Search for the lepton flavour violation in \mu \to e \gamma. The calibration methods for the MEG experiment.

The search for $\mu^+ \to e^+ \gamma$ decay began 10 years after the discovery of the muon (1937) and after sixty years this process continues to play a fundamental role in physics, although the motivations for its study have changed over the time. Today $\mu^+ \to e^+ \gamma$ decay is an important tool for investigating physics beyond the Standard Model. Fundamental theories such as supersymmetric unification predict that $\mu^+ \to e^+ \gamma$ decay should occur with a branching ratio that should be above $10^{-14}$. The MEG experiment was designed to measure a branching ratio of $\approx 10^{-13}$, if no event is observed. The experiment has therefore a real chance of making a discovery, which would provide very clear evidence for new physics beyond the Standard Model. Even a non-observation of decay at the predicted level of sensitivity would place a very tight constraint on these theories and on the general nature of the new physics, and will thus be of crucial importance in pointing out the future direction of particle physics, though with the evidence provided by neutrino oscillations the importance of such a search is greatly enhanced.\\ To reach this ambitious goal the experiment must use the most intense continuous beam available and rely on advanced technology (LXe calorimetry, a specially designed superconduction spectrometer, a flexible and powerful trigger system, etc.). The energy, time and space resolutions are the highest reachable to-day. The data collection will last about three years. On those terms, the only way to ensure that the required performances are reached and maintained in time is to use several complementary and redundant methods to calibrate and monitor the behaviour of all detectors.\\ This thesis deals with the design and the assembly of the calibration methods of the MEG experiment, their testing, to verify their reliability, their coupling to the MEG experiment, and the analysis of the acquired calibration data, during the MEG run 2008.\\ After a brief introduction to the Standard Model, its possible extentions and the phenomenology of the lepton flavour violation, an historical overview of the role of the $\mu^+ \to e^+ \gamma$ decay is given.\\ The MEG experiment is described.\\ A discussion of the liquid xenon as a scintillating medium is given. The LXe calorimeter, the Xe cryostat, the cryogenic equipment, the purification system, the photomultipliers are described. The expected LXe calorimeter performance and the reconstructed event algorithms are discussed.\\ An introduction to all the calibration methods is given. Liquid scintillator calorimeters and in particular liquid cryogenic noble gas detectors can be calibrated and monitored by the use of multiple $\alpha$-sources distributed in the detector sensitive volume. LXe PMT equalization and the Xe optical properties can be measured by means of this method, as described. The PMT behaviour, in conditions of high background induced by the muon beam, can be monitored by means of 9 MeV $\gamma$'s, produced by neutron thermal capture in Nickel. A neutron generator will be the neutron source. The LXe calorimeter energy resolution and linearity, the light yield and Xe purity are monitored by means of the 17.6 MeV $\gamma$-line from the $\rm{^{7}_{3}Li(p,\gamma)^{8}_{4}Be}$ nuclear reaction. A C-W accelerator is used for this purpose. $\gamma$'s at 54.9 MeV, with an energy very close to that of the expected signal, are obtained from the $\pi^{\circ}$ decay, produced from the $\pi^-$ charge exchange reaction at rest in liquid hydrogen. The PMT TC equalization and the LXe-TC time fine-tuning are performed by using concident $\gamma$'s from the $\rm{^{11}_5B(p,\gamma)^{12}_6C}$ nuclear reaction. The C-W accelerator is used for this method again. Independent measurement of the muon beam intensity is proposed by using muon induced X-ray emission and/or a He ionization chamber.\\ The last chapter deals with the detector performances achieved during the MEG run autumn 2008, measured by using the discussed methods. The achieved single event sensitivity of the MEG experiment is given and a clear evidence of the radiative muon decay signal is shown.