This applet provides a tool for investigations of the effect of neutrino oscillations. It includes three family oscillations formalism, but ignores possible CP violation and matter effects. For the moment, it assumes that the primary neutrino beam is the µ beam.
If you have comments or suggestions, or if you find errors, please send mail to Adam Para.
Mass eigenstates and flavor eigenstates
There are three mass eigenstates:
This program takes dm12 and dm23 as parameters, and computes masses to be:
Physical states e, µ and are combinations of the mass eigenstates. Mixing matrix is conveniently parametrized in terms of three mixing angles 12, 13 23. The resulting mixing matrix is shown at the bottom of the applet window. We use the PDG convention for the CKM matrix:
where cij and sij denote cosine and sine of the corresponding mixing angle.
c12*c13 s12*c13 s13
-s12*c23 - c12*s23*s13 c12*c23 - s12*s23*s13 s23*c13
s12*s23 - c12*c23*s13 -c12*s23 - s12*c23*s13 c23*c13
Squares of the matrix elements in a given row give the relative contribution of different mass eigenstates to a given physical states, whereas squares of elements in a given column give decomposition of a mass eigenstates in terms of the physical states.
The bar chart in the left lower corner shows a composition of the physical state µ in terms of the mass eigenstates.
Propagation of µ beam
Muon neutrino beam is produced by ->
µ + µ decays. The
produced µ state is a mixture of
different mass eigenstates, and they evolve in time with their proper
frequencies. As time evolution of mass eigenstates is different, the
propagating beam will have different composition at different
distances. The effect will depend on the beam energy.
The top plot
illustrates the change of the beam composition with the distance from
the source. The distance scale is from 0 to 10exp km, where
The blue/green/red curves show probabilities of observation of e, µ and , respectively, as a function of a distance from the neutrino source.
Energy of the propagating beam can be selected on the 'configuration' line too.
A detector located at the distance dist (selected in the 'Configuration' line) will detect neutrinos of different flavor. The relative probabilities of detecting different flavors is illustrated by a bar chart , bottom right.
Modification of the µ
energy spectrum as a result of neutrino oscillations
Oscillation frequency of mass eigenstates depends on the beam energy, therefore the neutrino oscillations depend on the energy too. If a beam of µ is produced with energies between elow and ehigh (in GeV!, Energy Spectrum line) and the neutrino detector is placed at the distance dist (in km, Configuration' line), than the observed energy spectrum of detected µ will exhibit oscillatory pattern shown in the middle graph.