Probing Neutrinos by DSNB(Diffuse Supernova Neutrino Background) Observation

Probing Neutrinos by DSNB(Diffuse Supernova Neutrino Background) Observation Sovan Chakraborty Saha Institute of Nuclear Physics, Kolkata JCAP09(2008)013 (S C, Sandhya Choubey, Basudeb Dasgupta, Kamales Kar) Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.1

Plan of the Talk: Core Collapse Supernova and Neutrino Emission Neutrino Mixing in Supernova Diffuse Supernova Neutrino Background(DSNB) Collective Neutrino Process and DSNB Remarks and Future Direction Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.2

Core Collapse Supernova and Neutrino Emission Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.3

Core Collapse SN and Neutrino Supernova Explosions are accompanied by Neutrinos These Neutrinos may play a crucial role in SN explosion. Neutrinos cross SN mantle and envelope Neutrinos may get affected by earth matter. Interaction with matter constituent particles are very crucial Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.4

Neutrino Mixing in Supernova: Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.5

Neutrino Mixing in Supernova: ρ L (10 1 g/cc) In Neutrino channel only. ρ H (10 4 g/cc) In Neutrino(antineutrino) channel for NH(IH). Flavor conversion depends on Flip Probability P J. (A.S.Dighe, A.Yu.Smirnov, PRD 62,2000) NH IH τ µ,, H L 3m 2m 1m H e τ, µ τ,, H 2m 1m 3m H L e µ, e µ, e τ, L H n H L n n n e -n n e e e e e Sovan Chakraborty (a) NuHoRIzons09 HRI 7th-9th (b) January 2009 p.6

Flip Probability Flip Probability is expressed as P ij = e ( γ sin2 θ ij ) Adiabaticity : γ = π m2 ji E dlnn e dr 1 r=r mva Adiabatic limit dlnn e dr Small = P ij 0 Non-Adiabatic limit dlnn e dr large / θ ij small = P ij 1 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.7

Flip Probability for SN P 12 (P L ) 0 ; P12 ( P L ) 0 P 13 (P H ) depends on sin 2 θ 13 (A.Bandyopadhyay et al, hep-ph/0312315) P L 1 0.8 0.6 0.4 0.2 tan 2 θ 12 = 0.42 tan 2 θ 12 = 0.28 tan 2 θ 12 = 0.72 P L P H 0 10-12 10-11 10-10 10-9 10-8 10-7 m 2 21 /ev2 0.6 0.5 tan 2 θ 12 = 0.42 0.4 tan 2 θ 12 = 0.28 0.3 tan 2 θ 12 = 0.72 0.2 0.1 0 10-12 10-11 10-10 10-9 10-8 10-7 m 2 21 / ev2 1 Atm range 0.8 0.6 tan 2 θ 13 = 10-6 tan 2 θ 13 = 10-5 0.4 tan 2 θ 13 = 10-4 0.2 tan 2 θ 13 = 10-3 0 10-7 10-6 10-5 10-4 10-3 10-2 10-1 m 2 31 /ev2 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.8

Flux at the detector SN neutrino flux in the detector F β = α F 0 αp αβ P αβ = i P M αi P L iβ ; P M αi = j U m αj 2 P ij ; P ij = i m j 2 where i,j = 1,2,3 ; α,β = e,µ,τ Earth Matter effect not considered Piβ = U iβ 2 L P αβ = i P M αi U iβ 2 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.9

TABLE The Probabilities P M ei and P M xi for three Anti-Neutrinos: Mass hierarchy i Pei M Pxi M NORMAL(NH) 1 1 0 2 0 1 3 0 1 INVERTED(IH) 1 P 13 1-P 13 2 0 1 1 1-P 13 P 13 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.10

FLUX NH Flux of Electron Antineutrino in Detector for NH F e = P ee F 0 e + (1 P ee )F 0 x P ee = U e1 2 F e = U e1 2 F 0 e + (1 U e1 2 )F 0 x Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.11

