The MUonE experiment

We propose a new approach to measure very precisely the hadronic leading order corrections to the muon g − 2, a HLOµ , with space-like data, measuring the hadronic contribution to the eﬀective electromagnetic coupling α , by means of the elastic scattering µ − e of 150 GeV muons (currently available at CERN North area) oﬀ atomic electrons. Such a direct measurement of a HLOµ will provide a new independent determination and will consolidate the theoretical prediction of the muon g − 2 in the Standard Model, which currently shows a 3.5 σ discrepancy between theory and experiments. This project is part of the Physics Beyond Colliders Working Group


Scientific context
The discrepancy between the experimental value of the muon anomaly a µ = (g − 2)/2 and the Standard Model (SM) prediction, ∆a µ ∼ (28 ± 8) × 10 −10 is a long standing issue in particle physics [2,3]. The current accuracy of the SM predictions, ∼ 5 × 10 −10 , is limited by strong interaction effects. The leading-order (LO) hadronic contribution to the muon g-2, a HLO µ , can be computed via a dispersion integral of the hadron production cross section in e + e − annihilation at low energy. They contribute to the present uncertainty of the SM prediction on a HLO µ , with ∼ 4 × 10 −10 . Alternative evaluations of a HLO µ can be obtained with QCD lattice calculations [4]. The current lattice QCD results are not yet competitive with the dispersive approach via timelike data, but errors are expected to decrease significantly in the next few years. The O(α 3 ) hadronic light-by-light contribution, which has the second largest error in the theoretical evaluation, contributing with an uncertainty of (2.5-4)×10 −10 , cannot at present be determined from data and its calculation relies on the use of specific models. The error achieved by the BNL E821 experiment [5], δa Exp µ = 6.3 × 10 −10 corresponding to 0.54 ppm, is dominated by statistics. New experiments at Fermilab and J-PARC, aim at measuring the muon g-2 to a precision of 1.6 × 10 −10 (0.14 ppm) [6,7]. Fermilab experiment started and has already exceeded the statistics of BNL E821. First results are expected in 2019.
Together with the experimental plans, an improvement on the determination of a HLO µ would be extremely beneficial. CERN played a primary role in the sixties and seventies in the determination of the anomalous magnetic moment through pioneering experiments and fundamental theoretical contributions. Despite European physicists have given essential contribution to the field, currently there are no programs of experiments devoted to this physics in Europe.

Objectives
Using the elastic reaction µe → µe to measure a HLO µ with space-like data is very appealing for several reasons. It is a t-channel process, making the dependence on t of the differential cross section proportional to |α(t)/α(0)| 2 : where dσ 0 /dt is the effective Born cross section, including virtual and soft photons. The vacuum polarization effects, in the leading photon t-channel exchange, are incorporated in the running of α.
Given an incoming muon energy E µ = 150 GeV, the t variable is related to the energy of the scattered electron E e , in the range (1-139.8) GeV, or its angle θ e , in the range (0-31.85) mrad. For E µ = 150 GeV, −0.143 GeV 2 < t < 0 GeV 2 . The region of x extends up to 0.93, covering the peak of the integrand function of Eq.(2) (x peak = 0.914, t peak −0.108 GeV 2 ), as shown in Fig. 1 (right), corresponding to an electron scattering angle of 1.5 mrad. The correlation between the angles of the scattered electron and muon shown in Fig. 2, is extremely important to select elastic scattering events, rejecting background from radiative or inelastic processes and minimizing systematic effects in the determination of t. Note that for scattering angles of 2-3 mrad there is an ambiguity in the mass assignment of the outgoing electron and muon, as their angles and momenta are similar, which must be resolved by means of µ/e positive identification.

