Probing the neutrino mass matrix in next-generation neutrino oscillation experiments
ABSTRACT We review the current status of the neutrino mass and mixing parameters needed to reconstruct the neutrino mass matrix. A
comparative study of the precision in the measurement of oscillation parameters expected from the next-generation solar, atmospheric,
reactor-and accelerator-based neutrino experiments is presented. We discuss the potential of 0νββ experiments in determining the neutrino mass hierarchy and the importance of a better ϑ
12 measurement for it.
arXiv:hep-ph/0509217v1 21 Sep 2005
Probing the neutrino mass matrix in next generation neutrino
Sandhya Choubey1, ∗
1Rudolf Peierls Centre for Theoretical Physics,
University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK
We review the current status of the neutrino mass and mixing parameters needed
to reconstruct the neutrino mass matrix. A comparative study of the precision in
the measurement of oscillation parameters expected from the next generation solar,
atmospheric, reactor and accelerator based experiments is presented. We discuss the
potential of 0νββ experiments in determining the neutrino mass hierarchy and the
importance of a better θ12measurement for it.
The last few years have provided us with conclusive proof of the existence of oscillations
and hence mass and mixing in the neutrino sector. While the atmospheric neutrino data
from Super-Kamiokande (SK) and the accelerator data from the K2K have confirmed os-
cillations in the νµ− ντ sector with best-fit ∆m2
31= 2.1 × 10−3eV2and sin22θ23= 1 ,
the combined data from the solar neutrino experiments and the latest spectacular results
from the KamLAND reactor experiment can be explained only by oscillations of νe(¯ νe) with
21= 8.0×10−5eV2and sin2θ12= 0.31 . Thus, having established the existence
of neutrino mass and mixing, these results have proclaimed a new era in Neutrino Physics,
where the emphasis has shifted from unveiling the reasons for solar/atmospheric neutrino
deficit to making increasingly precise measurements of neutrino oscillation parameters, a
prerequisite for any progress in our understanding of the origin of the patterns of solar and
atmospheric neutrino mass and mixing.
In the present article we discuss the possibilities of high precision measurement of the
solar and atmospheric neutrino oscillation parameters with future data from solar, reactor,
∗Electronic address: email@example.com
atmospheric and long baseline neutrino experiments. We expound the possibility of measur-
ing the deviation of θ23from maximality using earth matter effects in atmospheric neutrinos.
Finally we study the feasibility of using 0νββ experiments to determine the neutrino mass
hierarchy and point the necessity for better sin2θ12measurements for accomplishing it.
II.SOLAR NEUTRINO OSCILLATION PARAMETERS
A.Bounds from Current Solar and Reactor Experiments
Data set usedRange of ∆m2
Spread in ∆m2
Spread in sin2θ12
only solar (3.3 − 18.4)×10−5eV2
69%0.24 − 0.4126%
solar + 766.3 Ty KL(7.2 − 9.2)×10−5eV2
12%0.25 − 0.3922%
solar(SNO3) + 766.3 Ty KL (7.2 − 9.2)×10−5eV2
12%0.26 − 0.3718%
solar(SNO3) + 3KTy KL(7.6 − 8.6)×10−5eV2
6% 0.26 − 0.3616%
TABLE I: The 3σ allowed ranges and % spread of ∆m2
21and sin2θ12from a 1 parameter fit.
We present in Table I  the 3σ allowed range of ∆m2
21and sin2θ12that we have from the
current available solar and reactor neutrino data. We also show the corresponding “spread”
spread =prmmax− prmmin
× 100 .(1)
Sensitivity of KamLAND to the shape and hence distortion of the reactor ¯ νeinduced positron
spectrum, gives the experiment a tremendous ability to constrain ∆m2
21. However, we can
see from Table I that it is not much sensitive to the mixing angle θ12. The average energy
and distance in KamLAND corresponds to sin2(∆m2
21L/4E) ≈ 0, i.e, it is situated close to
a Survival Probability MAXimum (SPMAX). This means that the coefficient of the sin22θ12
term in PKL
¯ e¯ e
is relatively small, smothering the sensitivity of KamLAND to θ12[4, 5].
Also given in Table I are the expected bounds on ∆m2
21and sin2θ12after the prospective
future data from the running SNO and KamLAND experiments become available. For SNO
we assume that the third and final phase of the experiment will measure the same Neutral
Current (NC) and Charged Current (CC) rates as the salt phase, but with reduced errors of
6% and 5% respectively. For KamLAND we simulate the 3 kTy data at ∆m2
eV2and sin2θ12= 0.3 and use a systematic error of 5%. The uncertainty in ∆m2
% error in pp rate
% error in pp rate
pp rate = 0.68
pp rate = 0.72
pp rate = 0.77
3σ allowed band
2σ allowed band
90% C.L. allowed band
1σ allowed band
Solar + KL + pp
FIG. 1: Sensitivity plot showing the allowed range of sin2θ12as a function of the error in pp rate
for three different values of measured pp rate.
to reduce to 6% with 3 kTy data from KamLAND. The uncertainty in sin2θ12is expected
to improve after the phase-III results from SNO to 18%. This would improve to about 16%
if the SNO phase-III projected results are combined with the 3 kTy simulated data from
KamLAND. However, we note that even with the combined data from phase-III of SNO
and 3 kTy statistics from KamLAND, the uncertainty on sin2θ12would stay well above the
10-15% level at 3σ.