FLUX IH Flux of Electron Antineutrino in Detector for IH F e = P ee F 0 e + (1 P ee )F 0 x P ee = P 13 U e1 2 + (1 P 13 ) U e3 2 F e = P 13 U e1 2 F 0 e + (1 P 13 U e1 2 )F 0 x Can be written as F e = (1 U e1 2 ) F 0 x + U e1 2 ( P 13 F 0 e + (1 P 13 ) F 0 x) Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.12

FLUX IH F e = (1 U e1 2 ) Fx 0 + U e1 2 ( P 13 Fe 0 + (1 P 13 ) Fx) 0 In the Non Adiabatic limit P 13 = 1 Electron Antineutrino flux in the Detector for IH F e = U e1 2 F 0 e + (1 U e1 2 )F 0 x Same as NH Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.13

FLUX IH F e = (1 U e1 2 ) F 0 x + U e1 2 ( P 13 F 0 e + (1 P 13 ) F 0 x) In the Adiabatic limit P 13 = 0 Electron Antineutrino Flux for IH F e = F 0 x Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.14

NEUTRINO FLUX(NH) F e = U e1 2 F 0 x + (1 U e1 2 )( P 13 F 0 e + (1 P 13 ) F 0 x) In the Non-Adiabatic limit : P 13 = 1 F e = U e1 2 F 0 x + (1 U e1 2 )F 0 e In the Adiabatic limit : P 13 = 0 F e = F 0 x Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.15

NEUTRINO FLUX(IH) INVERTED HIERARCHY : F e = U e1 2 F 0 x + (1 U e1 2 ) F 0 e Same as NH with P 13 = 1 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.16

Flux in both neutrino and antineutrino channel can not distinguish between NH and IH for small θ 13 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.17

Diffuse Supernova Neutrino Background(DSNB) : Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.18

Diffuse SN Neutrino Background(DSNB) Neutrinos emitted from all past SN explosions fill the universe as a diffuse background,ie (DSNB). To estimate DSNB,model of neutrino spectrum from each SN(F 0 ) and SN Formation Rate(R SN ) are required. R SN is taken to be proportional to R SF,DSNB will give information on R SF DSNB may also be able to decide the Hierarchy. Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.19

DSNB: Present Number density of DSN( e ) in E and E + de from redshift z to z+dz is dn = R SN (z)(1 + z) 3 dt dz dzdn (E ) de de (1 + z) 3 = R SN (z) dt dz dzdn (E ) de (1 + z) de E =E (1+z) is the energy at redshift z,observed as E. Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.20

DSNB: Present Number density of DSN( e ) in E and E + de from redshift z to z+dz is dn = R SN (z)(1 + z) 3 dt dz dzdn (E ) de de (1 + z) 3 = R SN (z) dt dz dzdn (E ) de (1 + z) de R SN (z) is the supernova rate per comoving volume at z. Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.21

DSNB: Present Number density of DSN( e ) in E and E + de from redshift z to z+dz is dn = R SN (z)(1 + z) 3 dt dz dzdn (E ) de de (1 + z) 3 = R SN (z) dt dz dzdn (E ) de (1 + z) de R SN (z)(1 + z) 3 is the supernova rate per physical volume at z. Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.22

DSNB: Present Number density of DSN( e ) in E and E + de from redshift z to z+dz is dn = R SN (z)(1 + z) 3 dt dz dzdn (E ) de de (1 + z) 3 = R SN (z) dt dz dzdn (E ) de (1 + z) de dn (E )/de number spectrum of in one SN explosion. Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.23

DSNB: Present Number density of DSN( e ) in E and E + de from redshift z to z+dz is dn = R SN (z)(1 + z) 3 dt dz dzdn (E ) de de (1 + z) 3 = R SN (z) dt dz dzdn (E ) de (1 + z) de (1 + z) 3 For expansion of universe. Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.24

