Setup of a Drift Tube Muon Tracker and Calibration of Muon ...

e −ν eν xe −¡W ±ν ee−(a) CC elastic scattering¡Z 0ν xe−(b) NC elastic scatteringFigure 4.2: Elastic scattering of neutrinos in matter. The cross section is six timeshigher for ν e than for the other neutrino types due to the CC reaction.neutrinos is possible.Elastic scattering of neutrinos is also possible on protons. However, due to therelatively large proton mass, the transferred energy is much smaller than in theelectron’s case. Nevertheless, this reaction is of interest in the case of high energeticν x e.g. from super-nova explosions.4.1.2 Inverse β DecayThe main reaction channel for anti electron type neutrinos is the inverse β decay onprotons:¯ν e + p → e + + n. (4.2)The ¯ν e is captured by a proton under the emission of both a neutron and a positron.This process can be identified by the coincidence signal from the positron annihilationand the delayed neutron capture. It leaves a distinct signature which can beeasily identified: the positron carries away most of the reaction’s energy. It annihilatesalmost immediately thus producing a prompt signal from which the eventtime and the neutrino’s energy can be deduced. The second signal occurs whenthe free neutron is captured. This typically happens after 250ñs on a free protonand is accompanied by the release of a photon of 2.2 MeV which corresponds to thedeuteron’s binding energy. This coincidence signal of a distinct energy is a strongindicator of an inverse β decay.The energy threshold for the reaction can be derived easily using energy conservationby looking at the masses m x of the particles involved:E ν,min = (m n + m e ) 2 − m 2 p2m p= 1.806MeV.Anti electron neutrinos below this threshold cannot be detected. The energy E promptreleased in the prompt annihilation of the positron is directly connected to theincoming neutrino’s energy: E prompt = E¯νe − 0.782MeV.53