Vol. 49 (2018)

ACTA PHYSICA POLONICA B

No 6

MUON g − 2, CURRENT EXPERIMENTAL STATUS
AND FUTURE PROSPECTS∗
Alberto Lusiani
for the Muon g−2 Collaboration
Scuola Normale Superiore and INFN, Sezione di Pisa, Italy(Received April 27, 2018)
The muon gyromagnetic anomaly aµ has been measured with a precision δaµ /aµ = 540 ppb using magic-momentum muon decays recorded up
to 2001 by the E821 BNL experiment. Two projects aim at significantly
improving that experimental precision: the E989 Collaboration at Fermilab plans to collect 21 times the BNL statistics and to improve by a factor
four the uncertainty, the E34 Collaboration is designing a new experimentat J-PARC with a novel approach based on the production, injection andstorage of ultra-cold low-energy muons. E34 aims at matching the BNL
precision in a first phase, and to provide a significantly higher precision
measurement in a second phase.
DOI:10.5506/APhysPolB.49.1247

1. Introduction
The muon gyromagnetic anomaly is defined from the muon gyromagnetic
factor gµ as aµ = (gµ − 2)/2. A sequence of experiments has measured aµwith increasing precision over time, as shown in figure 1, achieving a remarkable sub-ppm accuracy. On the experimental side, it is a low-energy
measurement whose high precision allows testing quantum loop effects either
from high order Standard Model processes or from new physics processes.
The present experimental precision, δaµ /aµ = 540 ppb, is dominated by
the E821 Collaboration measurement, which uses the magic-momentum (p =3.094 GeV/c) muon decays collected at Brookhaven in the years from 1998
to 2001. The E821 2006 final report [1] concludes a series of measurementsthat started in 1960. Over the last several years, Standard Model (SM)∗

Presented at the Cracow Epiphany Conference on Advances in Heavy Flavour Physics,Kraków, Poland, January 9–12, 2018.

(1247)

1248

A. Lusiani
9.4 ppm CERN 1979 (µ+)
116591000 ± 1100
10 ppm CERN 1979 (µ-)
116593700 ± 1200
13 ppm BNL 1999 (µ+)
116592500 ± 1500
5 ppm BNL 2000 (µ+)
116591910 ± 590
1.3 ppm BNL 2001 (µ+)
116592020 ± 140 ± 60
0.7 ppm BNL 2002 (µ+)
116592030 ± 60 ± 50
0.7 ppm BNL 2004 (µ-)
116592140 ± 80 ± 30
0.54 ppm BNL 2006 (µ± average)
116592089 ± 54 ± 33
116590000

116592000

116594000

aµ × 1011

Fig. 1. Experimental measurements of aµ since 1979.

theory predictions of aµ have reached a precision δaµ /aµ = 300 ppb [2], andtoday the measured discrepancy between experiment and theory corresponds
to about 4 standard deviations [2].
Improvements on the experimental and theoretical precision are requiredin order to understand if the observed discrepancy is caused by physics
beyond the SM or by statistical fluctuations. Two projects aim at obtaining
significant improvements of the experimental accuracy in the incoming years:
the Fermilab E989 and the J-PARC E34 experiments.
2. The aµ measurement
A muon with charge q, mass m and energy described by the Lorentz
factor γ in an uniform magnetic field with intensity B revolves on a circular~orbit with cyclotron frequency ω~ c = −q B/mγ.
The muon spin precesses~~at frequency ω~ s = −(gq B/2m) − [(1 − γ)q B/γm] [3], where the two terms
describe the Larmor precession of a spin at rest, and the Thomas precession
contribution related to the circular motion of the muon. The muon anomalous precession frequency is the difference between the two frequencies
 ~~g − 2 qBqB
ω~a ≡ ω~s − ω~c = −= −aµ.
(1)2mm
The parity-violating decay µ− → e− νµ ν̄e produces electrons whose distribution in the solid angle and in energy depends on the muon-spin direction. In
the laboratory frame, the electron distribution in momentum and angle ismodified by the Lorentz boost due to the muon momentum. For a polarized
muon beam stored in magnetic field, detectors counting muon-decay electrons above an energy threshold record a rate that is modulated according toMuon g − 2, Current Experimental Status and Future Prospects1249

the angle between the muon spin and the muon momentum and, therefore,
with frequency ωa , as shown in figure 2. Fitting the detected electron ratewith an exponentially decay function modulated by a cosine returns ωa witha precisionr2δωa1=,(2)ωaωa γτµ N A2 P 2where γ accounts for the relativistic dilation due to the muon momentum, τµis the muon lifetime, N is the number of detected muons above threshold,
A is the amplitude of the muon rate modulation (which depends on thethreshold) and P is the muon polarization.

