{\beta\beta},\Sigma)$ parameter space, using oscillation data plus laboratory and cosmological data. With respect to Fig. 4, lower bounds on $m_{\beta\beta}$ from a claimed $0\nu2\beta$ signal are implemented. The globally allowed $2\sigma$ regions appear to be stretched somewhat beyond the separate $2\sigma$ bands. This feature reflects some tension existing between the $0\nu2\beta$ claim and cosmological CMB+LSS data within the $3\nu$ oscillation scenario.