Table Of ContentCPC(HEP&NP),2009,33(X):1—4 Chinese Physics C Vol.33,No.X, Xxx,2009
*
Status of the Fermilab Muon (g−2) Experiment
B. Lee Roberts1,2;1)
1(DepartmentofPhysics,BostonUniversity,Boston, MA02215,USA)
0 2(OnbehalfoftheNewMuon(g−2)Collaboration)
1
0 Abstract TheNewMuon(g−2)CollaborationatFermilabhasproposedtomeasuretheanomalousmagnetic
2
momentofthemuon,aµ,afactoroffourbetterthanwasdoneinE821attheBrookhavenAGS,whichobtained
n aµ=[116592089(63)]×10−11 ±0.54 ppm. The last digit of aµ is changed from thepublished valueowing toa
a
new value of the ratio of the muon-to-proton magnetic moment that has become available. At present there
J
appears to be a difference between the Standard-Model value and the measured value, at the ≃3 standard
0
deviationlevelwhenelectron-positronannihilationdataareusedtodeterminethelowest-orderhadronicpieceof
2
theStandardModelcontribution. Theimprovedexperiment,alongwithfurtheradvancesinthedetermination
] ofthehadroniccontribution,shouldclarifythisdifference. Becauseofitsabilitytoconstraintheinterpretation
x
of discoveries made at the LHC, the improved measurement will be of significant value, whatever discoveries
e
- may come from theLHC.
p
e Key words measurement, muon anomalous magnetic moment
h
[ PACS 13.40.Em, 12.15.Lk, 14.60.Ef
2
v
1 Introduction mostrecent,E821attheBrookhavenAGS,achieving
8
9 aprecisionofof±0.54partspermillion(ppm) [5,6]:
8
The anomalous magnetic moment (anomaly) of
2 a =[116592089(63)]×10−110.54ppm. (2)
the e, µ or τ lepton is defined by µ
.
1
The result has been slightly adjusted from the value
0 (g −2) Qe
0 ae,µ,τ= e,µ,2τ ; µ~e,µ,τ =ge,µ,τ 2m ~s, (1) reportedinRef.[5,6]becausethe valueofthefunda-
1 (cid:18) e,µ,τ(cid:19) mentalconstantλ=µ /µ ,themuontoprotonmag-
µ p
:
v where ~µ is the magnetic dipole moment, and the fac- netic moment ratio, (see Eq. (6)), has changed [7].
i tor g is equal to 2 in the Dirac theory. One of the The statistical error in the anomaly is ±0.46 ppm
X
importantdiscoveriesonthepathtothedevelopment and the systematic error is ±0.28 ppm. The goal of
r
a ofQED,andthenthe StandardModel,wasthe mea- the new Fermilab experiment [8] is equal statistical
surementbyKuschandFoley[1]whichshoweddefini- and systematic errors of ±0.1 ppm, for a combined
tively that g >2. Almost simultaneously, Schwinger error of 0.14 ppm.
e
showedthatthis differencecouldbe explainedbythe Interestingly enough, the measured muon
(one-loop in modern language) radiative correction anomaly seems to be slightly larger than the
withthe valueα/2π≃0.00116···,independentofthe Standard-Model value of [9]
lepton mass.
aSM[e+e−]=116591834(49)]×10−11 (3)
The Standard-Model value of a arises from loop µ
µ
contributions containing virtual photons, leptons, which uses e+e− annihilation into hadrons to de-
gauge bosons, and hadrons in vacuum polarization termine the hadronic contribution, and the value of
loops. Other talksatthis meeting havediscussedthe Pradeset al., [10]for the hadronic light-by-lightcon-
Standard-Model contributions in some detail. For a tribution. There is a difference of ∼ 3.2 σ between
general review the reader is referred to the review the two. If hadronic τ decays are used to determine
article by Miller, et al., [3]. the lowest-orderhadronic contribution (a determina-
The muonanomalyhasbeen measuredin a series tionthatreliesonsignificantisospincorrections),the
of experiments that began over fifty years ago[4], the difference drops to ∼2σ [11].
