Measuring the deviation of the 2--3 lepton mixing from maximal with atmospheric neutrinos

Measuring the deviation of the 2–3 lepton mixing from maximal with atmospheric neutrinos

M. C. Gonzalez-Garcia, M. Maltoni, and A. Yu. Smirnov

Phys. Rev. D 70, 093005 – Published 11 November 2004

Abstract

The measurement of the deviation of the 2–3 leptonic mixing from maximal, $D_{23} \equiv 1 / 2 - {sin }^{2} θ_{23}$ , is one of the key issues for understanding the origin of the neutrino masses and mixing. In the $3 ν$ context we study the dependence of various observables in the atmospheric neutrinos on $D_{23}$ . We perform the global $3 ν$ -analysis of the atmospheric and reactor neutrino data taking into account the effects of both the oscillations driven by the solar parameters ( $Δ m_{21}^{2}$ and $θ_{12}$ ) and the 1–3 mixing. The departure from the one-dominant mass scale approximation results into the shift of the 2–3 mixing from maximal by $Δ {sin }^{2} θ_{23} \approx 0.04$ , so that $D_{23} \sim 0.04 \pm 0.07$ $(1 σ)$ . Though the value of the shift is not statistically significant, the tendency of the allowed region to move towards smaller values of ${sin }^{2} θ_{23}$ is robust. The shift is induced by the excess of the $e$ -like events in the sub-GeV sample. We show that future large scale water Cherenkov detectors can determine $D_{23}$ with accuracy of a few percent, comparable with the sensitivity of future long-baseline experiments. Moreover, the atmospheric neutrinos will provide unique information on the sign of the deviation (octant of $θ_{23}$ ).

Received 2 September 2004

DOI:https://doi.org/10.1103/PhysRevD.70.093005

Authors & Affiliations

M. C. Gonzalez-Garcia^1,2,3,*, M. Maltoni^2,†, and A. Yu. Smirnov^4,5,‡

¹Physics Department, Theory Division, CERN, CH-1211, Geneva 23, Switzerland
²C.N. Yang Institute for Theoretical Physics, SUNY at Stony Brook, Stony Brook, New York 11794-3840, USA
³IFIC, Universitat de València—C.S.I.C., Apt. 22085, E-46071 València, Spain
⁴The Abdus Salam International Centre for Theoretical Physics, I-34100 Trieste, Italy
⁵Institute for Nuclear Research of Russian Academy of Sciences, Moscow 117312, Russia

^*Electronic address: concha@insti.physics.sunysb.edu
^†Electronic address: maltoni@insti.physics.sunysb.edu
^‡Electronic address: smirnov@ictp.trieste.it

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Vol. 70, Iss. 9 — 1 November 2004

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Images

Figure 1
Allowed regions (90%, 95%, 99%, and $3 σ$ C.L.) of the oscillation parameters $Δ m_{13}^{2}$ and ${sin }^{2} θ_{23}$ from the analysis of different atmospheric data samples. The best-fit points are marked with either a star ( $Δ m_{21}^{2} \neq 0$ ) or a triangle ( $Δ m_{21}^{2} = 0$ ). Colored regions and stars correspond to $Δ m_{21}^{2} = 8.2 \times 10^{- 5} {e V}^{2}$ and ${tan }^{2} θ_{12} = 0.42$ , whereas hollow regions and triangles are for $Δ m_{21}^{2} = 0$ . In both cases we assume $θ_{13} = 0$ .Reuse & Permissions
Figure 2
Allowed regions (90%, 95%, 99%, and $3 σ$ C.L.) of the oscillation parameters $Δ m_{31}^{2}$ and ${sin }^{2} θ_{23}$ from the combined analysis of all the atmospheric and CHOOZ data samples. The best-fit points are marked with either a star or a triangle. In the lower panels we show the dependence of the $χ^{2}$ function on $θ_{23}$ , marginalized with respect to $Δ m_{31}^{2}$ . Colored regions, stars, and solid blue lines correspond to ${tan }^{2} θ_{12} = 0.42$ , $θ_{13}$ free and $Δ m_{21}^{2}$ set to the value indicated in each panel. Hollow regions, triangles and dashed black lines are for $Δ m_{21}^{2} = 0$ and $θ_{13}$ free.Reuse & Permissions
Figure 3
Allowed regions (at 90%, 95%, 99%, and $3 σ$ C.L.) of oscillation parameters $Δ m_{13}^{2}$ and ${sin }^{2} θ_{23}$ expected from an atmospheric neutrino experiment with 20 times the present SK statistics and the same theoretical and systematic errors as in present SK. For definiteness, we choose ${\bar{θ}}_{13} = 0$ , $Δ {\bar{m}}_{21}^{2} = 8.2 \times 10^{- 5} {e V}^{2}$ , and ${tan }^{2} {\bar{θ}}_{12} = 0.42$ , and we scan different values of $Δ {\bar{m}}_{31}^{2}$ and ${\bar{θ}}_{23}$ . We also include the constraints from the CHOOZ experiment, as well as the sensitivity to $Δ m_{21}^{2}$ expected after three years of KamLAND data [Eq. (20)]. The undisplayed parameters $Δ m_{21}^{2}$ and $θ_{13}$ are marginalized.Reuse & Permissions
Figure 4
( $Δ {\bar{m}}_{31}^{2}$ , ${\bar{θ}}_{23}$ ) regions with $Δ χ_{n o - m a x}^{2}$ smaller than 1 (white), between 1 and 4 (blue/dark gray), between 4 and 9 (green/gray), and larger than 9 (yellow/light gray), respectively, for $Δ {\bar{m}}_{21}^{2} = 8.2 \times 10^{- 5} {e V}^{2}$ (the hollow regions are obtained for $Δ {\bar{m}}_{21}^{2} = 0$ ). We set ${\bar{θ}}_{13} = 0$ and ${tan }^{2} {\bar{θ}}_{12} = 0.42$ . The dashed oval marks the $3 σ$ region presently preferred by SK data.Reuse & Permissions
Figure 5
Dependence of $χ_{A T M + R E A C}^{2}$ (full black line) and $χ_{A T M + R E A C + L B L}^{2}$ (red dashed line) on ${sin }^{2} θ_{23}$ , for $Δ m_{31}^{2} = 2.2 \times 10^{- 3} {e V}^{2}$ and setting the simulated point ( $\bar{ω}$ ) to ${\bar{θ}}_{13} = 0$ , ${tan }^{2} {\bar{θ}}_{12} = 0.42$ , $Δ {\bar{m}}_{21}^{2} = 8.2 \times 10^{- 5} {e V}^{2}$ , ${sin }^{2} {\bar{θ}}_{23} = 0.42$ and $Δ {\bar{m}}_{31}^{2} = 2.2 \times 10^{- 3} {e V}^{2}$ . For the definition of $χ_{A T M + R E A C}^{2}$ and $χ_{A T M + R E A C + L B L}^{2}$ see Eqs. (20, 22).Reuse & Permissions
Figure 6
Dependence of $Δ χ_{d i s c}^{2}$ [see Eq. (23)] on ${\bar{θ}}_{23}$ , for ${\bar{θ}}_{13} = 0$ , ${tan }^{2} {\bar{θ}}_{12} = 0.42$ , $Δ {\bar{m}}_{21}^{2} = 8.2 \times 10^{- 5} {e V}^{2}$ , and $Δ {\bar{m}}_{31}^{2} = 2.2 \times 10^{- 3} {e V}^{2}$ . The different lines correspond to the same cases as in Fig. 5.Reuse & Permissions

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