Methodology
The proposal described here aims at determining a HLO µ from a measurement of the effective electromagnetic coupling α in the space-like region. In this approach the hadronic contribution to the running of α will be measured by means of the t-channel µ − e elastic scattering process, from which a HLO µ can be determined directly [8]. For the calculation of the hadronic leading contribution a HLO µ with the t-channel approach the formula is: where ∆α had (t) is the hadronic contribution to the running of α, evaluated at that is the space-like (negative) squared four-momentum transfer of the process. In contrast with the dispersive integral, the integrand of Eq.(2) is a smooth function and free of resonance poles. Fig. 1 (left) shows ∆α had , and for comparison ∆α lep , as a function of the variables x and t. The range x ∈ (0, 1) corresponds to t ∈ (−∞, 0), with x = 0 for t = 0. The expected integrand of Eq. (2), is plotted in Fig. 1 (right). Note that ∆α had (t peak ) 7.86 × 10 −4 . We propose to measure the running of α to determine a HLO µ by using the CERN muon beam M2 with energy E µ 150 GeV, colliding on atomic electrons. This technique is similar to the one used for the measurement of the pion form factor described in [9].

The detector
The target must be of low-Z material, but of sufficient thickness in order to get enough electron scattering centres. The idea is to use a segmented target, each of 1 cm thick Berillium (or 0.75 cm Carbon) layer. The long radiation length of this material minimizes the secondary electromagnetic interactions. Each module has a length between 50 cm and 100 cm, repeated several times, according to the available space. It consists of three Si planes for tracking following the target element. Figure 3 shows the basic layout which is the starting point of the undergoing optimization. No magnetic field is foreseen at this stage of the study. Downstream all the modules, we plan to use a calorimeter for the electron identification and a muon filter to reject pion  contamination. The calorimeter should solve the muon-electron ambiguity when the electron scattering angles are around 2-3 mrad (see Fig. 2). Due to the boosted kinematics of the collisions, the detector acceptance covers both the region of the signal, where the electron is emitted at extremely forward angles and high energies, and the normalization region, where the electron has much lower energy, O(few GeV), and an emission angle of some tens of mrad.
The tracking system, under study by using GEANT4, must be designed to perform an angular resolution of ∼ 0.02 mrad for the outgoing particles. Silicon sensors as the ones being produced for the upgrade of the CMS experiment [10] with a spatial resolution of less than 20 µm on a double module, could be a viable choice for the MUonE tracker. Such sensors provide very high efficiency, close to 100%, excellent uniformity and, with the CBC ASIC in preparation, can sustain a data acquisition rate of 40 MHz in triggerless mode, adequate for our application.
Other solutions With the idea of using existing solutions, to the extent they could provide the characteristics we need, in particular an angular resolution around 0.02 mrad, we are also considering what was developed for the experiment µ → eee planned at PSI [11]. This alternative seems very appealing, considering the small thickness of 50 µm, the very high efficiency, and the rate capability. We should build arrays, given the 2x2 cm 2 size of each such detector, while our need is 10x10 cm 2 . It is expected to be finalized in 2019. Other solutions, for example as studied for CLIC [12], are still in a R&D phase, and could go to production too late for the MUonE time plans.

The beam
The CERN muon beam M2, available in the CERN North Area, presents ideal characteristics to perform the measurement. The beam intensity, of more than 10 7 µ/s, can provide the required event yield and its time structure allows to tag the incident muon. We plan to use the Beam Momentum Station (BMS) of COMPASS to define the direction and the momentum of the incident muons. Studies performed by the EHN2 team Ref. [13] show that the position where the MUonE detector could be located will be upstream COMPASS and downstream the BMS. In such a location, the beam will have the space profile (see

Test beam performed
We performed already two beam-tests, with setups similar to the one we intend to adopt. In each case we had a Si-trackers (5 planes in 2017 and 8 planes in 2018) and a graphite target.
2017 testbeam In order to study Multiple Coulomb Scattering (MS) effects, a testbeam has been performed on the H8 line at CERN with graphite targets of different thickness. The experimental set-up employed was the one used by the UA9 collaboration [14]. It consists of two upstream planes of Si trackers distant ∼10 m one from the other, a target, and three downstream tracking planes covering ∼ 1 m distance along the beam direction. Each silicon plane is composed of two layers 320 µm thick, with a 3.8 × 3.8 cm 2 active area, to measure the x and y coordinates. The measurement greatly benefits from the precise tracking of the high-resolution silicon microstrip detectors of the UA9 apparatus.
Data were taken with electron momenta of 12 and 20 GeV/c, and a graphite target with different thickness, from 2 to 20 mm. For a determination of the contribution of the telescope, measurements without the graphite target were performed with different particle beams. For each data point we collected about O(10 million) triggers. Preliminary results for the deviation angle shown in Fig. 5, show good agreement between data and GEANT4 simulation, namely ∼ 1% is obtained in the core region [-0.5,+0.5] mrad, defined as the region which contains more than 90% of the events. Figure 5 (right) shows an example of the agreement, for 12 GeV electrons and 20 mm target.
2018 testbeam In 2018 we ran behind the COMPASS detector from May to November, taking data with muons. The muons were from the M2 beam, whenever COMPASS used it for calibration and alignment purpose, and from the pion decays exploiting the intense pion beam COMPASS used for their 2018 physics program. The data are being analysed.

