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
11H+11H→12H+e++ve
Equation 1: An example of one of the pp chains which yield electron neutrinos as a by-product
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 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
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 ‘right-handed’ neutrinos should be added to the standard model, when only left-handed 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
1 http://www.youtube.com/watch?v=9ugfTRKAYD0
‘Fundamental astronomy,’ Karttuen et al.
2Haxton, W.C. Annual Reviews of Astronomy and Astrophysics, vol 33, pp. 459–504, 1995.
http://en.wikipedia.org/wiki/Solar_neutrino_problem#Resolution
3 http://www-donut.fnal.gov/web_pages/neutrinospg/Neutrinos.html
http://physicsworld.com/cws/article/print/17755
1