Received14January2010
∗ FERMILAB-CONF-10-012-E:SupportedinpartbytheU.S.NationalScienceFoundationandtheU.S.DepartmentofEnergy
1)E-mail:[email protected]
(cid:13)c2009ChinesePhysicalSocietyandtheInstituteofHighEnergyPhysicsoftheChineseAcademyofSciencesandtheInstitute
No.X Author1 etal: Instruction fortypesetting manuscripts 2
Non-Standard-Model contributions could come period. Assuming that the muon velocity is trans-
from muon substructure, supersymmetry or extra verse to the magnetic field (β~·B~ = 0), the rate at
dimensions, to name a few possibilities. Excel- which the spin turns relative to the momentum vec-
lent reviews on this topic have been written by tor is given by the difference frequency between the
St¨ockinger [12], and Czarnecki and Marciano [13]. spin precession and cyclotron frequencies. With an
TheSUSYcontributiondependsontanβandthesign electric field present as well as a magnetic one, the
of the µ parameter [12, 13]: difference frequency becomes
100 GeV 2 ~ω = ~ω −~ω
aSUSY≃sgnµ130×10−11 tanβ. (4) a S C
µ (cid:18) m (cid:19) = − Qe a B~− a − 1 β~×E~ ,(5)
Both tanβ and the µ parameter will be difficult m " µ (cid:18) µ γ2−1(cid:19) c #
e
to determine at LHC.The signofthe deviationofa
fromthe StandardModelgivesthe signofµ, andthµe where γ = (1−β2)−21. (The reason for introducing
anelectricfieldwillbecomeapparentinthe nextsec-
plot below illustrates the sensitivity of LHC and a
µ
tion.) The experimentallymeasurednumbers arethe
to tanβ. It assumes that the SPS1a scenario is real-
muonspinfrequencyω andthemagneticfield,which
ized at LHC [12]. The difference between the Stan- a
ismeasuredwithprotonNMR,calibratedtotheLar-
dardModelandtheresultfromE821isassumedtobe
∆ =(255±80)×10−11. Thebandlabeled“Fermilab” mor precession frequency, ωp, of a free proton. The
aµ
assumesthesame∆ butwithanerrorof±34×10−11 anomaly is related to these two frequencies by
aµ
The improved error comes from the projected 0.14
ω˜ /ω R
ppm experimental error, and improved knowledge of aµ=λ−aω˜ /pω =λ−R, (6)
a p
the hadronic contribution to a . See Ref. [12, 14] for
µ
more details. λ=µ /µ =3.183345137(85), and R=ω˜ /ω . The
µ p a p
tilde over ω means it has been corrected for the
a
2255 electric-fieldandpitch(β~·B~ 6=0)corrections[3]. The
LHCplus ratioλ is determined experimentally fromthe hyper-
amu
finestructureofmuonium,theµ+e− atom[7,15]. As
2200 LHC
alone mentioned above, the recommended value of λ has
changed slightly since the final results of E821 were
published[5,6],increasingthevalueofa by9×10−11,
1155 µ
FNAL which is reflected in Eq. (2).
2
Χ
D
2.1 The Magic-γ Technique
1100 E821
In the 2001 data set, the systematic errorson the
magnetic field were reduced to 0.17 ppm. A num-
55
ber of contributions went into this small error, but
one which we wish to emphasize here is the aver-
age magnetic field experienced by the muon ensem-
00
2 4 6 8 10 12 14 16 18 20 ble. The magnetic field in Eq. (5) is an average that
tan Β can be expressed as an integral of the product of the
muon distribution times the magnetic field distribu-
Fig. 1. A “blueband” plot showing the LHC
and muon (g−2) sensitivities to tanβ. The tionoverthestorageregion. Sincethemomentsofthe
(Figure courtesy of D.St¨ockinger) muondistributioncoupletotherespectivemultipoles
of the magnetic field, either one needs an exceed-
ingly uniform magnetic field, or exceptionally good
2 Measuring a
µ information on the muon orbits in the storage ring,
to determine hBiµ−dist to sub-ppm precision. Thus
The measurement of a uses the spin precession traditional magnetic focusing used in storage rings,
µ
resulting from the torque experienced by the mag- which involves magnetic quadrupole and higher mul-
netic moment when placed in a magnetic field. An tipoles, will cause large uncertainties in the knowl-
ensembleofpolarizedmuonsisintroducedintoamag- edge ofhBiµ−dist. This problemwasmitigatedin the
neticfield,wheretheyarestoredforthemeasurement third CERN experiment[16], and in E821, by using
No.X Author1 etal: Instruction fortypesetting manuscripts 3
electrostatic quadrupoles to provide the vertical fo- neededtobewellbelowsaturationandwaschosento
cusing,freeingthemagnetic-fielddesigntobeasclose be 1.45 T. The resulting ring had a central orbit ra-
to a uniform dipole field as possible. Examination of dius of7.112m, and12detector stationswere placed
Eq. (5) shows that for γ = 29.3, called “the magic symmetrically around the inner radius of the stor-
γ,” an electric field will not contribute to ω . The age ring. The detector geometry and number were
a
electric-fieldeffectvanishesforparticleswiththecen- optimized to detect the high-energy decay electrons,
tralmomentumequaltop =3.09Gev/c,andisa which carry the largest asymmetry, and thus infor-
magic
small(sub-ppm)correctionforotherstoredmuons[6]. mation on the muon spin direction at the time of
The CERN experiment used a rectangular aper- decay. In this design, many of the lower-energy elec-
ture, which at their 7.3 ppm level of precision did trons miss the detectors, reducing background and
not cause problems in determining the average field. pileup. The electrostatic quadrupoles [18] cover 43%
However, the large moments of a rectangular beam of the ring, leaving significantgaps for the fast muon
were not acceptable for the BNL experiment, which kicker[19] and other objects in the ring.