Counts per 150 ns

1010101010654320204060Time (µs) modulo 100 µs

80100Fig. 2. Modulation of the rate of detected electron above threshold in E821. The
fit is overlaid on the data. The data is wrapped around every 100 µs. Courtesy ofthe E821 Collaboration.

The magnetic field is measured with pulsed proton Nuclear MagneticResonance (NMR) probes in terms of the proton Larmor precession frequency, ωp , and aexp
is obtained asµaexpµ =ge ωa mµ µp,
2 ωp me µe(3)where ge is the electron gyromagnetic factor, mµ and me are the electron
and muon masses, µp and µe are the proton and electron magnetic moments.
The uncertainty on aexp
µ is dominated by the uncertainty on the ratio ωa /ωp .
The electron ge factor, the muon-to-electron mass ratio, and the proton-toelectron magnetic moment ratio are known with high accuracy from otherindependent measurements [4].

1250

A. Lusiani

3. Muon magic momentum
The E989 project relies on the experimental arrangements that were firstused for the 1975 CERN measurements of the muon anomaly and since thenfor the following CERN and BNL measurements. A beam of polarized muons
with charge q, mass m, velocity v, β = v/c and Lorentz factor γ is stored in~ and electric quadrupoles fielda ring equipped with uniform magnetic field B~E for vertical confinement. Due to the motion of the muons through thequadrupoles electric field, there is an additional contribution to the muon
spin precession frequency, which modifies ωa as follows:" ~ ~#q
1β×E~ − aµ −ω
~a = −aµ B.
(4)m
γ2 − 1c
By setting the muon momentum around the “magic” momentum pµ =3.094 GeV/c, (γ = 29.4), the contribution proportional to the electric field
vanishes. Small deviations and uncertainties around the magic momentum
correspond to manageable systematic uncertainties on the aµ measurement.
4. Fermilab E989
As in the CERN measurements starting in 1975, E989 obtains a polarized
muon beam by colliding protons on a target, producing pions and accepting
muons from forward pion decays into a storage ring.
At FNAL, a flux consisting of 12 fills per seconds each containing 1012 ×
8.9 GeV protons hits a target producing a large number of secondary particles. For each fill, about 1.2 × 108 positive pions with suitable momentum
close to 3.1 GeV are accepted on a beam line ending in a pion temporarystorage ring with about 500 m circumference. Here, they complete a few
revolutions, eventually decaying into muons and neutrinos (π + → µ+ νµ ).
A 95% polarized positive-muon beam is obtained by extracting the muons
from the pion ring and moving them into a 14 m-diameter muon storage
ring, which accepts muons within ±0.5% of the magic momentum.
Thanks to improvements in the beam lines with respect to E821, E989
expects a high purity muon beam with no protons and about 10−5 pion
contamination. Muons in the storage ring decay with a dilated lifetime ofabout 64 µs, producing positrons that are tracked by 3 in-vacuum strawchamber modules inside the ring and by 24 lead–fluoride electromagnetic
calorimeter modules along the ring.
Each tracker module consists of 8 sub-modules made of 4 layers of 32
straws; the 4 layers are organized in 2 views at ±7.5◦ with respect to thevertical. Each calorimeter module consists of 54 crystals in a 6 × 9 matrix,
equipped with silicon photomultipliers to read the crystals’ Cherenkov light.

