Getting the most from the statistical analysis of solar neutrino oscillations

TL;DR

The paper performs a global fit of solar neutrino data within a two-flavor active-oscillation framework using a comprehensive pull-based χ^2 analysis that incorporates 81 observables and 31 correlated systematics, enabling precise propagation of input uncertainties to output predictions. It demonstrates the equivalence of the covariance and pull definitions of χ^2, highlighting the pull method as more practical for large, highly correlated data sets and for diagnosing tensions via observable and systematic pulls. The global fit identifies the large-mixing-angle (LMA) solution as the best fit (δm^2 ≈ 5.5×10^-5 eV^2, tan^2 θ12 ≈ 0.43) with acceptable support for LOW and QVO regions, while the small mixing-angle (SMA) solution is statistically disfavored; solar-KamLAND data and SNO/SK spectral information play pivotal roles in shaping these conclusions. The analysis also yields luminosity-constrained neutrino flux shifts, finding the LMA solution largely consistent with Standard Solar Model flux predictions, and demonstrates a robust, generalizable statistical framework for precision solar-neutrino fits and other global analyses.

Abstract

(Abridged.) We present a thorough analysis of the current solar neutrino data, in the context of two-flavor active neutrino oscillations. We aim at performing an accurate and exhaustive statistical treatment of both the input and the output information. Concerning the input, we analyze 81 observables, including the Cl rate, the total Ga rate and its winter-summer difference, the 44 spectrum bins from SK and the 34 spectrum bins from SNO. We carefully evaluate and propagate the effects of 31 correlated systematic uncertainties, including 12 SSM input errors, the 8B neutrino energy spectrum uncertainty, as well as 11 and 7 systematics in SK and SNO, respectively. Concerning the output, we express the chi-squared analysis results in terms of ``pulls,'' embedding the single contributions to the total chi-squared. It is shown that the pull method, as compared to the (numerically equivalent) covariance matrix approach, is not only simpler and more advantageous, but also includes useful indications about the preferred variations of the neutrino fluxes with respect to their SSM predictions. Our results confirm the current best-fit solution (LMA), but also allow, with acceptable statistical significance, other solutions in the low-mass (LOW) or in the quasi-vacuum oscillation (QVO) regime, while the small mixing angle (SMA) solution could be recovered only by ad hoc ``recalibrations'' of several SSM and experimental systematics.

Figures (9)

• Figure 1: Global results of the solar neutrino data analysis, including 81 observables and 31 sources of correlated systematics. The parameter space $(\delta m^2,\tan^2\theta_{12})$ refers to the scenario of $2\nu$ oscillations among active states. The relevant $\chi^2$ minima in the LMA, LOW, and QVO regions are given in Table \ref{['chisquares']}.
• Figure 2: Results of the solar neutrino data analysis, as obtained by separating four classes of observables: (i) the chlorine rate; (ii) the average SAGE+GALLEX/GNO gallium rate plus the GALLEX/GNO winter-summer difference; (iii) the SK energy-nadir spectrum; and (iv) the SNO day-night spectrum.
• Figure 3: Results of the solar neutrino data analysis, as obtained by excluding each of the four data sets in Fig. \ref{['fig02']} from the global set used in Fig. \ref{['fig01']}.
• Figure 4: Diagram of pulls $\{\overline x_n\}_{n=1,\dots,81}$ for observables at the LMA best-fit point. See the text for details.
• Figure 5: Diagram of pulls $\{\overline \xi_k\}_{k=1,\dots,31}$ for correlated systematics at the LMA best-fit point. See the text for details.