Proceedings of the 3rd J-PARC Symposium (J-PARC2019)
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Proc. 3rd J-PARC Symposium (J-PARC2019)
JPS Conf. Proc. 33, 011110 (2021)
https://doi.org/10.7566/JPSCP.33.011110

J-PARC muon g − 2/EDM experiment
Yutaro Sato1 on behalf of J-PARC E34 Collaboration
1

Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization, 1-1
Oho, Tsukuba, Ibaraki 305-0801 Japan
E-mail: syutaro@post.kek.jp(Received November 29, 2019)
The muon anomalous magnetic moment (g − 2)µ and the electric dipole moment are sensitive to newphysics beyond the Standard Model (SM). There is a discrepancy between the (g − 2)µ measured by
the E821 collaboration at Brookhaven National Laboratory (BNL) and the SM prediction at the morethan 3σ level. This may imply a presence of new physics, therefore, precision measurements of themuon anomaly with an independent method are crucial. We aim to measure (g−2)µ with a precision of
450 parts per billion and to search for the electric dipole moment with a sensitivity of 1.5×10−21 e·cm
in the initial phase with a method diﬀerent from the E821 at BNL and E989 at Fermilab experiments.
To reach the target precision, we utilize a high-intensity proton beam at J-PARC and newly developed
technique of reaccelerated thermal muon beam, which is produced by thermal muonium production
followed by laser ionization and linear acceleration. We report experimental approaches, current
status of each component of our experiment, and future prospects.
KEYWORDS: muon, J-PARC, g − 2, EDM

1.

Introduction

In the presence of static electric and magnetic fields, the spin precession vector with respect to its
momentum is given as()⃗β × E⃗ η e  ⃗1E⃗ ⃗⃗⃗ =−ω+ β × B +  ,(1)
aµ B − aµ − 2mµc2c
γ −1⃗ and E⃗ are the magnetic and electric fields, e is the elementary charge, mµ is muon mass,
where B√aµ = (g − 2)µ /2 is the muon anomalous magnetic moment, γ = 1/ 1 − v2 is the relativistic Lorentz
Factor, β is the ratio of particle velocity to the speed of light c, and η is the size of the electric dipole
moment (EDM). In the experiment, ωa and B are measured to determine aµ . In the Brookhaven National Laboratory(BNL)-E821 experiment, the muon momentum is chosen to be “magic momentum”
of 3.094 GeV/c such that aµ − 1/(γ2 − 1) = 0. There is a discrepancy between the (g − 2)µ measured
by BNL-E821 [1] and the Standard Model (SM) prediction at the more than 3σ level. To verify the(g − 2)µ anomaly, two new experiments are in progress. One is the experiment by the E989 collaboration at Fermilab [2]. It is in operation to reduce the combined statistical and systematic uncertainties
of the BNL experiment by a factor of 4.
The other is the experiment by our E34 collaboration at J-PARC [3]. We eliminate the second
term of Eq.(1) by choosing the null electric field instead of using the magic momentum. The spin
precession equation is simplified as:e [ ⃗ η (⃗ ⃗ )]⃗ =−aµ B + β × B .
(2)
ωmµ2
Since the rotation axes of the anomalous magnetic moment and electric dipole moment are orthogonal
to each other, we can separate signals due to the anomalous magnetic moment and electric dipole
1■■■011110-1©2021 The Author(s)This article is published by the Physical Society of Japan under the terms of the Creative Commons Attribution 4.0 License. Any further distribution of this work
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moment. In order to achieve our goal, we utilize the high-intensity proton beam at J-PARC and newly
developed technique of reaccelerated thermal muon beam. The muon beam can be stored without
requiring an electric focusing field, because the reaccelerated thermal muon beam has an extremely
small transverse momentum. A typical transverse-divergence angle of the muon beam becomes 10−5
radian. Figure 1 shows the overview of the J-PARC E34 experiment. A proton beam is transported
from the 3 GeV Synchrotron ring to the Materials and Life Science facility (MLF) and injected to thegraphite target. The generated surface muons are transported to one of the muon beam lines, H-line,
at the MLF. The reaccelerated thermal muon beam is generated from room-temperature muons by
the silica aerogel followed by the laser ionization, and then accelerated up to 300 MeV/c at a linac as
shown in Figure 2. The muon is injected to the superconducting storage magnet supplying 3 T fieldby the newly developed three-dimensional injection scheme and the decay positron is detected by thesilicon strip detector. We aim to measure (g − 2)µ with a precision of 450 parts per billion (ppb) andto search for the electric dipole moment with a sensitivity of 1.5 × 10−21 e·cm in the initial phase.

Fig. 1. Overview of the J-PARC muon g − 2/EDM
experiment [3].

2.

Fig. 2. Scheme of the reaccelerated thermal muon
beam [3].