Muon g − 2, Current Experimental Status and Future Prospects

1251

The measurement of ωa relies on fitting the rate of positrons with energy
larger than 1.86 GeV over time. To minimize muon contamination and losses
related to the injection, the fit starts 30 µs after injection. About 1.6 × 104
muons per fill are stored, and about 1.0 × 104 survive after 30 µs. About
1.1 × 103 positrons above threshold are detected per fill. By recording about
21 times the E821 statistics, E989 plans to reduce the statistical error on ωafrom 458 ppb to 100 ppb.
The systematic uncertainty on ωa is expected to improve from 180 ppm
with E821 to 70 ppm with E989. The largest systematic contribution on theE821 ωa measurement originated from uncertainties on how the calorimeter
gain varies for each detector element as a consequence of the exponentiallydecaying hit rate within each fill. A significantly more elaborate and redundant laser calibration system will accurately measure the calorimeter gain
variations with reference laser light pulses, reducing the expected systematic
contribution from 120 ppb to 20 ppb. Systematics from rate-dependent hit
pileup will be reduced by using a highly segmented calorimeter with very
fast silicon photomultiplier readout and higher digitization sampling rate.
Improvements on the storage ring collimators will reduce the systematics
from the muon loss rate. Improvements in the storage ring optics will reduce systematics from coherent betatron oscillations related to the weakelectric focusing field. Systematics from the quadrupole electric field andfrom deviations of the magnetic field direction with respect to the vertical
will be reduced by improvements in tracking and simulation.
E989 uses the BNL E821 14 m-diameter storage ring, which has beentransported from BNL to FNAL and reassembled. The 1.45 T magnetic
field is accurately mapped and measured along the muon path in the storage ring with a total of 400 pulsed proton NMR probes located above andbelow the muon storage volume, as shown in figure 3. Interpolation of themeasured field between these probes is cross-checked with measurements by
17 NMR probes in a trolley that is periodically moved on a rail along thewhole storage ring to measure the field exactly in the muon storage region.
The muon distribution along the storage ring is measured by tracking theirdecay electrons. The muon distribution is folded with the magnetic field
map to obtain the average effective proton precession frequency ωp for theaµ measurement. By means of a large number of improvements on several
sources of systematics, E989 expects to estimate a 70 ppb systematic uncertainty on ωp , significantly improving the 170 ppb systematic uncertainty
quoted by E821. One source of systematics is the uniformity of the fieldwithin the 4.5 cm radial acceptance of the storage ring. The magnetic field
uniformity is carefully optimized with corrective coils and a shimming procedure based on positioning a large number of magnetic elements along thering to remove any measured field inhomogeneity. With respect to E821,

1252

A. LusianiFig. 3. Cross section of E989 magnet.

local field inhomogeneities are now reduced from 100 ppm to 50 ppm. LikeE821, E989 expects to obtain an azimuthally averaged magnetic field uniformity of 1 ppm across the radial acceptance.
E989 plans to get measurements with 1–2 times the BNL statistics in2018, 5–10 times in 2019 and 21 times in 2020. Combining in quadrature
the expected statistical and systematic uncertainties on ωa with the expected
entirely systematic uncertainty on ωp , E989 ultimately aims to obtain a
140 ppb precision on the aµ measurement.
5. J-PARC E34
The J-PARC E34 Collaboration has proposed a novel scheme to measureaµ , based on “ultra-cold” muons stored at low momentum in a small magnet, where they can remain confined without focusing quadrupole electricfield. In more detail, E34 relies on a 3 GeV/c proton beam, which produces
pions at rest on a graphite target. The pions decay producing 29 MeV/csurface muons, which are stopped on a silica aerogel target equipped withmicro-channels obtained with laser ablation [5]. Here, positive muons bindwith electrons to form muonium atoms. By firing lasers with λ = 122 nm
and λ = 355 nm, the muonium atoms are first excited and then ionized,producing 50% polarized thermal muons with RMS(p) ∼ 3 keV/c. Laboratory tests show that J-PARC can assemble a muon source with a rateof about 2 × 105 µ/s [5]. These ultra-cold muons are accelerated to a momentum of 300 MeV/c with a LINAC and stored is a conventional magnetic

Muon g − 2, Current Experimental Status and Future Prospects1253

resonance imaging (MRI) magnet, operated at 3 T. Containment is obtainedwith a very weak radial magnetic field, whose intensity does not affect theaµ measurement. There will be no electric field. The experimental setup, illustrated in figure 4, is remarkably compact when compared to theCERN, BNL and FNAL storage rings. The storage radius is just 33 cm, thecyclotron period is only 7.4 ns, and the muon lifetime is ten times shorterthat at the magic momentum. Positrons from muon decays are detectedby a high granularity double-sided silicon microstrip detector, composed ofradially-arranged vertical planes with radial strips on one side and axial
strips on the other side.

