MUonE Experiment: Space-Like HVP Measurement

• The MUonE experiment is a fixed-target CERN initiative that directly measures space-like hadronic vacuum polarization to improve the precision of muon g‑2 calculations.
• It employs ultra-precise silicon trackers and calorimeters to achieve per-mille sensitivity, control systematic uncertainties, and validate advanced radiative correction techniques.
• The experiment also offers discovery potential for beyond Standard Model physics, including light mediators and axion-like particles, through displaced-vertex searches and innovative event reconstruction.

The MUonE experiment is a fixed-target high-statistics effort at CERN designed to provide a direct, space-like determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, $a_\mu^{\rm HVP,LO}$. Its unique measurement of the running electromagnetic coupling in the space-like region via elastic muon–electron scattering seeks to address the dominant Standard–Model theory uncertainty underlying the long-standing discrepancy in measurements of the muon's $g-2$. Leveraging an ultra-precise modular silicon-tracker geometry, MUonE also provides discovery potential for light, weakly coupled new particles through displaced-vertex searches, and is a test-bench for advanced event reconstruction methodologies.

1. Physics Motivation and Measurement Principle

The dominant theoretical uncertainty in the Standard–Model prediction of $a_\mu \equiv (g_\mu-2)/2$ originates in the hadronic vacuum polarization contribution, $a_\mu^{\rm HVP,LO}$. Standard approaches infer $a_\mu^{\rm HVP,LO}$ using a dispersion integral over time-like $e^+e^- \to \mathrm{hadrons}$ cross sections or via lattice QCD, both limited by uncertainties in hadronic data and theory (combined error $\sim0.6\%$) (Venanzoni, 2018, Abbiendi, 2020).

MUonE simultaneously avoids resonance structures and associated uncertainties by measuring the shape of the differential cross-section for elastic $\mu^{\pm} e^-\to \mu^{\pm} e^-$ scattering in the space-like region ($t=q^2<0$), specifically targeting sub-per-mille changes induced by the hadronic piece of the photon vacuum polarization, $\Delta\alpha_{\rm had}(t)$:

$$\frac{d\sigma}{dt} = \left(\frac{d\sigma}{dt}\right)_0 \left[\frac{\alpha(t)}{\alpha(0)}\right]^2, \qquad \alpha(t) = \frac{\alpha(0)}{1-\Delta\alpha(t)}$$

The key observable is the normalized ratio:

$$R_{\rm had}(t) = \frac{d\sigma/dt\,[\Delta\alpha_{\rm had}(t)\ne 0]}{d\sigma/dt\,[\Delta\alpha_{\rm had}(t)=0]} \approx 1 + 2\Delta\alpha_{\rm had}(t)$$

The extraction of $a_\mu^{\rm HVP,LO}$ employs the master integral:

$$a_\mu^{\rm HVP,LO} = \frac{\alpha}{\pi} \int_0^1 dx\, (1-x)\, \Delta\alpha_{\rm had}[t(x)], \qquad t(x) = -\frac{x^2 m_\mu^2}{1-x}$$

with the kernel peaking around $t \simeq -0.108\,\mathrm{GeV}^2$ (Venanzoni, 2018, Abbiendi, 2022).

2. Experimental Design and Detector Performance

MUonE comprises 40 identical stations arrayed along a 40 m baseline in the CERN SPS M2 muon beam [160 GeV, typical intensity $1.3\times 10^7\ \mu/\mathrm{s}$]. Each station consists of:

• Target: 1.5 cm Be plate (low-Z for minimal multiple scattering).
• Tracking: Three (or six) high-precision silicon microstrip planes (CMS 2S modules), total per-plane resolution $\sim8\,\mu\mathrm{m}$ (Abbiendi, 2022, Spedicato, 8 Jan 2024).
• Downstream PID: A PbWO$_4$ electromagnetic calorimeter (ECAL) and a muon filter for redundant e/μ separation, background veto, and systematic monitoring (Spedicato, 8 Jan 2024).

Geometric and tracking optimization emphasizes:

• Sub-10 μrad angular resolution per outgoing track, required for sensitivity to per-mille scale effects from $\Delta\alpha_{\rm had}(t)$ (Venanzoni, 2018, Dorigo, 2020).
• Material budget control ($<0.05\,X_0$ per tracker), thermal and mechanical stability (<10 μm), and precise (few MeV) calibration of the muon-beam momentum (using two-body kinematics).

Multiple scattering is modelled to $\sim1\%$ accuracy (beam tests, GEANT4 validation), and systematic uncertainties on reconstructed angles are targeted below $10^{-4}$ (Venanzoni, 2018, Abbiendi, 2022). Longitudinal and transverse alignment is monitored by kinematic constraints and interferometry.