Current status

2.1

Production of Thermal Muons from Surface Muons
Figure 2 shows the scheme of the reaccelerated thermal muon beam. Surface muons are transported to a silica aerogel target. A surface muon produces an atom-like state called muonium (e− µ+ )by a diﬀusion process through the target. A room-temperature target such as silica is suitable for theJ-PARC E34 experiment because the thermally-diﬀused muonium has much smaller momentum thanmuons after the acceleration. However, the muonium production rate is lower than our requirement.
The muonium production rate from the standard silica aerogel is limited because the muonium diﬀusion distances(∼ 30 µm [4]) is smaller than the scale of the muon stopping and muonium formation
distribution (∼a few mm). To increase a surface area of silica aerogel, we introduced many cylindricalholes created by laser ablation as shown in Figure 3. The muonium production rate from the laser ablated aerogel was measured at the TRIUMF M15 beamline [5]. Figure 4 shows the timing distributionof the reconstructed decay positrons downstream of the laser ablated aerogel with pitch holes of 300µm compared to that from the silica aerogel without laser ablation. We have succeeded to enhance
the muonium production rate from silica aerogel by introducing laser ablation. The emission rate forthe ablated aerogel with holes is at least eight times higher than that without the laser ablation. We
expect further improvement by optimizing such parameters as hole diameter, pitch, and depth.
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With Lyman-α lasers with wavelengths of 122 nm and 355 nm, electrons are detached from themuonia, and thermal muons with momentum of 2.3 keV/c are obtained.

Fig. 3. Muonium production target. Photo of surface on the laser ablated aerogel sample (left) and the laser
ablated aerogel installed on a target holder (right) [5].

Events / 3 ×10 muons

200 ×103Target plus vacuum-8 < z < 40 (mm)150

8Flat Aerogel (2013)
Drilled Aerogel

Events / 3 ×10 muons

0500

246881012Region 220 < z < 30 (mm)80024681012Region 330 < z < 40 (mm)

400
350
250
200

400

150
100

200000450

300

600

01500
1000

500Region 110 < z < 20 (mm)

2500
2000

100

1000

3000

50246810Time ( µ ) s

1200246810Time ( µ ) s

12Fig. 4. Time distributions of positrons in the entire region and in each of three vacuum regions, for aerogel
without laser ablation (open circles) and aerogel with laser ablation (closed circles) [5].

2.2Muon Linac
The room-temperature muons created by the laser ionization of thermal muonium are reaccelerated up to a momentum of 300 MeV/c. To suppress muon decay loss during the acceleration, the muons must be accelerated in a suﬃciently short time. Furthermore, the transverse emittance growth in the linac should be suppressed to as small a value as possible. In accelerating the3■■■Proceedings of the 3rd J-PARC Symposium (J-PARC2019)
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Events/50 ns/4×1011 µ+ incident

muons, the velocity of the muon beam (β) increases rapidly with the kinetic energy. To realize sufficiently eﬀective acceleration over the wide β region, we adopt several types of RF cavities; radio
frequency quadrupole (RFQ), interdigital H-type drift tube linac (IH-DTL) [6], disk-and-washerstructure (DAW), and disk-loaded traveling wave structure (DLS). The RFQ is the first RF accelerator in the muon LINAC in order to bunch the muons and accelerate them. IH-DTL and DAW, DLS
cover low β (β < 0.3), middle β (0.3 < β < 0.7), and high β (0.7 < β) regions, respectively. Fromsimulation, we do not find a significant emittance growth at the exit of the accelerator. The feasibilityof the muon acceleration has been demonstrated with RFQ for the first time in the world as shown inFigure 5.
RF on40RF oﬀsimulation

2005001000

Time of ﬂight [ns]

1500

2000

Fig. 5. Time-of-flight spectrum with and without the RF operation [7]. The signal of accelerated muons areseen at expected timing.

2.3Beam Injection and Storage Magnet
A 3T MRI-type superconducting solenoid magnet will be used to inject and store the muon beam.
The magnet generates a magnetic field of 3 T with a local uniformity less than 1 ppm peak-to-peak,
and the integrated magnetic field uniformity along the beam orbit in the storage region is controlledwith a precision of 100 ppb peak-to-peak. The radius of our storage ring is 66 cm, which is about
20 times smaller than that at BNL and Fermilab. To inject the muon beam into our compact storage
ring, it is impossible to adopt the procedures used at BNL and Fermilab. We have designed a new
injection scheme, a so called spiral injection scheme [8]. Figure 6 shows the concept of the spiralinjection scheme. The muon beam is injected into the injection volume in an oblique direction. Thespiral motion of the muon beam is compressed by a radial magnetic field, which will be arisen as aradial fringe field. The pulser magnetic kicker is used to guide the spiral muon beam into a stableorbit at the center of the storage region. The spiral injection scheme is being demonstrated with anelectron gun. We successfully injected the electron beam into the storage chamber and observed its
trajectory [9]. Further study for stable injection is ongoing.
2.4

