Ara N. Ioannisian YerPhI and ITPM, Armenia CERN

Transcription

1 Scanning the Earth s core with solar neutrinos at future very large neutrino detectors Ara N Ioannisian YerPhI and ITPM, Armenia CERN TAUP 2015, Turin

2

3 Dependance of average annual weight function on the nadir angle of neutrino trajectory(η is in radians) JUNO is on tropic Outer core is visable at SD site about 9% of time

4 Dependance of average annual weight function on the nadir angle of neutrino trajectory(ω is in radians) Outer core is visable at Kamioka site about 44 hours per day Kamioka, SD, Finland

5 Averaging over solar neutrino production size From the Earth 8 B neutrino production region in the Sun is seen as a disk where more neutrinos come from the center of the disk It turns out that that distribution can be appoximated as a normal one with a variance δ η : f (η, η) = 1 e (η η ) 2 2δη 2 = δ η 2π 1 e (L 2R cos η) 2 8δη 2 R2 sin2 η δ η 2π the change of the solar neutrino flux due to the eccentricity of the Earth orbit (±3%) must be taken into account

6 ϵ 2V ee m 2 21 where ϕ m x k x n ( ρ g cm 3 ( ev 2 l ν 330 xn dx m2 21 x k 2E )( ev 2 )( m 2 21 m 2 21 P N P D P D = f ( m 2 21, θ 12 ) 1 2 f ( m 2 21, θ 12 ) = )( E 10 MeV ) E km 10 MeV )( ) Ye 05 (cos 2θ 12 ϵ(x)) 2 + sin 2 2θ 12 L 2 cos 2 θ 12 sin2 2θ cos 2 θ 12 cos 2θ 12 0 dx V (x) sin ϕ m x L = (2P ee 1) P ee sin 2 2θ 12 cos 2θ 12 f ( m21 2, θ 12) 23 for tan 2 θ = 045 ( θ = 34 0 ) and m 2 = ev 2 (P ee 1/3)) V V cos(θ 13 ) 2 V 098

7 P D P ee = 1 2 (1 + cos 2 θ 12 cos 2θ) + s4 13

8 Averaging over neutrino energy A e = de g(e, E) P N P D P D A e = f ( m 2 21, θ 12 ) 1 2 L 0 dx V (x)f (L x) sin ϕ m x L, The decrease of F means that contributions from the large distances to the integral are suppressed Gaussian energy resolution function g(e, E ) = 1 σ (E E ) 2 2π e 2σ 2, F (L x) e Box like energy resolution function πσ(l x) 2( ) E lν 2 F (L x) 1 Q(L x) A e = 1 2σ E+σ E σ de P N P D P D sin Q(L x), Q(L x) 2πσ(L x) E l ν,

9 The attenuation factor F as function of (L x) (distance from detector) E = 10 MeV, σ = 1 MeV, and m 2 21 = ev 2

10 WC A e (T, η) = dt g(t, T ) T + m ede P ee (E)j B (E)( dσ νe e dt 2 dt g(t, T ) dσ T + m ede j B (E)(P νe e ee dt 2 dσ ναe dt ) + (1 P ee ) dσ ναe dt ) P ee = P N P D = ( 1 2 P ee) sin2 2θ 12 cos 2θ 12 dσ ν e e dt / dσν αe dt 6 L 0 dx V (x) sin ϕ m x L

11

12 T e = 13,12, 11 MeV

13 T e = 9,7, 5 MeV

14 SK First Indication of Terrestrial Matter Effects on Solar Neutrino Oscillation Phys Rev Lett 112, , 2014

15 SK recent result A= 32 ± 11 ± 05 and got m ev 2 2 sigma away from KamLAND m ev 2 FULL 3D analise of the data fit with Kamland m 2 = ev 2 make use periodograms look to the high energy edge of the spectrum

16 Liquid Argon A e (E) = de g(e, E ) σ νar (E ) f B8 (E ) P ee (E ) de g(e, E ) σ νar (E ) f B8 (E )P ee (E ) P ee = P N P D = (P ee 1 2 )sin2 2θ 12 cos 2θ 12 L 0 dx V (x) sin ϕ m x L

17

18 E=12 MeV

19

20

21 the change of the solar neutrino flux due to the eccentricity of the Earth orbit (±3%) must be taken into account Each bin mush cover nadir angle diapason larger then the visible sun size ( (η i+1 η i ) > 6 δ η ) if one choose the bins in such a way that in each bin (without regeneration effect) it is expected to have a equal detected neutrinos (η i+1 η i ) = y 0 /W (η i ) where W (η) is average annual weight function Then the χ 2 method gives χ 2 = 1 N n (y ( η i ) y 0 y 0 A(η i )) 2 i Here y i is number of registered neutrinos at the i-rd bin and A(η i ) is expected regeneration effect at nadir angle η i N is number of all detected neutrinos during the night time

22 Let rewrite it χ 2 = 1/N n (y ( η i ) y 0 ) 2 + y0 2 A(η i ) 2 + y0 2 A(η i ) 2y ( η i )A ( η i )) i During the run of variables ( m21 2 and θ 12) for minimization of χ 2 the second and thierd terms under the sum are averaged to y0 2Ā and y0 2Ā2 3/2 (Ā is an average value of relative change of the electron neutrino flux) And they are weakly depend on neutrino oscillation parametres Only the last term variate strongly and we may write the following periodogram n y ( η i )A ( η i ) i and look for its maximum for determination of solar 2 21 with high precision

23 Due to excellent energy resolution LiAr DUNE far detector may see deep layers of the Earth DUNE expected to detect about 100 solar neutrinos per day Even with 3 captured neutrinos per day DUNE can see the Day-Night effect with over 2 sigma in just one year It can determine solar m 2 with 10 % accuracy (or better) independent measurement of electron number density chemical composition of the Earth matter some lights on chemical composition of the Earth s core

24 LS, JUNO AI, A Smirnov PRD2015

25 The relative variations of the electron neutrino flux as function of the nadir angle of the neutrino trajectory Dotted (red) line shows A 0 e without averaging; solid (blue) line is A e which corresponds to the variations averaged over the energy spectrum of the 7 Be neutrinos Spherical symmetry of the Earth is assumed

26 with two zoomed regions: η = [058 65] (left) and [13 135] (right)

27 Effect of averaging over the production region of 7 Be neutrinos in the Sun The relative change of the electron neutrino flux for mantle crossing trajectories with η = (left) and (right) without (dotted line) and with (dash-dotted line) averaging

28 The relative change of the electron neutrino flux for the mantle crossing trajectories as the function of η for two different values of width of the 7 Be line which correspond to two different temperatures in the center of the Sun: Solid line for sun central temperature T = (solid line) degree (dashed line)

29 Summary WC detectors are shortsighted and cannot see deep layers of the Earth LS JUNO has excellent location (tropic) and will be able to see the core of the Earth LiAr DUNE has very good energy resolution, it can measure the electron number density profile of the Earth, chemical composition of the mantle, and chemical composition of the core

30 THANK YOU