Determination of Neutrino Mass Hierarchy at an Intermediate Baseline Liang Zhan 2008-9-16 Liang Zhan

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 2008-9-16 Liang Zhan

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 2008-9-16 Liang Zhan

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. 2008-9-16 Liang Zhan

Reactor neutrino production Electron antineutrino flux from reactor Reactor fuels U235, Pu239, U238, Pu241 P. Vogel’s parameterization formula 2008-9-16 Liang Zhan

Reactor neutrino detection IBD cross section with proton in liquid scintillator detector P. Vogel’ s formula at first order of 1/M 2008-9-16 Liang Zhan

Reactor neutrino oscillation Oscillation probability P21 dominates the oscillation, effect of mass hierarchy is suppressed by small value of theta13 2008-9-16 Liang Zhan

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 2008-9-16 Liang Zhan

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. 2008-9-16 Liang Zhan

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. 2008-9-16 Liang Zhan

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: 2008-9-16 Liang Zhan

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 2008-6-6 Liang Zhan

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 2008-6-6 Liang Zhan

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 2008-9-16 Liang Zhan 14

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. 2008-9-16 Liang Zhan

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 2008-9-16 Liang Zhan

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. 2008-9-16 Liang Zhan

At low sin^2(2theta13) value Still sensitive to mass hierarchy when sin^2(2theta13)=0.005 2008-9-16 Liang Zhan

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. 2008-9-16 Liang Zhan

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. 2008-9-16 Liang Zhan