Measurement of the muon anomaly to high and even higher precision

0.55 MB·English

by  David W. Hertzog

Measurement of the muon anomaly to high and even higher precision
5
0 David W. Hertzoga∗
0
2 aDepartment of Physics
University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA
n
a
J Ourrecent series of measurements at Brookhaven National Laboratory determinedthemuon anomalous mag-
0 netic moment aµ to a precision of 0.5 ppm. The final result—representing the average of five running periods
2 using both positive and negative muons—is a± = 11659208(6)×10−10. It lies 2.7 standard deviations above
µ
thestandard model expectation, which is based on updatesgiven at this Workshop. Importantly,only the e+e−

1 annihilation and newKLOEradiativereturn dataareused for thehadronicvacuumpolarization input. Because
v
thesystematic limit has not been reached in theexperiment, a new effort has been proposed and approved with
3
the highest scientific priority at Brookhaven. The goal is an experimental uncertainty of 0.2 ppm, a 2.5-fold
5
reductionintheoverallexperimentaluncertainty. Todosowillrequireasuiteofupgradesandseveralqualitative
0
changes in the philosophy of how the measurement is carried out. I discuss the old and new experiments with a
1
0 particular emphasis on thetechnical matters that require changefor thefuture.
5
0
/ 1. Introduction equally precise a determinations from positive
x µ
e and negative muon samples—the results are per-
- The muon anomalous magnetic moment aµ is fectly compatible—the CPT-combined final re-
ep oqnueanotfitthieesminospthpyrseiccsis.elTyhmeesatsaunrdeadradnmdocadleclu(laStMed) sult is a±µ = 11659208(6)×10−10. The statisti-
h cal and systematic uncertainties are combined in
: theoreticalexpectationandtherecentexperimen- quadratureandthe0.5ppmprecisionrepresentsa
v
tal measurements have both achieved sub-ppm
i 15-foldimprovementcomparedtoCERN-III.The
X precision, enabling a sensitive comparison hav-
uncertaintyisdominatedbystatisticssoitisnat-
r ing new-physics ramifications. A significant de- ural to contemplate an upgrade program aimed
a
viation implies “missing” physics in the model,
at increasing the data accumulation rate while
which is expected to occur in the most popular
maintaining or reducing the systematic uncer-
SMextensionssuchasSUSY.Herewediscussthe
tainties. To this end, the E969 Collaboration—
status of the most recent experiment and the re-
formed largely from the present group plus key
cently approved new experiment aimed at push-
new institutions—has proposedandhasbeen ap-
ing the precision frontier further by a factor of
proved for new running. Several significant con-
approximately 2.5. We give a brief review of the
ceptualchanges,whichwillincreasethedatarate
current standard model expectation.
fivefoldormoreandreducesystematicuncertain-
The E821 Brookhaven National Laboratory
ties further, are required.
(BNL) experiment [1] is the fourth in a se-
The standard model expectation for the muon
quence of a measurements. The rich history in-
µ anomaly is based on QED, hadronic and weak
cludes three ingenious efforts at CERN, the final
loopcontributions. DavierandMarcianohavere-
one [2] achieving a precision of 7.3 ppm. Our
cently publishedareviewofthe theory[9]andat
BNL Collaborationtook data from 1997 through
thisWorkshop,numerousspeakersprovidedtech-
2001. The analysis is complete and all results
nicalupdatestospecificcontributions. Ireferthe
have been reported [3,4,5,6,7] and a comprehen-
readertotheirexpertreportsintheseproceedings
sive review has been published [8]. With nearly
and summarize the current standard model ex-
pectationbrieflyinTable1. Onlythee+e− anni-
∗Representing the E821 [1] and the E969 [20] Collabora- hilation data are used, together with the new ra-
tions.
1
2
diativereturnresultsfromKLOE[10],asthelow-
eplingoehlartgriyszcaaitntitopenurticnotgnotcrtoihnbeturti1ibosutn-t.oiorTdnheherahhsaadbdreroeonnniiccadlivdgahrcetus-subeymd- per 149.2ns 10
by many authors. I use the recommendation in nts 1
Ref. [9], which attempts to find a central value n Eve
with an expanded uncertainty to accommodate Millio 10-1
different individual evaluations.
