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Mathematically one can describe the mixture between flavours and mass-eigenstates with a mixture-matrix. Looking at the simplified case of two-flavour-oscillations (in principle one has to take all three neutrino flavours electron, muon and tau into account) on gets the following formalism:
Here P measures the probability to detect a neutrino flavor l in a distance L from the neutrino source. The process is periodic, shown in the follwing picutre. The shape of P with increasing distance from the source is plotted there. One sees that there are distances from the source, where the probability detecting a electron-antineutrino in a pure muon-antineutrino beam comes to a maximum.
A positive evidence for neutrino oscillations would be a proof of a non-zero rest mass of the neutrino. Due to the huge number of neutrinos in the universe (1 billion times the number of protons and electrons) also small neutrino masses would have big implications on creation and evolution of the universe. Thus an intense search for neutrino oscillations is carried out at KARMEN.
The neutrino source ISIS produces muon-antineutrinos but no (at least 3000 times less) electron-antineutrinos. So KARMEN looks for the appearance of electron-antineutrinos. Electron-antineutrinos would be detected via the charged current reaction on the protons (hydrogen) of the scintillator in the KARMEN detector. There the proton changes to a neutron while emitting a positron. The positron carries nearly all of the energy of the neutrino an is detected as prompt event. The neutron is thermalized within the scinitllator and captured by the gadolinium sited in the lucite segmentation of the KARMEN detector. After the capture, the binding energy of the neutron is released. The nucleus emits up to three gammas about 100 microseconds after the positron appeared, roughly at the same position in the detector. This signature allows a clear identification of electron-antineutrinos. The following picture shows the expected energy and time distribution for such events. Events within the yellow shaded areas are accepted for the following analysis.
During the analysis of the data taken in the past five years in total 147 events have been found, fulfilling this signature. This does not mean, that there are neutrino oscillations. A pre beam analysis of the data (one looks for neutrinos in a time window before the beam) also gives rise to events showing the full oscillation signature, but coming from cosmic muons. With the help of a sophisticated maximum likelihood method, taking into account the energy and time information of the events, one can test the hypothesis, that there are some oscillation events among the data. The result of this analysis shows, that there is no hint for oscillations at KARMEN. This zero result can be expressed by the exclusion of combinations of the oscillation parameters (difference of the squared masses and the squared sine of the mixing angle). The following picture shows in a double-logrithmic scale such an exluded area, coming from the analysis of the KARMEN data. All combinations of parameters right to the red curve can be excluded with a probability of 90%.
The blue curve shows a second zero-result of KARMEN, the search for muon-neutrino to electron-neutrino oscillations. KARMEN is less sensitive in this channel, because the cross section for the detection of electron neutrinos is much lower than for electron anti-neutrinos. The blue area represents the recently published result of the LSND experiment claiming a positive evidence for neutrino oscillations in the muon-antineutrino to electron-antineutrino appearance channel. The sensitivity of KARMEN is restricted due to the remaining number of background events and cannot cover the whole evidence area of LSND. Thus currently an upgrade of the KARMEN experiment is beeing performed in England, in order to reduce the background and increase the sensitivity. This upgrade allows a final decision in the next 2-3 years, wether neutrino oscillations exist in the paramater area proposed by the LSND-Experiment.
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