Detector and Track Reconstruction
To detect positrons from muon decays, we locate high granular and fast response silicon strip
detector in the storage magnet. The silicon strip sensors are radially placed in the detection volume
to eﬃciently detect the circular track of the positrons as shown in Figure 7. Geometrical coverageof the detector is 90-290 mm in the radial direction and within ±200 mm in height. The detector
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Fig. 6. Spiral injection scheme. The muon beam momentum is deflected vertically by a radial magnetic field,
which will be built into the solenoid fringe field (Br ) [8].

consists of 40 radial modules called vanes. Each vane consists of 16 sensors. Silicon strip sensor
are made by Hamamatsu Photonics K.K with p-on-n technology. The active area of a sensor is97.28 mm × 97.28 mm with a thickness of 0.32 mm. A sensor has two blocks of 512 strips witha pitch of 190 µm. Mass production of sensors started. Basic characteristics such as the full depletion
voltage, the bulk capacitance, and the inter-strip capacitance were measured and we found no serious
problems. The front-end ASIC is required to tolerate a high hit rate (∼ a few MHz) and the hit-ratechanges by a factor of 150 from the beginning to the end of the measurement. We have fabricatedprototype ASICs [10]. Each ASIC has 128 channels, with Silterra 0.18 µm CMOS technologies. We
will use 640 sensors and 5,120 ASICs for 40 vanes. The number of strips is 655k in total.
To estimate detector performance, we have assembled detector modules, which consist of a production version of a silicon strip sensor and eight prototype ASICs. We operated the assembled detector modules with a pulsed muon beam at J-PARC and positron beam at the Research Center forElectron Photon Science (ELPH), Tohoku University. As a result of the performance test, we estimated the noise to be 725 electrons and the time resolution to be 3.2 ns with a detector capacitanceof the silicon strip sensor of 17 pF [11]Fig. 7.

Perspective view (left) and top view (right) of the positron detector.
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The track reconstruction tool is being developed for positron tracking. Figure 8 shows a simulated
event display and reconstructed tracks. A Hough transformation is used for the track finding. The
expected highest number of muon decays is 6 in 1 ns and the highest hit rate is estimated to be
1.4 MHz per strip. With this algorithm, a track reconstruction eﬃciency estimated to be greater than
90% is achieved in the positron energy range of 200 MeV < E < 275 MeV even at the highest
positron rate from the simulation study.

Fig. 8. All reconstructed hits from 25 muon decays obtained from simulation projected onto the horizontal(x-y plane) (bottom left) and in the ϕ-z plane (bottom right), and perspective view in 3D space (top) are shown.

3.

Sensitivity to aµ and EDM

Figure 9 shows an expected muon-decay time distribution for the measurement of the aµ and theEDM. Assuming 2.2 × 107 seconds of data taking, we expect the statistical and systematic uncertainties on the aµ measurement to be 450 ppb and less than 70 ppb, respectively. Systematic uncertaintiesof aµ are studied and summarized in Table I. For the EDM measurement, we expect 1.5 × 10−21 e·cm
and 0.36 × 10−21 e·cm of statistical and systematic uncertainties with the same data taking time,respectively. A dominant source of the systematic uncertainties is the misalignment of the detector.
We will spend three and a half years for the construction of infrastructure and apparatus and halfa year for the commissioning run. After that, we will start data taking.
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Fig. 9. Simulated time distribution of reconstructed positrons (left) and the up-down asymmetry as a functionof time modulo of the g − 2 period (right) [3]. The solid curve is a fit to simulated data. We assumed the EDM
to be dµ = 1 × 10−20 e·cm in this plot.

Table I. Estimated systematic uncertainties on aµ .
Anomalous spin precession (ωa )SourceTiming shift
Pitch eﬀect
Electric field
Delayed positrons
Diﬀerential decay
Quadratic sum

Estimation (ppb)< 3613100.81.5< 40

Magnetic field (ω p )SourceAbsolute calibration
Calibration of mapping probe
Position of mapping probe
Field decay
Eddy current from kicker
Quadratic sum

Estimation (ppb)252045< 100.156

4. Summary
The E34 experiment at J-PARC aims to measure (g − 2)µ with a precision of 450 ppb and search
for the electric dipole moment with a sensitivity of 1.5 × 10−21 e·cm in its initial phase. To achieve
our goal, we utilize the high-intensity proton beam at J-PARC and newly developed technique ofreaccelerated thermal muon beam. Since our experimental approach is diﬀerent from the BNL andFermilab, the sources of systematic uncertainties are also diﬀerent. Basic studies on each componentof the experiment have been performed and we are about to proceed to the construction phase.
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JPS Conf. Proc. 33, 011110 (2021)[11] T. Aoyagi et al., arXiv:1910.13087.

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