DSNB Flux: Thus the differential number flux of DSN df de = c dn de = c H 0 Zmax 0 R SN (z) dn (E ) de dz (Ω m (1 + z) 3 + Ω λ ) 1/2 As from Friedmann equation dz dt = H 0(1 + z)(ω m (1 + z) 3 + Ω λ ) 1/2 Ω m = 0.3 ; Ω λ = 0.7 ; H 0 = 70 h 70 km s 1 Mpc 1 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.25

DSNB Flux: Thus the differential number flux of DSN df de = c H 0 Zmax 0 R SN (z) dn (E ) de dz (Ω m (1 + z) 3 + Ω λ ) 1/2 Ω m = 0.3 ; Ω λ = 0.7 ; H 0 = 70 h 70 km s 1 Mpc 1 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.26

SN Rate and IMF: R SN (z) is obtained from SFR and IMF(ϕ(m)). 125M 8M R SN (z) = R SF (z) ϕ(m)dm 125M ϕ(m)mdm 0 BG IMF { m 2.15 (m > 0.5M J ) ϕ(m) m 1.50 (0.08M J < m < 0.5M J ) [I.K.Baldry, K.Glazebrook, ApJ.593.258.(2003)] For BG IMF R SN (z) = 0.0132 R SF (z)m 1 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.27

Star Formation Rate: R SF (z) (rate per comoving volume) is taken as R SF (z) = { R SF (0)(1 + z) 3.44 z < 0.97 R SF (0)(1.97) 3.70 (1 + z) 0.26 0.97 < z < 4.48 R SF (0)(1.97) 3.70 (5.48) 7.54 (1 + z) 7.8 z < 4.48 R SF (0) = 0.0197 M yr 1 Mpc 3 [A.M.Hopkins, J.F.Beacom, ApJ.651.142.(2006)] Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.28

SN Number Spectrum: The initial differential number Spectrum: dn 0 α de α ) 1+β α = (1 + β α Γ(β α + 1) Φ α Ē α ( Eα Ē α ) β α exp ( (1 + β α Ē α α ) E ) [Keil et al, ApJ.590,971(2003)] Fitting parameter for SN neutrino spectrum: Model Ē e Ē e Ē x β e β x Φ e /Φ x Φ /Φ x (Mev) (Mev) (MeV) (erg) (erg) LL 12 15 24 3 4 2.0 1.6 G1 12 15 18 3 4 0.8 0.5 G2 12 15 15 3 4 0.5 0.5 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.29

DSNB Flux Vs E : 2.5 Number Flux[cm -2 sec -1 MeV -1 ] 2 1.5 1 0.5 Without Collective Effects e IH(P 13 = 0) NH IH (P 13 = 1) 0 0 10 20 30 40 Antineutrino Energy [MeV] Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.30

DSNB Flux Vs E : Number Flux [cm -2 sec -1 Mev -1 ] 3 2.5 2 1.5 1 0.5 Without Collective Effects NH (P 13= 1) NH (P 13 = 0) e IH 0 0 10 20 30 40 Neutrino Energy [MeV] Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.31

Collective Neutrino Flavor Transformation and DSNB Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.32

Collective Neutrino Flavor transition Neutrino-Neutrino interaction inside SN is not negligible. neutrino-neutrino interactions can lead to conversion of neutrinos and antineutrinos of different energies with same frequency = Collective Oscillation After a few hundred kilometers these interaction effects become smaller and eventually ends with Swapping of e and τ above a critical Energy(E c ) in IH Complete swapping of the e and τ IH No effect on flux if the Hierarchy is Normal (NH). Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.33

Inside Supernovae Collective Flavor transitions dominates at about 400 km. MSW resonances happens at about 10 4 km. Thus MSW and Collective neutrino resonances in Supernovae happen independently. Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.34

Level Crossing in Supernova: With out Collective Conversion NH IH τ µ,, H L 3m 2m 1m H e τ, µ τ,, H 2m 1m 3m H L e µ, e µ, e τ, L n e H n e n e H -n e L n e n e (a) (b) Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.35

µ e τ Collective Neutrino Flavor transition,, H 2m 1m 3m H L τ µ e,, H L -n n e e n e (d) IH Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.36