Fig. 4. (Colour on-line) The proposed set-up for the J-PARC g − 2 Experiment.
Muons enter at the top left (green trajectory) and spiral into the highly uniform
magnetic field region. Their decay positrons curl inward to an array of silicon
tracking detectors. Courtesy of T. Mibe.

Having a small magnet facilitates the attainment of a very uniform magnetic field. The detector has high and uniform efficiency, and is also wellsuited for the detection of the muon electric dipole moment (EDM) effects,
which modulate the muon spin vertical angle and, as a consequence, thepositron rate distribution in the vertical angle. The E34 set-up will haveto compensate its smaller muon polarization and shorter measurement timewith a larger muon statistics. On the other hand, its muon production
scheme is very efficient and the highly segmented silicon detector is expected
to be very resilient to pileup effects.

1254

A. Lusiani

The novel approach of E34 requires a large amount of research and development activity, which is expected to be complete in 2018. So far, theCollaboration has measured the yield and properties of thermal muonium
production, has built and operated a ionization laser system at 10% of thedesign power, has demonstrated the feasibility of electro-static accelerationof thermal muons, has obtained a magnetic field uniformity at the 1 ppm
level, and has built a full size silicon detector complete with custom frontend electronics.
A first phase of the E34 experiment is approved, and the Collaborationis going to start data taking in 2020, with the goal to measure aµ with astatistical uncertainty of 370 ppb. The systematic uncertainties are substantially different from the ones estimated for the BNL and FNAL experiments
and there are not yet estimates. The Collaboration expects to be able toobtain a 100 ppb statistical precision in a second phase of operations, which
is not yet approved. Table I summarizes the comparison of E34 with E989.
TABLE I
Comparison between E34 and E989, reproduced from [6]. The events in the final
fit for E34 correspond to the goal for the second phase of operations.
Parameter

FNAL E989

J-PARC E34

Magnetic field
RadiusCyclotron period
Precession frequency, ωaLifetime, γτµTypical asymmetry, A
Beam polarization
Events in the final fit

1.45 T711 cm149.1 ns
1.43 MHz
64.4 µs
0.4
0.97
1.5 × 1011

3.0 T
33.3 cm
7.4 ns
2.96 MHz
6.6 µs0.4
0.50
8.1 × 1011

6. Summary
In the next years, the muon anomaly experimental precision will improvesignificantly with the operation of two very different experiments. The firstone, E989, improves the “magic momentum” scheme used at CERN since1975 and later remarkably exploited in BNL. The second one relies on anovel scheme based on thermal muons accelerated to a low momentum andstored in a small magnet with no electric field focusing. The two experiments will have different and mostly independent systematic uncertainties.
Table II summarizes the existing uncertainties on the muon anomaly andthe expected improvements with the two new forthcoming experiments.Muon g − 2, Current Experimental Status and Future Prospects

1255
TABLE II

Reported and expected uncertainties on the muon anomaly measurements.

δωa statisticalδωa systematicδωp systematic
δaµE821
[ppb]

E989
[ppb]

E34-1
[ppb]

E34-2
[ppb]

458
180
170
540

100
70
70
140

370

100

REFERENCES[1] G.W. Bennett et al. [Muon g − 2 Collaboration], Phys. Rev. D 73, 072003(2006) [arXiv:hep-ex/0602035].
[2] F. Jegerlehner, Acta Phys. Pol. B 49, 1157 (2018), this issue.
[3] V. Bargmann, L. Michel, V.L. Telegdi, Phys. Rev. Lett. 2, 435 (1959).
[4] P.J. Mohr, D.B. Newell, B.N. Taylor, Rev. Mod. Phys. 88, 035009 (2016)[arXiv:1507.07956 [physics.atom-ph]].
[5] G.A. Beer et al., Prog. Theor. Exp. Phys. 2014, 091C01 (2014)[arXiv:1407.8248 [physics.ins-det]].
[6] T.P. Gorringe, D.W. Hertzog, Prog. Part. Nucl. Phys. 84, 73 (2015)[arXiv:1506.01465 [hep-ex]].