• running
• muone
• hadronic contribution
• muon
• g-2
• experiment
• anomaly
• alpha

The muon magnetic anomaly is defined as a_μ = (g_μ − 2)/2, where g_μ is the muon gyromagnetic ratio. It is a low energy observable which can be computed and measured with very high precision. The most recent value of a_μ was measured with an accuracy of ∼ 0.54 ppm by the experiment E821 at BNL, in 2001. It exhibits a ∼ 3.7σ discrepancy from the theoretical prediction, and this makes a_μ an important observable to search for physics beyond the Standard Model. For this reason, a new experiment is presently running at Fermilab, with the aim to improve the accuracy on a_μ by a factor of four, corresponding to a precision goal of 0.14 ppm. Furthermore, a new experiment to measure the muon anomaly with a different approach is being developed at J-PARC, with a comparable precision goal.
Given this remarkable experimental effort, the theoretical prediction can become the main limitation for a precision test of the Standard Model. The accuracy on the Standard Model calculation is limited by the evaluation of the leading order hadronic contribution a_μ^HLO which cannot be computed perturbatively at low energies. Consequently, the hadronic contribution is traditionally determined by means of a dispersion integral on the annihilation cross section e+ e− → hadrons. The hadronic cross section is densely populated by resonances and influenced by flavour threshold effects, which limit the final precision achievable by this method on the evaluation of a_μ^HLO. Despite these difficulties, the calculation of a_μ^HLO has reached an accuracy of 0.5%. To claim for possible new physics it is important to crosscheck this calculation in an independent way.
The MUonE experiment has been recently proposed, with the aim to measure a_μ^HLO in a completely independent way. It is based on the measurement of the hadronic contribution to the running of the electromagnetic coupling constant (∆α_had) in the space like region, by means of μ e− → μ e− elastic scattering. The measurement of the shape of the differential cross section provides direct sensitivity to ∆α_had, and it is carried out by scattering a high energy muon beam on a Beryllium target. A beam with the proper energy and intensity is available at CERN. It allows to achieve a statistical uncertainty of ∼ 0.3% on a_μ^HLO in 2 years of data taking. This makes such a measurement of a_μ^HLO competitive with the dispersive approach.
The challenge of the proposed measurement is to achieve a systematic accuracy at the same level of the statistical one. For that, the differential cross section must be measured with a systematic uncertainty better than 10 ppm. Systematic uncertainties arise both from experimental and theoretical aspects, such as bad reconstruction of the elastic events, miscontrol of the experimental apparatus conditions, missing contributions in the computation of the theoretical cross section.
This Thesis focuses on the analysis of two different systematic effects: the multiple scattering and a constant, correlated systematic error on the signal events. This latter effect can be due to, for instance, a bad count of events in the normalization region required to perform the measurement.
The Thesis is structured as follows: Chapter 1 introduces the status of the muon anomalous magnetic moment, discussing both the experimental technique adopted to perform the measurement and the current Standard Model calculation, with a focus on the determination of a_μ^HLO. Chapter 2 describes the MUonE experimental proposal, which has been recently submitted to the Super Proton Synchrotron Committee (SPSC) at CERN. The main personal contribution in this Thesis are presented in the following two chapters. A procedure to extract ∆α_had from the elastic scattering cross section at Leading Order is discussed in Chapter 3, together with a method to determine a correlated systematic error. The method consists in constraining the measurement to the time-like prediction at the boundary of the MUonE signal region, where ∆α_had is less than 10^−5. It allows to correctly determine a source of correlated systematics with a sensitivity of ∼ 1 ppm, without any loss of accuracy on the final a_μ^HLO measurement.
Chapter 4 is dedicated to discuss the multiple scattering effects of the experimental apparatus on muons and electrons, and build an analytical parameterization of the scattered angle.
Since the measurement of the differential cross section is performed using only the angular information of the scattered particles, the requested level of precision on the scattering angle measurement is challenging. Therefore, the non-Gaussian tails of the scattering angle distribution need to be taken into account. In 2017 a Test Beam was dedicated to the study of multiple scattering of electrons of 12 and 20 GeV on Carbon targets, which led to identify a function describing with good accuracy the behaviour of the scattering angle distribution in the projected transverse plane. Such a function is given by the sum of a Gaussian and a t-Student distribution, the latter used to model the tails of the distribution. A good agreement between data and the Monte Carlo simulation, based on the GEANT4 toolkit, was obtained. A parameterization of such a curve has been developed as a function of the scattered electron energy. Several samples of electrons at fixed energy have thus been generated employing a GEANT4 simulation, and the behaviour of the parameters which define such a parameterization has been determined as a function of electron energy. Momentum and energy conservation in the interaction connect the direction of the scattered electron to its energy, allowing to reproduce the distribution of electrons scattered at a given angle. Thanks to the analysis exploited on the projected deflection angles, it was possible to establish that a precision ∼ 1% on the knowledge of the Gaussian core of the multiple scattering distribution is sufficient to keep this systematic effect within the main goal of 10 ppm. In addition to this, a study on the tails of the distribution has been also performed. For this purpose, a parameterization of the spatial deflection angles distribution was proposed, following what has been done on the projected angles. Given the limited statistics generated, the performed analysis indicates that a miscalibration ∼1% on the knowledge of the non-Gaussian tails of the spatial angles distribution does not give a significant effect on the determination of the differential cross section. Therefore it does not represent a showstopper for the MUonE experiment.