FLUX IH(COLLECTIVE EFFECT) Flux of Electron type Antineutrino in Detector for IH Flux without Collective Conversion F e = (1 U e1 2 )F 0 x + U e1 2 (P 13 F 0 e + (1 P 13 )F 0 x) Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.37

FLUX IH(COLLECTIVE EFFECT) Flux of Electron type Antineutrino in Detector for IH Flux without Collective Conversion F e = (1 U e1 2 )Fx 0 + U e1 2 (P 13 Fe 0 + (1 P 13 )Fx) 0 Flux with Collective Conversion F e = (1 U e1 2 )Fx 0 + U e1 2 ((1 P 13 )Fe 0 + P 13 Fx) 0 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.38

FLUX IH(COLLECTIVE EFFECT) Flux of Electron type Antineutrino in Detector for IH Flux without Collective Conversion F e = (1 U e1 2 )Fx 0 + U e1 2 (P 13 Fe 0 + (1 P 13 )Fx) 0 Flux with Collective Conversion F e = (1 U e1 2 )Fx 0 + U e1 2 ((1 P 13 )Fe 0 + P 13 Fx) 0 In Non Adiabatic Limit P 13 = 1 Different than NH. F e = F 0 x Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.39

FLUX IH(COLLECTIVE EFFECT) Flux of Electron type Antineutrino in Detector for IH Flux without Collective Conversion F e = (1 U e1 2 )Fx 0 + U e1 2 (P 13 Fe 0 + (1 P 13 )Fx) 0 Flux with Collective Conversion F e = (1 U e1 2 )Fx 0 + U e1 2 ((1 P 13 )Fe 0 + P 13 Fx) 0 In Adiabatic Limit P 13 = 0 F e = U e1 2 F 0 e + (1 U e1 2 )F 0 x Same as NH Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.40

DSNB Flux Vs E : 2.5 Number Flux[cm -2 sec -1 MeV -1 ] 2 1.5 1 0.5 With Collective Effects e IH(P 13 = 1) NH IH (P 13 = 0) 0 0 10 20 30 40 Antineutrino Energy [MeV] Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.41

FLUX IH(COLLECTIVE EFFECT) Flux of Electron type neutrino in Detector for IH Flux without Collective Conversion F e = (1 U e1 2 )F 0 e + U e1 2 F 0 x Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.42

FLUX IH(COLLECTIVE EFFECT) Flux of Electron type neutrino in Detector for IH Flux without Collective Conversion F e = (1 U e1 2 )F 0 e + U e1 2 F 0 x Flux with Collective Conversion F e = { (1 Ue1 2 )F 0 e + U e1 2 F 0 x (E < E c ) F 0 x (E > E c ) Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.43

DSNB Flux Vs E : 3 With Collective Effects NH(P 13 =1) Number Flux [cm -2 sec -1 Mev -1 ] 2.5 2 1.5 1 0.5 e NH (P 13 =0) IH 0 0 10 20 30 40 Neutrino Energy [MeV] Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.44

Detection of DSNB : Water Cherenkov Detector: SK,HK Dominant Reaction e + p e + + n Liquid-scintillator Detector: example LENA. Dominant Reaction e + p e + + n Liquid-Argon(Ar) Detector: GLACIER. Dominant Reaction e + 40 Ar e + 40 K Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.45

DSNB Background in Detectors e flux (cm -2 s -1 MeV -1 ) 10 7 10 6 10 5 10 4 8 B 10 3 10 2 hep 10 1 10-1 10-2 SRN atm 10-3 10 20 30 40 50 60 70 80 90 100 E (MeV) Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.46

Energy Window of Different Detectors For Different Detectors the window of detection SK GDSK LENA 19.3 MeV <E e < 30.0 MeV 10.0 MeV <E e < 30.0 MeV 10.0 MeV <E e < 25.0 MeV LIQUID Ar 20.0 MeV <E e < 40.0 MeV Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.47

