Impact of hierarchy upon the values of neutrino mixing parameters

Abstract

A neutrino-oscillation analysis is performed of the more finely binned Super-K atmospheric, MI-NOS, and CHOOZ data in order to examine the impact of neutrino hierarchy in this data set upon the value of θ13 and the deviation of θ23 from maximal mixing. Exact oscillation probabilities are used, thus incorporating all powers of θ13 and ε := θ23 − π/4. The extracted oscillation parameters are found to be dependent on the hierarchy, particularly for θ13. We find at 90% CL are ∆32 = 2.44 +0.26 −0.20 and 2.48 +0.25 −0.22 × 10 −3 eV 2 , ε = θ23 − π/4 = 0.06 +0.06 −0.16 and 0.06 +0.08 −0.17 , and θ13 = −0.07 +0.18 −0.11 and −0.13 +0.23 −0.16 , for the normal and inverted hierarchy respectively. The inverted hierarchy is preferred at a statistically insignificant level of 0.3 σ.PACS numbers: 14.60.Pq Keywords: neutrino oscillations, three neutrinos, mixing angles, mass-squared differences, mass hierarchyThe field of neutrino oscillations has progressed rapidly over the past fifteen years. The data can largely be understood by the oscillation of the three known neutrinos [1, 2]. Oscillation phenomenology invokes a unitary matrix that relates the flavor basis, in which the neutrinos are created or destroyed, to the mass basis, in which the neutrinos propagate through vacuum. This matrix can be written in terms of three real mixing angles, θ 12 , θ 23 , and θ 13 , and a phase δ that determines CP violation. Oscillations also require nonzero neutrino mass differences, being dependent upon the difference of the square of the masses, ∆ ij := m 2 i − m 2 j with m i the mass of neutrino i. A recent analysis [3] reports the present knowledge of the values of the oscillation parameters. In particular, we note that only an upper limit exists on the size of the "reactor" mixing angle |θ 13 | = 0.19 +0.12 −0.19 (1σ), a constraint which arises, in part, from the null oscillation result of the CHOOZ experiment [4]. A nonzero value of θ 13 is requisite for the existence of CP violation in neutrino oscillations; hence, we presently have no knowledge of the value of δ. We also have no knowledge of the ordering of the neutrino mass eigenstate; namely, is m 3 greater or less than m 1 and m 2 ? The former (latter) situation is termed the normal (inverted) hierarchy.Recently, hints of nonzero θ 13 have been reported as a means by which to ease the tension between the determination of the oscillation parameters θ 12 and ∆ 21 by the solar and KamLAND experiments [5,6]. At a smaller significance, analyses of atmospheric data also hint at nonzero θ 13 [7,8], though one study shows that the significance of the results are dependent upon the precise nature of the statistical analysis [9]. Furthermore, an analysis of the updated atmospheric data finds no preference for nonzero θ 13 [10]; however, this analysis employs approximate oscillation formulae and cannot be directly compared to these other works. Should these various hints be cleanly confirmed in current neutrino oscillation experiments [11-13], then one might be able to attack the issue of C...

Implications of nonzero θ13for the neutrino mass hierarchy

“…This behavior can be seen in the graphs depicting ∆χ 2 versus θ 13 found in Ref. [5]. We note that these results are similar to those presented in Fig.…”

“…Recent long-baseline reactor experiments [2,3,4] have accurately measured the value of θ 13 and found it to be large, sin 2 (2 θ 13 ) ≈ 0.1. Before these measurements, the world's data demonstrated very little preference for either the hierarchy or the sign of θ 13 [5]. The goal of this work is to examine the effect that the recent knowledge of θ 13 has on the hierarchy question and on the sign of θ 13 .…”

Analysis Tool for Atmospheric Neutrino Oscillations

“…The quality of our approach can be measured by comparing to the analysis provided by the experimentalist in [4]. These results will [17] be presented elsewhere soon. This finer binning reduces the errors on the parameters extracted.…”

Status of three‐neutrino oscillation parameters

“…An additional hint for a non-zero value of θ 13 can be obtained from the combination of atmospheric and long-baseline neutrino data [31,32]. Atmospheric neutrino data from Super-Kamiokande I+II+III described in the previous section implies a best fit point very close to θ 13 = 0 [22], with ∆χ 2 = 0.0(0.3) for θ 13 = 0 for NH (IH).…”