B. Precision Expected from Next Generation Experiments
In this sub-section we explore the possibility of new solar and reactor neutrino experiments
and make a comparative study of their sensitivity to ∆m2
The Generic pp experiment: Sub-MeV solar neutrino experiments (LowNu experi-
ments) are being planned for detecting the pp neutrinos using either charged current reac-
tions (LENS, MOON, SIREN) or electron scattering process (XMASS, CLEAN, HERON,
MUNU, GENIUS) . It has been realized that high precision measurement of the pp
neutrino flux can be instrumental for more accurate determination of the neutrino mix-
ing parameter, which as we have seen in the earlier section, will not be determined to an
accuracy of below 10-15% by the current set of experiments.
0.1 0.30.5 0.70.9
99.73 % C.L. from 3 kTy KamLAND
shaded contours are for
5 years of SK−Gd
FIG. 2: The 90%, 95%, 99%, 99.73% C.L. allowed regions in the ∆m2
21− sin2θ12 plane from
an analysis of prospective data, obtained in 5 years of running of the SK-Gd detector. The open
contours shows the 99.73% C.L. allowed areas expected from 3 kTy of KamLAND data.
We consider a generic νe-e scattering experiment with a threshold of 50 keV. This exper-
iment will be sensitive to the pp neutrinos. In Fig. 1 we plot the two-generation allowed
range of sin2θ12from the global analysis of KamLAND and solar data including the LowNu
pp rate, as a function of the error in the pp measurement. We consider three illustrative pp
rates of 0.68, 0.72 and 0.77 and vary the experimental error in the pp measurement from 1
to 5%. By adding the pp flux data in the analysis, the error in sin2θ12determination reduces
to 14% (19%) at 3σ for 1% (3%) uncertainty in the measured pp rate. Performing a similar
three-neutrino oscillation analysis we have found that, as a consequence of the uncertainty
on sin2θ13, the error on the value of sin2θ12increases correspondingly to 17% (21%) .
The SK-Gd reactor experiment:
There has been a proposal to dope Super-
Kamiokande (SK) with Gd by dissolving 0.2% of gadolinium chloride in the SK water .
SK gets the same reactor flux as KamLAND, and in principle could detect these reactor ¯ νe
through their capture on protons, which releases a positron and a neutron. The detector
has to tag these neutrons through delayed coincidence to be able to unambiguously observe
the reactor ¯ νe. However, neutron capture on proton releases a 2.2 MeV γ, which is unde-
tectable in SK. Addition of Gadolinium in SK would circumvent this problem since neutron
capture on gadolinium releases a 8 MeV γ cascade, which is above the SK threshold and
40 50 60708090100
40 50 60 7080 90100
FIG. 3:Sensitivity plots for the SPMIN reactor experiment showing the 1σ, 1.64σ, 2σ, and 3σ
range of allowed values for sin2θ12as a function of the baseline L.
hence possible to observe. With its 22.5 kton of ultra pure water, the SK detector has about
1.5×1033free protons as target for the antineutrinos coming from various reactors in Japan.
Therefore for the same measurement period, the SK-Gd reactor experiment is expected to
have about 43 times the statistics of the KamLAND experiment.
We simulate the reactor ¯ νedata expected in the proposed SK-Gd detector at ∆m2
8.3 × 10−5eV2and sin2θ12= 0.27 and divide it into 18 energy bins, with a visible energy
threshold of 3 MeV and bin width of 0.5 MeV. The results of the statistical analysis of this
prospective data is presented in Fig. 2 for 5 years of exposure. Also shown in the figure for
comparison is the 99.73% C.L. line expected from a 3 kTy prospective data in KamLAND.
We can clearly see that the precision expected in both ∆m2
21and sin2θ12is much better in
SK-Gd. The spread in ∆m2
21and sin2θ12expected from 5 years of data in SK-Gd would be at
the level of 2-3% and 18% respectively at 3σ. This can be compared with the corresponding
spread of 6% and 32% expected from 3 kTy of KamLAND data.
The SPMIN reactor experiment: The solar mixing angle could be measured with
unprecedented accuracy in a reactor experiment with the baseline tuned to the Survival
Probability MINimum (SPMIN). This idea was proposed in , where the optimal baseline
for the most accurate measurement of sin2θ12for the old low-LMA best-fit ∆m2
eV2 was found to be 70 km from a statistical analysis.