The Solar Neutrino Problem

Introduction Experiment and their results Conclusion
The Solar Neutrino Problem
Project work in Space Physics
Martin Lahrz
Department of Physics
Umeå University
19 October 2009
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Overview
1 Introduction
Outline
Neutrinos
2 Experiment and their results
Homestake
SuperKamiokande
Sudbury Neutrino Observatory
3 Conclusion
Neutrino Oscillations
Outlook
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Neutrinos
The Standard Model of particle physics
Open letter to the group of radioactive people at the Gauverein
meeting in Tübingen signed by W. Pauli from Dec. 4, 1930
Dear Radioactive Ladies and Gentlemen,
As the bearer of these lines, to whom I graciously ask you to
listen, will explain to you in more detail, because of the
"wrong" statistics of the N- and Li-6 nuclei and the continuous
beta spectrum, I have hit upon a desperate remedy to save the
"exchange theorem" (1) of statistics and the law of
conservation of energy. Namely, the possibility that in the
nuclei there could exist electrically neutral
particles, which I will call neutrons, that have
spin 1/2 and obey the exclusion principle and that
further differ from light quanta in that they do not
travel with the velocity of light. The
mass of the neutrons should be of the same order of
magnitude as the electron mass and in
any event not larger than 0.01 proton
mass. - The continuous beta spectrum would then make
sense with the assumption that in beta decay, in addition to
the electron, a neutron is emitted such that the sum of the
energies of neutron and electron is constant.
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Neutrinos
Interactions
Now it is also a question of which forces act upon neutrons. For me, the most likely model for the neutron seems
to be, for wave-mechanical reasons (the bearer of these lines knows more), that the neutron at rest is a magnetic
dipole with a certain moment µ. The experiments seem to require that the ionizing effect of such
a neutron can not be bigger than the one of a gamma-ray, and then µ
is probably not allowed to be larger than e · (10 −13 cm).
But so far I do not dare to publish anything about this idea, and trustfully turn first to you, dear radioactive
people, with the question of how likely it is to find experimental evidence for such a neutron if it would have the
same or perhaps a 10 times larger ability to get through [material] than a
gamma-ray. [...]
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Neutrinos
The Standard Solar Model (SSM)
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Brief overview
1 Introduction
2 Experiment and their results
Homestake
SuperKamiokande
Sudbury Neutrino Observatory
3 Conclusion
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Homestake
Head
Raymond Davis, Jr.
John N. Bahcall
Period 1970-1994
Base
E min
ν e + 37 Cl → e − + 37 Ar
0.814 MeV
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Homestake
Head
Raymond Davis, Jr.
John N. Bahcall
Period 1970-1994
Base
E min
ν e + 37 Cl → e − + 37 Ar
0.814 MeV
Φ Cl (Homestake) = 2.56 ± 0.16 ± 0.16 SNU
while Φ Cl (SSM) = 7.6 +1.3
−1.1 SNU
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
SuperKamiokande
Head Masatoshi Koshiba
Period 1996-
Base ν e + e − → ν e + e −
E min
5 MeV
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
SuperKamiokande
Head Masatoshi Koshiba
Period 1996-
Base ν e + e − → ν e + e −
E min
5 MeV
(
Φ ES (SK) = 2.42 ± 0.06 +0.10
−0.07
(
while Φ ES (SSM) =
6.5 +0.14
−0.17
)
· 10 6 cm −2 s −1
)
· 10 6 cm −2 s −1
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Sudbury Neutrino Observatory
Head
Arthur B. McDonald
Period 1999-2006
Base
E min
ν x + e − → ν x + e −
d + ν e → p + p + e −
d + ν x → ν x + p + n
5 MeV
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Sudbury Neutrino Observatory
Head
Arthur B. McDonald
Period 1999-2006
Base
E min
ν x + e − → ν x + e −
d + ν e → p + p + e −
d + ν x → ν x + p + n
5 MeV
(
Φ total =
5.54 +0.33
−0.31 +0.36
−0.34
)
· 10 6 cm −2 s −1
Φ e = (1.76 ± 0.05 ± 0.09) · 10 6 cm −2 s −1
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Brief overview
1 Introduction
2 Experiment and their results
3 Conclusion
Neutrino Oscillations
Outlook
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Neutrino Oscillations
A short introduction
Flavor α = e, µ, τ and mass i = 1, 2, 3 eigenstates are not the
same ⇒ linear combination
|ν α 〉 = U αi |ν i 〉
Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix U describes
charged-current interaction (beta decay)
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Neutrino Oscillations
A short introduction
Flavor α = e, µ, τ and mass i = 1, 2, 3 eigenstates are not the
same ⇒ linear combination
|ν α 〉 = U αi |ν i 〉
Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix U describes
charged-current interaction (beta decay)
Interference through propagation as plane wave (vacuum)
|ν i (t)〉 = e −i(E i t− #» p i · #» x ) |ν i (0)〉 = e −im2 i t/2E |ν i (0)〉
leads to transition probability
(
P α→β = |〈ν β (t) |ν α (0)〉| 2 ∆m
≈ sin 2 2θ sin 2 2 )
L
, (α = e, β = µτ)
4E
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Neutrino Oscillations
Matter effects
Assume two types of neutrinos. Equation of motion:
i d dt |ν〉 = 1 (
−
∆m 2
2 H |ν〉 with H = 4E cos 2θ )
∆m 2
4E
sin 2θ
∆m 2
4E sin 2θ ∆m 2
4E cos 2θ
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Neutrino Oscillations
Matter effects
Assume two types of neutrinos. Equation of motion:
i d dt |ν〉 = 1 (
−
∆m 2
2 H |ν〉 with H = 4E cos 2θ )
∆m 2
4E
sin 2θ
∆m 2
4E sin 2θ ∆m 2
4E cos 2θ
But: matter changes Hamiltonian
(
−
∆m 2
H = 4E cos 2θ + √ )
∆m
2G F N 2
e 4E
sin 2θ
∆m 2
4E sin 2θ ∆m 2
4E cos 2θ
⇒ resonances, Mikheev-Smirnov-Wolfenstein (MSW) effect
⇒ Day/night asymmetry
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Outlook
Fit Standard Solar Model to neutrino flux
8 B flux since Φ( 8 B) ∝ T 25
“monoenergetic” neutrinos 7 Be, pep
Registrate cosmic events, e.g. supernovas
Improve Standard Model of particle physics
Martin Lahrz
Solar Neutrino Problem