aimedatafactor-of-twentyimprovement. Thusacir- While alternate schemes for measuring a have
µ
cular beam aperture was chosen for E821, which re- been proposed, the magic γ technique has a number
sultedinasystematicerroronhBiµ−dist of0.03ppm, of things in its favor. One of the most important is
certainly adequate for the experiment now proposed thatsinceE821,itisquitewellunderstoodandoffers
at Fermilab. astraightforwardpathtoa0.1ppmmeasurement,or
The experiment consists of repeated fills of the perhaps somewhat beyond. Its features are:
storage ring, each time introducing an ensemble of
• high muon polarization and decay asymmetry;
muons into a magnetic storage ring, and then mea-
suringthe twofrequencies ω andω . The muonlife- • large storage ring with ample room for detec-
a p
time is given by γτ =64.4 µs, and the data collec- tors, field mapping, kickers, etc.;
µ
tion period is typically ∼ 10 muon lifetimes in the
• muoninjection, whichhasbeen shownto work;
ring. The (g−2) precession period is 4.37 µs, and
the cyclotron period is 149 ns. As the µ− (or µ+) • rates in the detectors that are easily handled
decay, e− (e+) are emitted in the decay µ−(µ+) → with conventional technology;
e−(e+)+ν (ν¯ )+ν¯ (ν ). The high-energy decay elec-
µ µ e e • data are fit overmany (g−2) cycles, which is a
trons(positrons)carryinformationonthe muonspin
powerful tool to unmask systematic errorsthat
directionatthedecay. Thusasthespinturnsrelative
depend on time;
to the momentum, the number of high-energy decay
• precision magnetic field techniques which are
electronsismodulatedbythefrequencyω ,asshown
a
well understood;
in Fig. 2.
• well understood systematic errors.
s
9.2n 10 3 The Fermilab Proposal: P989
4
1
er
p
s 1
nt The Fermilabproposal[8]usesthe magicγ inthe
e
v
E precision storage ring developed for E821, with new
n
Millio 10-1 detectors, electronics, along with improved magnetic
field measurement and control. Central to the new
10-2 proposal is the use of features unique to Fermilab
that will provide copious proton bunches of ∼ 1012
10-3 protonsat10to 20ms intervals. This compareswith
0 20 40 60 80 100 ∼4−5×1012 protonsper bunchatBNL,withamax-
Time modulo 100m s [m s]
imum of 12 bunches per machine cycle time of 2.7 s.
Fig. 2. The time spectrum of decay electrons
from the2001 E821 runningperiod, when µ− The effective fill rate at BNL was 4.4 Hz, compared
with a projected rate of 18 Hz at Fermilab.
were stored. (From Ref. [5] )
At BNL, pions 1.7% above the magic momentum
The E821 storage ring was constructed as a decayed in an 80 m long FODO line, producing a
“super-ferric”magnet[17],meaningthatthe ironde- beamthatcontainedanequalnumberofpions,muons
termined the shape of the magnetic field. Thus B and electrons. A large hadronic “flash” accompanied
0
No.X Author1 etal: Instruction fortypesetting manuscripts 4
the injection into the ring causing a significant base- informationfor the interpretationof new phenomena
line shift in the detectors near the injection point. that might be discovered at LHC.
AtFermilab,theRecyclerRingwillbeusedtore- I wish to thank my many colleagues on E821, and
bunch each proton batch from the Booster into four the New (g−2) for useful discussions. Thanks to D.
bunches with ∼1012 protons each. These will be ex- Hertzog for comments on this manuscript, and to K.
tracted one at a time to a production target at the Ellis for editorial help. My participation in this work
location of the present antiproton target. The an- was supported in part by the U.S. National Science
tiproton debuncher ring will be used as a 900 m long Foundation.
pion decay line. The resulting pion flash will be de-
creased by a factor of 20 from the BNL level, and
5 References
the muon flux will be significantly increased because
of the ability to take zero-degree muons. The stored
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