A New Approach for Measuring the Muon Anomalous Magnetic Moment and Electric Dipole Moment

Abstract: This paper introduces a new approach to measure the muon magnetic moment anomaly $a_{\mu} = (g-2)/2$, and the muon electric dipole moment (EDM) $d_{\mu}$ at the J-PARC muon facility. The goal of our experiment is to measure $a_{\mu}$ and $d_{\mu}$ using an independent method with a factor of 10 lower muon momentum, and a factor of 20 smaller diameter storage-ring solenoid compared with previous and ongoing muon $g-2$ experiments with unprecedented quality of the storage magnetic field. Additional significant differences from the present experimental method include a factor of 1,000 smaller transverse emittance of the muon beam (reaccelerated thermal muon beam), its efficient vertical injection into the solenoid, and tracking each decay positron from muon decay to obtain its momentum vector. The precision goal for $a_{\mu}$ is statistical uncertainty of 450 part per billion (ppb), similar to the present experimental uncertainty, and a systematic uncertainty less than 70 ppb. The goal for EDM is a sensitivity of $1.5\times 10^{-21}~e\cdot\mbox{cm}$.

• The paper presents a new methodology using low muon momentum and vertical injection into an MRI-type solenoid to achieve a precision of 450 ppb for aμ and an EDM sensitivity of 1.5×10⁻²¹ e·cm.
• The design features a compact 66 cm storage ring with a highly uniform 3 T magnetic field (100 ppb uniformity) and employs reaccelerated thermal muons with reduced transverse emittance.
• Simulation results project the detection of approximately 5.7×10¹¹ positrons over 2.2×10⁷ seconds, offering potential insights into new physics beyond the Standard Model.

Measuring the Muon Anomalous Magnetic Moment and Electric Dipole Moment

This paper presents a novel experimental design to measure the muon anomalous magnetic moment ($a_{\mu} = (g-2)/2$) and the electric dipole moment (EDM, $d_{\mu}$) at the J-PARC muon facility. These measurements are crucial, as a more than 3.5$\sigma$ discrepancy has been observed between the theoretical predictions of the Standard Model (SM) and the experimental values for $a_{\mu}$. Precision in these measurements could potentially shed light on new physics beyond the SM.

Experimental Design and Methodology

The experiment employs a significantly different approach compared to previous and ongoing studies, such as those conducted at Brookhaven National Laboratory (BNL) and Fermilab. The key distinctions in this new methodology include the use of a lower muon momentum (300 MeV/$c$) and a smaller diameter storage ring (66 cm). The method also features a reaccelerated thermal muon beam with significantly smaller transverse emittance and employs a vertical injection into an MRI-type solenoid, enhancing the injection efficiency.

The experiment targets a statistical precision of 450 parts per billion (ppb) for $a_{\mu}$ and an EDM sensitivity of $1.5\times 10^{-21}~e\cdot\mbox{cm}$. The systematic uncertainties are anticipated to be less than 70 ppb for $a_{\mu}$, showcasing improvements over previous systematic constraints.

Experimental Setup

The setup comprises an intricate series of steps beginning with the thermalization of surface muons in silica aerogel, followed by laser ionization to produce thermal muons. These muons are then accelerated through a series of linear accelerators to the required momentum. The storage magnet system, a 3 T MRI-type superconducting solenoid, houses the muon beam where it undergoes precision measurements.

The key to the storage magnet’s performance lies in its highly homogeneous magnetic field, with a precision requirement of 100 ppb peak-to-peak across the muon orbit. The injection of the muon beam utilizes a novel three-dimensional spiral technique, and a weak magnetic focusing field helps maintain beam orbit stability.

In terms of detection, the experiment employs silicon strip sensors to track the decay positrons from stored muons, allowing determination of the precession frequencies necessary for calculating $a_{\mu}$ and $d_{\mu}$. The setup promises to handle a broad dynamic range of positron detection rates, thereby addressing the systematic uncertainties that could arise from variations in positron rates during data acquisition.

Results and Sensitivity

Simulations predict that the experiment will reconstruct approximately $5.7 \times 10^{11}$ positrons over $2.2 \times 10^7$ seconds of data taking, leading to a statistical uncertainty of 450 ppb for $a_{\mu}$. EDM measurements, capable of detecting a minimum measurable value of $1.5 \times 10^{-21}~e\cdot\mbox{cm}$, demonstrate the experiment's sensitivity to potential new sources of CP-violation.

Implications and Future Prospects

This experiment represents a significant advancement in measuring $a_{\mu}$ and $d_{\mu}$, offering a method with enhanced precision and reduced systematic uncertainties compared to past efforts. The findings have substantial implications for potential new physics scenarios. The novel experimental design and its alignment with anticipated theoretical discrepancies may bridge gaps between current experimental results and SM predictions.

The techniques and methodologies established here could pave the way for future experiments in precision measurements of elementary particles. Enhanced magnetic field uniformity and novel injection techniques might be applied to other realms of particle physics research, expanding the potential to explore phenomena beyond the Standard Model.