NO OF EVENTS(per year)for DIFFERENT DETECTORS FOR DIFFERENT SPECTRUM MODELS odel Hierarchy SK GDSK HK GDHK LENA 1 NH IH(P 13 = 0) 1.7 4.9 67.8 196.0 6.4 IH(P 13 = 1) 2.7 7.4 109.6 296.0 9.5 2 NH IH(P 13 = 0) 1.1 3.5 42.6 139.5 4.6 IH(P 13 = 1) 1.5 5.1 58.5 205.7 6.9 L NH IH(P 13 = 0) 2.5 6.2 98.2 246.0 7.7 IH(P 13 = 1) 4.4 8.9 175.7 356.0 10.6 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.48

NO OF EVENTS(per year)for LIQUID Ar DETECTORS FOR DIFFERENT SPECTRUM MODELS Hierarchy G1 G2 LL NH(P 13 = 1) 3.6 1.7 7.3 NH(P 13 = 0) 4.9 2.3 9.9 IH 4.9 2.3 9.9 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.49

No of Events [22.5 kton.yr.mev] No of Events [1000 kton.yr.mev] No of Events [50 kton.yr.mev] 2 1.5 1 0.5 0 60 50 40 30 20 10 NH SK NH SK 0 10 20 30 40 50 NH HK IH HK 0 0 10 20 30 40 50 2 1.5 1 0.5 GD SK LOWER LIMIT GD HK LOWER LIMIT LENA LOWER LIMIT SK LOWER LIMIT HK LOWER LIMIT LENA UPPER LIMIT SK / GDSK UPPER LIMIT HK / GDHK UPPER LIMIT NH LENA IH LENA 0 0 10 20 30 40 50 Positron Energy (MeV) Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.50

Liquid Argon: GLACIER No of Events [100 kton.yr.mev] 1 0.5 Liq Ar LOWER LIMIT IH Liquid Ar NH Liquid Ar Liq Ar UPPER LIMIT 0 10 20 30 40 50 Neutrino Energy [MeV] Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.51

3 2.5 2 1.5 0 0.2 0.4 0.6 0.8 1 P 13 8 7 6 5 0 0.2 0.4 0.6 0.8 1 P 13 No of Events [22.5 kton.yr] (-1) No of Events [22.5 kton.yr] (-1) 120 100 80 60 0 0.2 0.4 0.6 0.8 1 P 13 300 250 200 150 0 0.2 0.4 0.6 0.8 1 P 13 No of Events [1000 kton.yr] (-1) No of Events[ 1000 kton.yr] (-1) 6 5 4 3 No of Events[100 kton.yr] (-1) 10 9 8 7 6 SK GD SK HK GD HK LENA Liq Ar 0 0.2 0.4 0.6 0.8 1 P 13 2 0 0.2 0.4 0.6 0.8 1 P 13 NH IH IH WOC Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.52 No of Events [50 kton.yr.] (-1)

CONCLUSION Neutrino-Neutrino interaction in SN generates Collective Flavor transitions Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.53

CONCLUSION Neutrino-Neutrino interaction in SN generates Collective Flavor transitions Collective Flavor Conversion affects the SN as well as DSN Flux Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.54

CONCLUSION Neutrino-Neutrino interaction in SN generates Collective Flavor transitions Collective Flavor Conversion affects the SN as well as DSN Flux It would be possible to detect DSNB in future experiments like GDSK,HK,GDHK and can be used to probe hierarchy at small θ 13. Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.55

CONCLUSION Neutrino-Neutrino interaction in SN generates Collective Flavor transitions Collective Flavor Conversion affects the SN as well as DSN Flux It would be possible to detect DSNB in future experiments like GDSK,HK,GDHK and can be used to probe hierarchy at small θ 13. Advantage with DSNB over usual SN events is repeatability. Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.56

THANK YOU Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.57

No of Events No of events in any Detector for DSNB is N = N T 0 0 df e (E e ) de e σ( e )ε( e )R(E e;t,e e;m )de e de e,m N T Number of target nucleons in the detector σ( e ) Cross section ε( e ) Efficiency of detector R(E e;t,e e;m ) Energy resolution function E e;t True Energy of positron/electron. E e;m Measured Energy of positron/electron. Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.58

