A new approach to muon g-2 with space-like data: analysis and fitting procedure

In the thesis I have studied a new method to measure the Hadronic Leading-Order (HLO) contribution to the muon anomalous magnetic moment (a_mu). In the first part I have described the Standard Model approach to evaluate a_mu. From the perturbative expansion we know that there are many contributions to a_mu: QED, electroweak and hadronic. While the QED and the electroweak contributions can be calculated with increasing precision with the perturbative method, the hadronic contributions at this energy scale cannot, hence experiments are required to estimate it. It is known since long time that a_mu can be calculated by means of the dispersive approach using electron positron annihilation data. I have studied the this method and discussed why this method could hardly further improve the theoretical uncertainty. In the second part of the thesis I studied an innovative proposal to measure the HLO contribution to a_mu. The novel method is based on the idea of using the elastic scattering of high energetic muons on at rest electrons. The strength of the idea is to rely on t-channel scattering data, to measure the HLO to a_mu. In this case the differential elastic crosssection allows to measure the running of α(t) with very high precision and to determine the hadronic shift ∆αhad(t) subtracting all the contributions due to QED and electroweak. Through ∆αhad(t) the HLO contribution to a_mu can be calculated integrating a smooth function, of the transferred momentum, exploiting just a single scattering process. I have performed a preliminary study of the fitting procedure to extract ∆αhad(t). At this stage I used a sample of data obtained using the Leading-Order approximation of the scattering cross-section. According to the present estimates this new approach, which represents an independent complementary technique to evaluate the HLO corrections to a_mu, will reach a precision competitive with the precision of the present results, in just two years of data taking.