# MUonE experiment plans to shed light on the muon anomalous magnetic moment

The long-standing discrepancy between the experimental value and the Standard Model (SM) prediction of the anomalous magnetic moment of the muon remains one of fundamental parameters in Quantum Field Theory that still lacks an explanation. The discrepancy could be due to the presence of new physics, or to a lack of precision in the determination of the expected SM value or perhaps to a lack of precision in experimental measurements.

Presently, the most accurate experimental value of the muon anomalous magnetic moment a_{µ}, has been measured by the BNL E821 experiment with an uncertainty of 0.54 parts per million and disagrees with the most accurate theoretical predictions at more than a 3.5σ level (it can reach 4σ depending on certain underlying theoretical assumptions). The new results expected from the next-generation of (g-2) experiments at Fermilab (USA) and J-PARC (Japan) will reach the impressive precision of 0.14 parts per million.

These extremely precise results will open the possibility of testing with unprecedented precision the internal consistency of the SM at the level of quantum loop corrections. The uncertainty on the leading order hadronic (HLO) contribution to a_{µ}, dominates the SM value prediction and remains the main limitation of this formidable test of the SM. The MUonE collaboration proposes the use of a new method to measure these contributions. This method could further boost experimental sensitivity and shed light to one of the most prominent discrepancies in particle physics.

The MUonE proposal aims at providing a completely new and independent experimental measurement of the hadronic contributions to the muon anomalous magnetic moment, allowing a direct comparison to theoretical expectations.

Currently, the determination of HLO contributions is based on the measurement of the total hadronic cross-section in the electron-positron annihilation process at lepton^{-} colliders in the time-like region [1]. The newly proposed method is based on a completely different approach, and, instead of considering the electron-positron annihilation cross-section, it uses a scattering process of muons on atomic electrons, to measure directly the HLO hadronic vacuum polarization [2].

According to this approach the quantity a_{µ}^{HLO} can be extracted by comparing the measurement of the muon-electron elastic scattering µ-e →µ-e differential cross-section as a function of the momentum transfer* t* in the space-like region, with the theoretical predictions calculated with an adequate precision. To achieve a meaningful measurement, a strong collaboration between experimental and theoretical communities is needed.

The proposed experiment needs a high energy muon beam, covering a region in momentum transfer up to the value of *t *= -0.108 Gev^{2} , covering the region where the hadronic corrections mostly affect the cross-section [2]. The muon beam energy of 150 GeV, available at the beam line M2 at CERN will allow to collect data covering ~87% of the cross-section curve (Fig. 1) whose integration allows to calculate a_{µ}^{HLO}_{ . }The remaining part of the integral (~13%), cannot be reached directly but can be determined by using time-like data and perturbative QCD, or eventually lattice QCD results.

**Figure 1. shows the integrand that MUonE plans to measure as discussed in the text. **

With a muon beam with an average flux of the order of 10^{7} μ’s/s as the one present in the CERN North Area complex, a statistical accuracy of the order of 0.3% on a^{HLO}_{µ} could be reached in a couple of years of data taking. The challenge of the proposed measurement is the control of the systematics, both on the theoretical and experimental side, at a comparable level of accuracy.

On the theory side there is an intense research program as part of this project, including important efforts by the lattice QCD community. Calculations are under way to improve the evaluation of the leading order contribution to a_{μ}, due to the hadronic vacuum polarization corrections to the one-loop diagram, as well as the next-to-leading (NLO) hadronic ones. Very recently, also the next-to-next-to-leading (NNLO) hadronic corrections have been addressed, by computing the insertions of hadronic vacuum polarization diagrams and estimating the hadronic light-by-light contributions.

Moreover, the collaboration has proposed a design for the MUonE detector; a modular system, made up of 40 identical stations, each consisting of a 15 mm thick layer of Be (or ~1.0 mm C) followed by three silicon tracking layers, covering a lever arm of about a meter. The detector is sketched in Fig. 2. The transversal size is small, 10x10 cm, but it is enough to contain the kinematics of an elastic event. The configuration must provide an angular resolution for the outcoming directions of the muon and electron to better than 0.02 mrad. The tracker will be the heart of the MUonE detector, and the measurement will be based on the two outgoing angles, of muon and electron, and their kinematical correlation.

**Figure 2. Drawing of the detector of the proposed MUonE experiment. **

The design of the detector and a trigger that can address the systematic uncertainties is one of the main challenges for MUonE. The silicon sensors, the electronics and the DAQ architecture are inspired from the CMS tracker upgrade-II project, which has agreed to provide the MUonE collaboration with the necessary 40 stations of the final detector.

Two beam tests took place in 2017 (in H8 line) and in 2018 (downstream the COMPASS detector). In 2017 the aim was to test how precisely one can model the multiple scattering of electrons towards the low energy range. The data taken in 2018, running with muons, aim at studying elastic scattering events and their kinematical correlation. If approved, the experiment should run during the Run 3 period. You can read more details in [3].

**Further Reading**

[1] F. Jegerlehner, Acta Phys.Polon. B49 (2018), arXiv:1804.07409; EPJ Web Conf. 166 (2018) 00022, arXiv:1705.00263.

[2] G. Abbiendi, C.M. Carloni Calame, U. Marconi, C. Matteuzzi, G. Montagna, O. Nicrosini, M. Passera, F. Piccinini, R. Tenchini, L. Trentadue, G. Venanzoni, Eur. Phys. J. C 77 (2017) no.3, 139