10-2
2. The Old BNL Experiment: E821
10-3
The central element of the BNL experiment is 0 20 40 60 80 100
Time modulo 100m s [m s]
the muon storage ring [15], which has a highly
uniform 1.45 T magnetic field, a 7.1 m radius,
and vertical containment of the muons by elec-
trostatic quadrupoles [16]. At the magic mo- Figure 1. Distribution of counts versus time for
mentum of 3.094 GeV/c the relativistic gamma the 3.6 billion decays in the 2001 negative muon
is 29.3, the dilated muon lifetime is 64.4 µs, and data-taking period.
the decay electrons2 havean upper lab-frameen-
ergyofapproximately3.1GeV.The basic ideaof
the measurement is to inject and store a bunch
rotation. In the presence of a magnetic and elec-
of polarized muons into the ring, contain them tricfieldhavingB~·P~ =E~·P~ =0,ω isdescribed
a
sufficiently well while they make many revolu-
by
tions, and record their decay time by detecting
the emitted electrons that curl inward and strike ω~ ≡ ~ω −~ω (1)
a a c
electromagnetic calorimeters. If g =2, the initial
e 1
muon spin direction would remain aligned with = m c(cid:20)aµB~ −(cid:18)aµ − γ2−1(cid:19)(β~×E~)(cid:21).
µ
its momentum and the rate of decay electrons in
the detectors would follow a smoothly falling ex- Theterminparenthesesmultiplyingβ~×E~ van-
ponential. For g >2, the muon spin precesses at
ishes at γ = 29.3 and the electrostatic focussing
a rate faster than the muon rotation rate; this
does not affect the spin (except for a correction
additional rotation—the difference between the
necessary to account for the finite momentum
spin rotation and the cyclotron frequency—is di-
range ∆P/P ≈ ±0.14% around the magic mo-
rectlyproportionaltoa . Theaveragemuonspin
µ mentum). Equation 1 can be rearranged to iso-
direction is revealed because parity violation in
latea ,givingω /Bmultipliedbyphysicalquan-
µ a
the weak muon decay correlates the electron en-
tities that are known to high precision. The ex-
ergy (on average) with the muon spin direction.
periment is described below with emphasis on
The rate of detected electrons having an energy
various specific details that will be upgraded for
greaterthana set thresholdis anexponential(as
the new E969 effort.
above), but modulated at the anomalous preces-
Polarized muons are obtained from the decay
sion frequency, see Fig. 1. The key to the ex- π− → µ−ν¯ . In the massless neutrino limit, he-
µ
periment is to determine this frequency to high
licityconservationimpliesthattheoutgoinganti-
precision and to measure the average magnetic
neutrino is right-handed; its spin is in the direc-
field to equal or better precision.
tion of its motion. The negative muon—emitted
The anomalous precession frequency ω de-
a in the opposite direction—is polarized along its
pends on the cyclotron frequency and the spin
motion. In the CERN-III effort, a 3.1 GeV/c
2Byconvention, wediscuss negative muons and their de- pion beam was injected into a storage ring. De-
cayelectronsthroughout thispaper. caymuons,bornduringthefirstturnofthebeam
3
Table 1
Standard model theory and experiment comparison.
Contribution Value Error Reference Comment
×1010 ×1010
QED 11658471.94 0.14 [11] 4 loops; 5th estimated
Hadronic vacuum polarization 693.4 6.4 [12] e+e− + KLOE
Hadronic light by light 12.0 3.5 [14] val. from Ref. [9]
Hadronic, other 2nd order -10.0 0.6 [13] alt.: −9.8±0.1
Weak 15.4 0.22 [9] 2 loops
Total theory 11659182.7 7.3 – –
Experiment 11659208 6 [7] –
Expt. - Thy. 25.3 9.4 – 2.7 standard deviations
in the ring, could fall (with very low probability, the ring through the superconducting inflector is
≈ 100ppm)ontostableorbitswithinthestorage roughly 1:1 at nominal settings. The ratio can
ring aperture. The captured muons came from be adjusted: higher muon rates are obtained at
thenearlyforward-emittedmuons,whichhadthe the expense of greater pion contamination; lower
right momentum but also a small transverse de- rates are obtained for lower pion contamination.
cay “kick” that placed them in the storage ring The employed operating conditions represented
acceptance. The majority of the pions struck de- an appropriate compromise.
tectors or the storage ring yoke causing an enor-
mous prompt hadronic “flash” in the detectors,
whichwasfollowedbyaslowlydiminishingback-
ground from the thermalization and capture of
neutrons. AGS
E821 improved on this method of muon load-
ing significantly by directly injecting an enriched
U−V line
muon beam into the storage ring and then using
apulsedmagnetickicker[17]todeflectthemuons VD3
into the ring acceptance. A pion-muon beamline VD4 V line
Pion Production Target
upstreamoftheringwasdevelopedtoservethree
tpaioskns-:to1-)mauponiondeccraeyatsieocntiaonnd;caanpdtu3r)easeficntiaolnm;2u)ona U line Q2 Q1D1,D2D3,D4 Pion Decay Channel D5 K3−K4 D6
selection at Pmagic = 3.094 GeV/c. Figure 2 (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) Beam Stop
is a schematic of the beamline and storage ring. K1−K2
Inflector
Thepioncaptureandmuonselectionsectionsare
tuned to slightly different momenta. Typical op- g−2 Ring
erating conditions set the pion momentum 1.7%
greater than P . Forward decay muons, but
magic
slightlyoffaxisfromzerodegrees,arecapturedin Figure 2. Plan view of the pion/muon beamline.