Readiness and expected challenges
If the solution chosen by the CMS collaboration for their Upgrade Phase-II will be adopted for the MUonE experiment, we plan already in 2021 to assemble a setup of 10 modules, located in the place foreseen for the final experiment, if approved.
The most challenging aspect of this proposal lies in performing a measurement with a very low systematic uncertainty, ideally at the level of the statistical one.

Considerations on systematic uncertainties
The net effect of the contributions of the hadronic vacuum polarization to the µe → µe differential cross section is to increase the cross section by a few per mille, mainly in the kinematical region where the outgoing electron angle is below 10 mrad. A precise determination of a HLO µ , both theoretically and experimentally, requires not only high statistics, but also a high level of control of systematic uncertainties, as the final goal of the experiment is equivalent to a determination of the differential cross section with ∼10 ppm systematic uncertainty at the peak of the integrand function (see Fig. 1).
Experimental systematic uncertainties Several crucial requirements on the experimental side are: i) to keep the efficiency highly uniform over the entire q 2 range, including the normalization region, and over all the detector components; ii) to control the alignment of the tracker elements with very high precision; iii) to describe with an accuracy at the level of 1% the effects of the multiple scattering on the electrons of relatively low energy in the normalization region. Multiple scattering breaks the muon-electron two-body angular correlation, moving events out of the kinematic line in the 2D plot of Fig. 2. In addition, multiple scattering in general causes acoplanarity, while two-body events are planar, within the resolution.
The data themselves will be used to measure directly some of the quantities which must be kept under control. For example, the high number of muons passing through the apparatus will be used to monitor periodically the alignment and the efficiency. The muon interactions like µ → µγ and µ → µe + e − must be recorded to extrapolate precisely the background subtraction and contamination to the final elastic sample. In this respect the proposed modularity of the apparatus will help.
Theoretical systematic uncertainties The differential cross section must be calculated by including all the radiative corrections relevant at the scale of precision of 0.01% at least. At the next-to-leading order (NLO), the class of QED corrections are known for µe scattering and have been already implemented in a Monte Carlo event generator. The typical theoretical uncertainty of a QED NLO calculation is of the order of 1%. The techniques to match NLO fixed order calculation with all-orders resummed calculations of leading logarithmic contributions are well known and allow to reach accuracies at the 0.1% level. In order to go beyond this limit, the NNLO QED corrections and relevant weak contributions are required. First results towards the final goal have been recently obtained [15].

Summary
The experiment MUonE is dedicated to measure the leading hadronic contribution to the muon g-2, by scattering high-energy muons on atomic electrons through the process µe → µe. It is primarily based on a precise measurement of the scattering angles of the two outgoing particles, as the q 2 of the reaction can be directly determined by the electron (or muon) scattering angle. The use of the muon beam allows making a modular apparatus, with the target subdivided in subsequent layers. The normalization of the cross section is provided by the very same µe → µe process in the low-q 2 region (i.e. for electron large scattering angle), where the effect of the hadronic corrections on α(t) is negligible. Such a simple technique has the potential to keep systematic effects under control, aiming at reaching a systematic uncertainty of the same order as the statistical one. A preliminary detector layout is under study and optimization. A pilot run using 10 detector modules, exploiting the muon beam facility in 2021, will provide a validation of the proposed method.