PHYS 564 – Fall 2007
SOLAR NEUTRINOS
&
NEUTRINO OSCILLATIONS
12/03/2007*
Ozgur UNAL
Solar Neutrinos & Neutrino Oscillations
Standard Solar Model
Neutrino Oscillations
Solar Neutrino Experiments
– Homestake
– SAGE
– GALLEX/GNO
– SNO
Standard Solar Model (SSM)
SSM:
 The best physical
model of the Sun
 Describes the nuclear
reactions taking place
in the Sun (p-p chain
and CNO cycle)
 Most of the neutrinos
come from p-p chain
Standard Solar Model (SSM)
SSM:
 Neutrino fluxes and energy
spectrum can be predicted
by SSM
 First experiment
(Homestake) to detect
the solar neutrinos found
much less than predicted
Solar Neutrino Problem
SSM?
Neutrino Oscillations?
Neutrino Oscillations
 The flavor change of neutrinos suggests that they are not massless
 Eigenstates of the weak interaction,v f , are linear superpositions of
mass eigenstates, vi ,
v f  U fi vi
where, U is a unitary matrix
 For simplicity, consider a two mass eigenstates and two
corresponding flavor eigenstates,
 ve   cos  sin   v1 
   
 v   sin  cos   v 
 2 
  
 Time evolution of an electron neutrino with momentum p is,
ve (t )  cos eiE1t v1  sin  eiE2t v2
where E1 and E2 are the energies of the mass eigenstates,
mi2
2
2
2
Ei  p  mi  Ei  p 
2p
Neutrino Oscillations
 The probability of an electron neutrino remains an electron neutrino
after travelling a distance L is,
 2 2 
1

2
2  m2  m1 
 L
P(ve  ve )  ve (t ) ve (0)  1  sin (2 ) sin  ( E1  E2 ) L  1  sin (2 ) sin 
2

 4 E  
2
2
and the probability to observe a muon neutrino is,
 m 2  
 L 
P(ve  v )  sin (2 ) sin 
4
E
 

2
2
 The transition probability depends on the mixing angle, θ, mass
square difference, Δm2, the energy and the distance traveled for
vacuum oscillations
 In medium with constant density, neutrinos interact with matter
through electroweak interaction: V  2G Fn e
 This interaction changes the mixing angle and the effective mass of
the neutrino eigenstates: sin 2 (2 )  sin 2 (2 m ) and m  mm
Neutrino Oscillations
 The transition probability is maximum for a certain energy of the
neutrino and the electron density of matter
 Resonance condition:
2EV  cos(2 )m2
 If the density is not constant, the mixing angle and the effective
masses and the eigenstates change continuously
 Adiabatic conversion: If density is assumed to change very slowly,
some approximations can be made
 There are three effects for solar neutrinos on their way to Earth:
 Adiabatic conversion inside the Sun
 Loss of coherence of the neutrino state
 Oscillation of the neutrino mass states in the matter of the Earth
Solar Neutrino Experiments
Homestake Experiment:
 First SN experiment started in the mid 1960s by Ray Davis
 Used 615 tons of dry-cleaning fluid, C2Cl4
 The detection of neutrinos was achieved through the reaction,


ve  37Cl  e   37Ar
with 0.814 MeV energy threshold
Announced the first results in 1968:
One quarter of the predicted amount of SN
Took data between 1970-1995 and found,
ФCl = 2.56 ± 0.16 ± 0.16 SNU
whereas SSM prediction is,
ФCl (SSM) = 8.1 ± 1.3 SNU
1 SNU is equal to 10 36 captures
per target atom per second.
Solar Neutrino Experiments
SAGE:
 Russian-American Experiment started in 1990 at Baksan
Laboratory in Russia
 Used 50 tons of liquid gallium metal
 Based on the reaction,
ve  71Ga  e   71Ge
with 0.233 MeV threshold energy
 Data collected between the years 1990 and 2003 yielded,
ФGa = 66.9 ± 3.9 ± 3.6 SNU
whereas SSM prediction is,
ФGa (SSM) = 126 ± 10 SNU
Solar Neutrino Experiments
GALLEX:
 Another gallium based experiment started in 1991 at LNGS
 Used 30 tons of Ga in an aqueous acid solution (GaCl3-HCl)
 Obtained the following capture rate
between 1991 and 1997,
ФGa = 77.5 ± 6.2 ± 4.5 SNU
GNO:
 Successor of GALLEX
 Took data between 1998 and 2003,
ФGa = 62.9 ± 5.4 ± 2.5 SNU
SAGE/GALLEX/GNO:
 An overall analysis yields,
ФGa = 68.1 ± 3.75 SNU
Solar Neutrino Experiments
Sudbury Neutrino Observatory (SNO):
 Located in 2 km underground in Creighton mine in Canada
 Used 1,000 tons of heavy water (D2O)
in a 12 m diamater acrylic vessel
 Consists of 3 phases:
1) Phase 1: Only D2O
2) Phase 2: D2O + NaCl (2 tons)
3) Phase 3: D2O + NCDs
Solar Neutrino Experiments
SNO:
 Thanks to D2O, three types of interactions take place in the
vessel,
νe + d → p + p + e(CC)
νx + d → p + n + νx
(NC)
νx + e- → νx + e(ES)
 CC is only sensitive to electron neutrinos,
→ ФCC = øe
 NC is equally sensitive to all types of neutrinos,
→ ФNC = øe + øμτ
 ES is mainly sensitive to the electron neutrinos,
σ(νe) = 6.5*σ(νμτ)
→ ФES = øe + 0.15*øμτ
Solar Neutrino Experiments
SNO Phase 1:
SNO Phase 2:
Total 8B flux predicted by SSM: (5.69 ± 0.91)*10-6cm-2s-1
Concluding Remarks
 SSM seems to be the best solar model
 Success of the theory of neutrino oscillations in explaining the
Solar Neutrino Problem
 Neutrinos are not massless
 A global (Radiochemical + SNO +
KamLAND experiments) 2-flavor
neutrino oscillation analysis has
the best fit values:
m 2  8.0 00..64 10 5 eV 2
  33.922..24 deg
References
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12)
http://www.columbia.edu/~ah297/unesa/sun/sun-chapter4.html
http://www.sno.phy.queensu.ca/
http://www.physics.purdue.edu/Zope/courses/phys570E/posting/lecture/Files/lec21.ppt
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