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Neutrino OscillationsMichiel Bosma

•Why study neutrino oscillations ?

•What are neutrino oscillations ?

•How could one detect them ?

•Have neutrino oscillations been found to exist ?

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Why study neutrino oscillations ?

It might partially solvethe dark matter problem since:

• Huge amounts of neutrinos exist

• Neutrino oscillations imply a nonzero neutrino rest mass

• Even a tiny neutrino rest mass contributes enormously to the total mass in the universe

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And there’s also the solar neutrino problem:

Lots of neutrinos are produced in the sun through the

following reactions :

p + p 2H + e+ + e

8B 8Be + e+ + e

7Be + e- 7Li + e

Normalized flux Neutrino energy (MeV)

1 0.420.08 0.862

0.0001 14

But only roughly 2/3 of the expected neutrinos are measured on earth !

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What are neutrino oscillations?

Consider our neutrinos as mixed states :e = cos 1 + sin 2 = -sin 1 + cos 2

These neutrinos will develop in space - time as follows:| k(x,t) = | k(0,0) exp[i(pkx - Ekt)]

where Ek is given by (pk2 + mk

2)1/2 ,which we can approximate for relativistic particles as the neutrino by pk + mk

2/2pk

Since we wouldn’t like the states to go spatially out of synchronization we must demand p1= p2=pCombining the above, we arrive at:| k(x,t) = | k(0,0) exp(-imk

2t/2p)

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If we further define m2 = m22 - m1

2 we arrive at the followingexpressions for the chances of finding either a e or a :

P(e e ) = 1 - sin2(2) sin2(m2t / 4p)P(e ) = sin2(2) sin2(m2t / 4p)

Or, if we introduce L = t and = 4p / m2 : P(e e ) = 1 - sin2(2) sin2(L / )P(e ) = sin2(2) sin2(L / )

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How to detect neutrino oscillations ?

First of all: fill a huge underground area with lots of fluid

There are specific detectors, which use reactions like:

e + 37Cl 37Ar + e- Davise + 71Ga 71Ge + e- GALLEX

e + d 2p + e- SNO (Charged Current)k + d p + n + k SNO (Neutral Current, d-Breakup)k + e- k + e- SNO,Super-K (Elastic Scattering)where k = e, , e-, -, - are measured by means of Cherenkov-radiation

Or more general ones,which use:k + n p + k- Super-Kamiokande

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How Cherenkov-radiation detection works

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The different regions in which the experiments measure

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ResultsSuper-Kamiokande concluded that atmosferic neutrinos oscillate , and placed some limits on sin22 and m2

The SNO experiment has observed neutrino oscillations and can solve the solar neutrino problem with their data

KAMLand also placed some limits on sin22 and m2

Super-Kamiokande

KAM-Land