Nick L. Theodorou
Prof. Kohler (tutor)
21-Feb-10
Revising the ‘Solar neutrino problem’
Previously there has been a discrepancy between the theoretical prediction of
the number of neutrinos produced in the sun and the number detected by
experiment.
An explanation has been formulated by introducing ‘neutrino oscillation,’
however some modification is to be made on the standard model of particle
physics.
Neutrino oscillation predicts neutrinos are produced with one of three lepton
flavours and can later be measured to have a different flavour.
As the original experiments were not engineered to detect all three flavours, the
observed number was typically one third to one half of the predicted number.
This explanation implies neutrinos have a non-zero mass – how that mass arises
has not been answered conclusively.
The three flavours of neutrinos have since been observed in the lab, but the
question of which modification should be made still remains.
In the standard model of particles physics, neutrinos are necessary by-products
of certain reactions and radioactive decays. They were first suggested by
Wolfgang Pauli in order to conserve energy, momentum, and angular
momentum –following observations made in beta decay. They are of the
fundamental particle class known as leptons. They are neutral in charge and
travel close to the speed of light. Before experimental observations, the zero vs.
non-zero value of the neutrino’s mass was a central debate.
By modelling the sun, stellar structure can be summarised in four equations.
The original equations were expressed by Eddington who described hydrostatic
equilibrium, mass related to density, the equation of state, and radiation
generated in the inner regions. After calculating the temperature of the sun’s
interior, the prophetic suggestion was made that the central temperature was
high enough to release nuclear energy in sufficient quantities to provide for the
Sun’s luminosity. This nuclear fusion is given by proton-proton reactions, and it
is in these pp chains that neutrinos are produced in vast numbers
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1𝐻
+ 11𝐻 → 21𝐻 + 𝑒 + + 𝑣𝑒
Equation 1: An example of one of the pp chains which yield electron neutrinos as a by-product
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Nick L. Theodorou
Prof. Kohler (tutor)
21-Feb-10
Physicists used this model of the sun to calculate an estimate for the number of
neutrinos that should pass through the earth. The answer yielded was 7x1010 per
square cm per second.1 This is a theoretical prediction that is important to test
by experiment because the soundness of two models is being put to scrutiny. In
this way neutrinos provide a direct check of nuclear energy generation in the
sun and serve as a means of verifying the projected life span of the sun.
However, neutrinos are extremely difficult to detect because they are so weakly
interacting with other matter, which is why they escape directly from the stellar
interior.
Fortunately in the 60s experimenters devised a way to detect the neutrinos. This
first method of detection was radiochemical and used a chlorine based reactive
agent. When a neutrino hits a chlorine atom it transforms into radioactive argon
with an electron freed. Only one third of the radioactive argon atoms expected
were observed from this Davis experiment. This result became known as the
‘solar neutrino problem’ and during this era many theorists attempted to
develop a coherent explanation.
Today’s neutrino detectors, for example the Japanese Kamiokande detector
(see fig.2), employ a superior method. By utilising the Čerenkov effect, each
neutrino produces flashes of light that are registered with photomultipliers.
When particles enter a medium and travel faster than the speed of light for that
medium, Čerenkov radiation is produced. By orientating the photomultipliers it
is then possible to deduce the direction of the radiation, and thus only register
those sourced from the sun’s direction. However using this method, experiments
still detected a deficit of at least one half in the flux of neutrinos from the sun.
Early attempts to explain the deficit proposed that the modelling of the sun was
incorrect including the possibility that nuclear processes in the sun had slowed
down. However this was rendered invalid, especially since later experiments
detected more neutrinos. More extensive analysis of results from more
advanced neutrino observatories showed, exhaustively, that ‘no combination of
adjustments of the solar model was capable of producing the observed neutrino
energy spectrum.’2
The currently accepted resolution has exposed that the previous understanding
of neutrinos was inadequate. Pontecorvo proposed that if neutrinos had mass,
then they could oscillate. The three flavours of a neutrino are electron, muon,
and tau. And although it is only the electron neutrino which is produced in solar
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Nick L. Theodorou
Prof. Kohler (tutor)
21-Feb-10
reactions, the probability of detecting an electron neutrino changes because the
neutrino changes flavour as it propagates. Adhering to quantum mechanics, Fig.
1 shows how the probability of detecting the respective flavours varies with
distance.
Figure 1: The oscillation probabilities for an initial electron neutrino as distance from the source
increases.
This theory sufficed as a tenable explanation for which there is now conclusive
experimental evidence. The Japanese Super-Kamiokande (see fig.2) produced
observations consistent with muon neutrinos changing into tau neutrinos,
although it did not detect tau neutrinos directly.
Figure 2: Super-Kamiokande, which became operational in 1996, Koshiba found strong evidence for
what scientists had already suspected—that neutrinos, of which three types are known, change from
one type into another in flight; this resolves the solar neutrino problem, since early experiments
could only detect one type, not all three.3
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Nick L. Theodorou
Prof. Kohler (tutor)
21-Feb-10
In 2001, the Sudbury Neutrino Observatory in Canada provided the first direct
evidence of solar neutrino oscillation, by detecting the three types of neutrino
coming from the sun’s direction. After statistical analysis it was found 35% of
the arriving solar neutrinos were electron neutrinos, with the rest being muon
neutrinos or tau neutrinos. There are also other efforts to confirm the existence
of the independent neutrino flavours, with DONUT in 2000 being the first to
provide direct evidence for the more elusive tau neutrino.3
Now that neutrino oscillations can explain the experimental deficit, there is a
necessary modification to made to the standard model. The two main possible
sources of neutrino mass put forward from the standard model are; the Majorana
mass term, and interaction with the Higgs field (Dirac mass). The former would
mean neutrinos and anti-neutrinos are the same particle, but then the neutrino
mass is implausibly smaller the other particles. The latter requires that ‘righthanded’ neutrinos should be added to the standard model, when only lefthanded neutrinos have been observed (see fig.3).
Figure 3: A schematic diagram of the relative directions of spin and momentum in so called right- and left-handed
particles.
There are numerous possible modifications and combinations of modifications
that could be made that are allowed under the basic theoretical framework. The
problem is that many of these suggestions are apparently not phonologically
excludable, but there are still hopeful ongoing developments.
One can notice that it was the strength in the solar model that gave rise to
neutrino physics; perhaps the confidence in neutrino physics will someday do
the same.
References
http://en.wikipedia.org/wiki/Neutrino_oscillation
http://www-donut.fnal.gov/web_pages/neutrinospg/Neutrinos.html
‘The lighter side of gravity,’ Jayant V. Narlikar
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Nick L. Theodorou
1
Prof. Kohler (tutor)
21-Feb-10
http://www.youtube.com/watch?v=9ugfTRKAYD0
‘Fundamental astronomy,’ Karttuen et al.
2
Haxton, W.C. Annual Reviews of Astronomy and Astrophysics, vol 33, pp.
459–504, 1995.
http://en.wikipedia.org/wiki/Solar_neutrino_problem#Resolution
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http://www-donut.fnal.gov/web_pages/neutrinospg/Neutrinos.html
http://physicsworld.com/cws/article/print/17755
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