Introduction Experiment and their results Conclusion
Thank you for your attention.
Martin Lahrz
Solar Neutrino Problem

Bibliography
Figures
Bibliography I
The Super-Kamiokande Collabora al.
Measurements of the solar neutrino flux from super-kamiokande’s first 300
days.
ERRATUM-IBID., 81:4279, 1998.
John N. Bahcall and M. H. Pinsonneault.
Solar models with helium and heavy element diffusion, 1995.
John N. Bahcall and Aldo M. Serenelli.
How do uncertainties in the surface chemical abundances of the sun affect
the predicted solar neutrino fluxes
ASTROPHYS.J, 530, 2005.
John N. Bahcall, Aldo M. Serenelli, and Sarbani Basu.
New solar opacities, abundances, helioseismology, and neutrino fluxes,
2005.
Martin Lahrz
Solar Neutrino Problem

Bibliography
Figures
Bibliography II
Alain Bellerive.
Review of solar neutrino experiments.
International Journal of Modern Physics A, 19:1167, 2004.
B. T. Cleveland et al.
Measurement of the solar electron neutrino flux with the Homestake
chlorine detector.
Astrophys. J., 496:505–526, 1998.
SNO Collaboration.
Direct evidence for neutrino flavor transformation from neutral-current
interactions in the sudbury neutrino observatory.
Physical Review Letters, 89:011301, 2002.
The SNO Collaboration.
The sudbury neutrino observatory.
NUCL.INSTRUM.METH.A, 449:172, 2000.
Martin Lahrz
Solar Neutrino Problem

Bibliography
Figures
Martin Lahrz
Solar Neutrino Problem

Bibliography
Figures
Martin Lahrz
Solar Neutrino Problem

Bibliography
Figures
Martin Lahrz
Solar Neutrino Problem