Neutrino Oscillation in Matter Scattering of Neutrino in matter = Matter density dependent Potential. V e = 2G F (N e N n /2) ; V µ = V τ = 2G F N n /2 The evolution equation in Matter in the flavor basis is i d dt e µ = 2 12 cos 2θ + 2G 4E F N e 2 12 4E 2 12 4E 2 12 4E sin 2θ cos 2θ e µ Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.59

Neutrino Oscillation in Matter: Consider states where effective Hamiltonian is Diagonal A = e cosφ + µ sin φ B = e sin φ + µ cosφ where, the mixing angle φ is given by tan2φ = 2 H 12 H 22 H = 11 ( 2 12/2E) sin 2θ ( 2 12/2E) cos 2θ 2G F N e Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.60

Neutrino Oscillation in Matter: The conversion probability becomes where, P l, l (X) = sin 2 2φ sin 2 ( π X L mat ) L mat = 2π E A E B = 2π ( 2 12 cos 2θ ) 2 ( 2 2G 2E F N e + 12 2E ) 2 sin 2 2θ sin 2 2φ = 2 12 2E sin2 2θ (E A E B ) 2 Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.61

Neutrino Oscillation in Matter: ( P l, l (X) = sin 2 2φ sin 2 π X ) L mat sin 2 2φ = 2 12 2E sin2 2θ ( 2 12 cos 2θ ) 2 ( ) 2 2 2G 2E F N e + 12 2E sin 2 2θ At the density N e = 2 12 2E cos 2θ 2 2G F E = Maximal Mixing MSW Matter enhanced resonance condition( 2 m > 0) Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.62

Varying Density: Mass eigenstates in matter A = e cosφ + µ sin φ ; B = e sin φ + µ cosφ E B e µ A N e Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.63

Matter Effect in Antineutrino: For oscillation between two antineutrinos i d e = 2 12 cos 2θ 2G 4E F N 2 12 e 4E dt µ 2 12 sin 2θ 2 12 4E 4E sin 2θ cos 2θ e µ Mixing angle in matter for antineutrinos tan2φ = ( 2 12/2E) sin 2θ ( 2 12/2E) cos 2θ + 2G F N e 2 12 2E cos 2θ N e = 2 2G F E = Maximal Mixing MSW Matter enhanced resonance for Antineutrino ( 2 m < 0 ). Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.64

TYPE II SN AND NEUTRINO : Onion Shell like structure with Iron core at the center and burning of Si,S,O,C,He,H. Photodisintegration of Fe and Neutronisation reduce pressure support = Rapid Core Collapse Neutrino Trapping at a core density 10 11 gm/cc. Density of core ρ nuclmatter More contraction = Shock wave. Thermal from pair production revitalize stalled shock = SUPERNOVA Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.65

Vacuum Oscillation Solar and Atmospheric Neutrino experiments indicate Neutrinos are Massive. Mixing is the most sensitive probe of mass Mass eigenstate m is different than flavor eigenstate l. l = u lm m u lm =Mixing Matrix At time t l (t) = u lm m e ie mt Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.66

Vacuum Oscillation The conversion probability P l l (t) = l l (t) 2 = α,β u lα u l αu lβu l β cos[ 2πx L αβ φ ll αβ] (1) [c = 1, = 1;x t] where, φ ll αβ = arg(u lα u l α u lβ u l β) Oscillation length L αβ = 4π p m 2 α m 2 β = 4π p 2 αβ Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.67

Two Flavor vacuum Oscillation For 2 flavor the mixing matrix is U = cosθ sinθ sin θ cos θ Here U is a real unitary matrix. Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.68

Two Flavor vacuum Oscillation For 2 flavor the mixing matrix is U = cosθ sinθ sin θ cos θ Here U is real unitary matrix. Therefore, ( ) P l l (X) = sin 2 2θ sin 2 2 12 x 4E Sovan Chakraborty NuHoRIzons09 HRI 7th-9th January 2009 p.69