3. Systematics, Backgrounds, and Calibration

Achieving the desired $\le10\,\mathrm{ppm}$ relative shape sensitivity in $d\sigma/dt$ (Venanzoni, 2018, Abbiendi, 2020, Abbiendi, 2022) requires robust control of:

• Multiple Scattering: Modelled, tested, and constrained to sub-percent level, with correction from in-situ data and test-beam results.
• Angular and Vertex Alignment: Controlled by hardware (Invar frames, laser systems, temperature stabilization) and continuous real-time tracking; further refined by exploiting overconstrained kinematics (Abbiendi, 2022, Dorigo, 2020).
• Beam Characteristics: Continuous monitoring of beam energy and profile; kinematic reconstruction used for calibration.
• Radiative Corrections: NLO and NNLO QED, including photonic, leptonic, and pair-production terms, resummed large logarithms (via QED parton shower and YFS exponentiation) are included in state-of-the-art Monte Carlo generators (Mesmer, McMule) (Gurgone, 12 Jan 2024).
• Backgrounds: Pair production in muon-nucleus interactions, π$^{0}$ emission, and other real/irreducible backgrounds studied in detail; their contribution is modelled in exclusive MC, and selection cuts (e.g., on muon angle or ECAL cluster energy) are tuned to suppress contamination to well below $10^{-5}$ (Budassi et al., 2022, Gurgone, 12 Jan 2024, Spedicato, 8 Jan 2024).

The ECAL supplements the tracking vertex, providing independent cross-checks of tracking alignment (sub-mm accuracy), e/μ separation, and strong control over background and pile-up, with reconstructed energy resolution $\sim1.5\%$ at 150 GeV and $\lesssim$2% linearity for 1–150 GeV (Spedicato, 8 Jan 2024).

4. Theory, Data Analysis, and Extraction of $a_\mu^{\rm HVP,LO}$

Theoretical precision matching experimental goals (~10 ppm) requires:

• Complete inclusion of NLO and (for target uncertainty) NNLO QED corrections, analytic calculation of large logarithms from phase-space cuts, matching to resummation for leading- and next-to-leading logarithms (Gurgone, 12 Jan 2024).
• Fully exclusive event generators (Mesmer, McMule) simulating all backgrounds, radiative corrections, and detector effects (Gurgone, 12 Jan 2024).

Data analysis proceeds by building binned angular spectra, forming normalized ratios $R_{\mathrm{had}}(t)$, and fitting templates with floating $\Delta\alpha_{\rm had}(t)$ parameters (Venanzoni, 2018, Abbiendi, 2022). The extraction of $a_\mu^{\rm HVP,LO}$ requires high-fidelity extrapolation of $\Delta\alpha_{\rm had}(t)$: Padé and D-Log Padé approximants, exploiting the analyticity and Stieltjes nature of the vacuum polarization, provide robust, model-independent interpolation and extrapolation from the measured t-range to the required domain, yielding sub-$10^{-4}$ systematic uncertainty (P. et al., 15 Nov 2024).

Table: Representative Padé/D-Log Padé Results for $a_\mu^{\rm HVP,LO}$ (statistical spread over 30 pseudo-data points, $x\in[0.2,0.93]$):

Approximant	$a_\mu^{\rm HVP,LO}\times 10^{11}$	$\chi^2/n_\mathrm{dof}$
Padé $P_2^2$	$6980^{+46}_{-34}$	$1.05^{+0.29}_{-0.27}$
Padé $P_2^3$	$6994^{+85}_{-49}$	$1.11^{+0.29}_{-0.31}$
D-Log $D_3^2$	$6999^{+48}_{-39}$	$1.10^{+0.29}_{-0.28}$
D-Log $D_3^3$	$6977^{+72}_{-53}$	$1.14^{+0.30}_{-0.29}$

These approximants converge to the true (model-input) value at the per-mille level; extrapolation uncertainty is dominated by the $x\sim0.93\to1$ region, reducible by limiting the extrapolation domain (P. et al., 15 Nov 2024).

