1. Determination of Neutrino Mass Hierarchy at an Intermediate Baseline
Liang Zhan
Liang Zhan

2. Outline
Introduction to neutrino mass hierarchy and determination methods
Reactor neutrino E and L/E spectrum
Fourier transform to neutrino L/E spectrum
Features of Fourier transform spectrum
Summary
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3. Neutrino mass hierarchy
Three unknowns in neutrino oscillation parameters:
1. delta-CP phase
2. theta13 value
3. mass hierarchy (sign of )
Global fit in 2007
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4. Several neutrino mass hierarchy determination methods
Accelerator neutrino experiments (T2K, NOvA, T2KK)
Utilize matter effect of neutrino and antineutrino at long baseline
Require large theta13 value (i.e )
Affected by delta-CP and mass hierarchy degeneracy
Experiment at a ‘magic baseline’ (~7000 km, CERNINO)
No delta-CP and mass hierarchy degeneracy problem
Require high intensity beam (neutrino factory, beta-beam…)
Reactor neutrino experiment
Precision measurement of spectrum distortion due to oscillation of non zero theta13 value.
This talk introduces a robust method using Fourier transform to reactor neutrino spectrum and analysis of oscillation frequency distribution.
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5. Reactor neutrino production
Electron antineutrino flux from reactor
Reactor fuels
U235, Pu239, U238, Pu241
P. Vogel’s parameterization formula
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6. Reactor neutrino detection
IBD cross section with proton in liquid scintillator detector
P. Vogel’ s formula at first order of 1/M
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7. Reactor neutrino oscillation
Oscillation probability
P21 dominates the oscillation, effect of mass hierarchy is suppressed by small value of theta13
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8. Observed neutrino spectrum
Peak of energy spectrum is around 3.6 MeV, oscillation maximal is about 60 km
Energy spectrum
No oscillation, Pee = 1
EL/E
No so sensitive to mass hierarchy
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9. Why use L/E spectrum?
In L/E space, oscillation P is periodic function with oscillation ‘frequency’ proportional to deltaMsq
With Fourier transform to L/E spectrum, there will be three frequency peaks at deltaMsq21, deltaMsq32 and deltaMsq31.
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10. Fourier transform spectrum
t=L/E, F(t) is neutrino L/E spectrum
Calculate |FT(w)| distribution
P21 oscillation is separated from P32 and P31 oscillation.
P32 is a small peak adjoin to P31 peak.
Determination of mass hierarchy by the relative position of P32 and P31 peak.
Liang Zhan

11. Fourier sine and cosine transform
t = L/E
Combination of FST(w) and FCT(w) is more informative than |FT(w)| because of including the phase information.
We will study the P31 and P32 components of the FCT and FST spectrum in the P31 and P32 dominative frequency range:
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12. FCT spectrum Red line: P31 (symmetric shape)NH
Red line: P31 (symmetric shape)
Blue line: P32 (symmetric shape)
Black line: P31+P32 (symmetry-breaking)
For NH, P32 is at the left valley of P31; while for IH, P32 is at the right valley of P31. IN
Liang Zhan

13. FST spectrum Red line: P31 (symmetric shape)
normal NH
Red line: P31 (symmetric shape)
Blue line: P32 (symmetric shape)
Black line: P31+P32 (symmetry-breaking)
P32 counteracts with the valley or peak of P31.
inverted IN
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14. FCT and FST spectrum
The features can be used to determine the mass hierarchy.
P31 and P32 is distinctive.
1 – P21 oscillation frequency power is low.
The full oscillation FCT and FST spectrums approximate to be P31 + P32
Baseline = 60 km
Best fit value for neutrino mixing paras
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15. Features of FCT and FST spectrum
P31 and P32 spectrum is symmetric, while P31 +P32 is symmetric breaking, as well as Pee .
For NH, P31 is on the right of P32
For IH, P31 is on the left of P32
To quantify the symmetry breaking, we define parameters RL and PV
RV and LV is the amplitude of the right and left valley in FCT spectrum.
P and V is the amplitude of the peak and valley in FST spectrum.
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16. RL and PV values
Because of the different ways of symmetric breaking for NH and IH, we have.
For NH, RL>0 and PV>0
For IH, RL<0 and PV<0 V P VR VL VL VR
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17. Baseline and theta13 Baseline: 46-72 km Sin^2(2theta13): 0.005--0.05
Other mixing parameters are global fit values.
Two clusters of RL and PV values show the sensitivity of mass hierarchy determination.
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18. At low sin^2(2theta13) value
Still sensitive to mass hierarchy when sin^2(2theta13)=0.005
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19. Further work
Further work considering detailed experiment set-up is on-going.
Backgrounds
Statistics error
Energy resolution
Energy scale error …
Preliminary results show this method has capability to determinate mass hierarchy when sin^2(2theta13)>0.02.
Liang Zhan

20. Summary
Fourier sine (cosine) transform is applied to reactor neutrino L/E spectrum.
P21 oscillation is separated from P32 and P31 in FCT and FST spectrum due to different frequencies (deltaMsq).
FST and FCT spectra are very sensitive to mass hierarchy.
Analytic result shows the mass hierarchy determination capability when sin^2(2theta13) = 0.005
Considering experimental details, it maybe determine mass hierarchy when sin^2(2theta13) = 0.02.
Liang Zhan