5. New Physics Reach: Light Mediators and Displaced Vertices

MUonE can probe a range of new-physics scenarios, leveraging its high angular and vertex resolution and large integrated luminosity ($\sim10^{16}$ muons on target):

• Light Vector Mediators (A′, Z′, etc): Displaced-vertex searches using final-state e⁺e⁻ pairs from processes $\mu N \to \mu N V$, $V \to e^+e^-$ or $\mu e \to \mu e V$, with sensitivity to kinetic mixing parameters $\epsilon \sim 10^{-6}-10^{-4}$ in the $m_V\sim 10–150\,\mathrm{MeV}$ region; uniquely covers the “gap” between collider and beam-dump sensitivity (Rocha et al., 5 Nov 2025, Cortona et al., 2022, Galon et al., 2022).
• Axion-like Particles (ALP): For $g_{a\ell}\gtrsim10^{-5}$ and $m_a\sim200\,\mathrm{MeV}-3\,\mathrm{GeV}$, MUonE complements existing bounds, especially where ALP decay is visible and background-free (Cortona et al., 2022).
• Unparticles (broken scale invariance): Sensitivity to vector unparticle scaling dimensions $1<d\lesssim1.4$ and scales $1\le\mu\lesssim12\,\mathrm{GeV}$, with $|C_V| \sim \text{few}\times10^{-2}$, exceeding previous collider limits (Le et al., 2023).
• Inelastic Dark Matter: For scenarios where long-lived, heavier pseudo-Dirac states decay downstream to displaced lepton pairs, MUonE reaches thermal relic cosmological benchmarks inaccessible to other facilities (Krnjaic et al., 30 Aug 2024).

Table: Projected (95% CL) Sensitivity to Light Vector Bosons

Process	Mass Range	Coupling Reach	Notes
μN→μN V →e⁺e⁻	10–150 MeV	ε ~ $10^{-6}-10^{-4}$	Fills gap between colliders and beam dump
μe→μe V→e⁺e⁻	5–60 MeV	ε ~ few×$10^{-6}$	Strongest at low mass/short decay lengths
ALP	200–3000 MeV	$g_{a\ell}\gtrsim10^{-5}$	Competes with E137, (g−2)_μ limits
Unparticle vector	--	$$1<d\lesssim1.4, \, |C_V| \sim \text{few} \times 10^{-2}$$	Unique for broken scale invariant regime

Control of backgrounds is achieved by kinematic, angular, and energy cuts (e.g., displaced-vertex requirement $z_{decay}>10\,\mathrm{mm}$), PID vetoes (ECAL+muon filter), and tracking all three charged tracks in a module; total effective SM backgrounds are negligible (≪1 event for zero-background searches) (Galon et al., 2022, Rocha et al., 5 Nov 2025, Krnjaic et al., 30 Aug 2024).

6. Event Reconstruction and Advanced Algorithms

Event reconstruction relies on high-precision 3D track-finding in the silicon tracker. Proof-of-concept studies show that deep neural networks (DNNs), trained on hit vectors from simulated μe→μe events, achieve equal or better slope/intercept resolution than conventional pattern recognition/Kalman-filter methods, at near-100% efficiency and with orders-of-magnitude speed-up (Zdybal et al., 5 Feb 2024):

• Metrics: μ (x–z slope) σ=1.8×10^-5 mrad (DNN), electron σ1,2=1.29/0.245 mrad (DNN); classical methods within 5% of these.
• Execution time: Large reduction in pattern-recognition phase by shifting to GPU-accelerated forward passes (Zdybal et al., 5 Feb 2024).
• Outlook: Transition to graph neural networks for efficient, scalable treatment of detector geometry and realistic detector effects.

7. Timelines, Current Status, and Future Prospects

The MUonE Letter of Intent was submitted in 2019, endorsed by SPSC; pilot and test runs (2–3 stations) have demonstrated mechanical, thermal, and DAQ capabilities, as well as alignment and resolution performance (Abbiendi, 2020, Abbiendi, 2022). Full construction of the 40-station baseline is scheduled for the current LHC run period; full data-taking aims for an integrated luminosity of $1.5\times 10^7\,\mathrm{nb}^{-1}$ over $\sim3$ years.

Projected uncertainties (statistical + systematic) on $a_\mu^{\rm HVP,LO}$ are $\sim0.35\%+<0.5\%$, competitive with and orthogonal to both dispersive and lattice-QCD approaches (Venanzoni, 2018, Abbiendi, 2020, Abbiendi, 2022). The space-like approach, with its independent systematics, will test the robustness of the Standard–Model prediction and clarify whether the observed $g-2$ tension is due to hadronic theory, new physics, or experimental factors. In parallel, the MUonE apparatus offers a high-acceptance, ultra-low-background environment for BSM searches in the sub-GeV regime, leveraging its advanced tracking for displaced-vertex discovery.

The analysis methodologies, especially Padé/D-Log Padé fits for analyticity-driven extrapolation (P. et al., 15 Nov 2024), and the integration of advanced machine learning for pattern recognition (Zdybal et al., 5 Feb 2024), position MUonE as a leading experiment at the interface of precision Standard–Model physics and discovery of new light particles.