the decay channel. A final bend in the beamline
is made by setting dipoles D5 and D6 to trans-
portparticleshavingmomentumP . Thisex-
magic
cludes a largefraction of the pions, because their
averagemomentumishigher. SlitsK3/K4adjust
Direct muon injection resulted in an approx-
the momentum bite that is passed into the stor-
imately 10-fold increase in the effective stored
age ring. The ratio of pions to muons entering
muon rate and a reduction of the hadronic flash
4
by a factor of 50. But the hadronic flash is not ensemblebeatwiththecyclotronfrequencycaus-
eliminated by this technique. The pions that ac- ing an observable modulation in the normaliza-
company the muons into the ring still cause sig- tion term N above because of a modulation in
nificant neutron production and create a prompt the effective detector acceptance. In a more sub-
flash at injection. Because of this, each of the 24 tle manner,the modulationextends to the asym-
electromagnetic calorimeters is gated off during metry andphase terms. Equation3canbe easily
injection and turned back on 5 to 30 µs after in- modified to accountfor these modulations. Simi-
jection; the turn-ontime depends onthe location larly, gain (or energy-scale) stability, pileup, and
in the ring. When the physics fits start, typically muon loss terms require small corrections or fit-
30 µs after injection, the photomultiplier tubes function modifications in order to obtain a good
(PMTs) are still affected by a slowly decaying fit. But these are well-understood procedures
background, which appears as a time-dependent having carefully understood implications on the
pedestal in the recorded digitized pulses. The extracted precession frequency ω . In general,
a
electron rate in each detector at this time is typ- they do not couple strongly to ω , but they do
a
ically severalMHz. affect the goodness-of-fit criterion.
Parityviolationinthemuonweakdecayµ− → Equation1alsocontainsthetermB,whichim-
e−ν¯ ν allows the spin direction to be measured pliesknowingthemagnitudeofthemagneticfield
e µ
as a function of time (on average). The angular within the storage volume as a function of time
distribution of emitted electrons from polarized and weighting the data with the average field.
muons at rest is dn/dΩ = 1−a(E)cosθ where The best way to make this otherwise daunting
θ is between the spin and momentum directions task manageable is to shim the field to high uni-
andthe asymmetrya dependsonelectronenergy formity. The uniformity is well illustrated by the
E. Expressions for n and a are: three contour maps shown in Fig. 3. Each fig-
urerepresentsanazimuthiallyaveragedmagnetic
n(y) = y2(3−2y) fieldfromthebeginningofcommissioningin1997,
a(y) = (2y−1)/(3−2y), (2) tothefirstmuon-injectionrunsin1998/1999,and
later to the high-statistics run in 2000. The con-
with y = Pe/Pe,max. The asymmetry is nega- tours in these figures represent 1 ppm deviations
tive for low-energy electrons and rises to a= +1 from the central average field value. The final
when y = 1. The higher-energy electrons have 2001 field, with reversed polarity, was equally
thestrongestcorrelationtothemuonspin. Inthe good to the 2000 map. The field is very uniform,
lab frame, it is most probable to detect a high- not only for the present experiment, but also for
energy electron when the muon spin is pointing the future.
oppositetothedirectionofmuonmomentumand All field measurements rely on proton NMR
leastlikelywhenthespinisalignedwiththemuon using a system of probes that obtains the ab-
momentum. The rateofdetectedelectronsabove solute field value, the relative field versus time,
energy threshold Eth is and the relative field inside the storage volume.
This system[18]usesa standardreferenceprobe,
dN(t;E )
th =N0e−t/γτµ[1+Acos(ωat+φ)], (3) a “plunging” probe that is inserted into the vac-
dt
uum chambers to transfer the calibration, an
where A is the effective integrated asymmetry NMR “trolley” to map the field inside the stor-
with A ≈ 0.4 for E = 1.9 GeV. Equation 3 is age ring volume, and 378 fixed probes located in
th
the simplest expression that describes the data. the vacuum chamber walls to monitor the field
In practice,it can only be used to obtain anesti- versus time. The magnetic field is measured in
mate of parameters because perturbations to the units of the free proton precession frequency, ωp.
spectrum are caused from beam dynamics or de- Muonium measurementsdetermine the ratio λof
tector and electronic effects. For example, the muon-to-proton magnetic moments [19] and, in
natural betatron oscillations of the stored muon
5
practice, a is determined from the expression 3.1. Backward decay and beamline modifi-
µ
cations
When the pion capture section of the beam-
R
a = , (4) line is tuned 0.5% above the muon magic mo-
µ λ−R mentum, the highest muon flux is achieved. As
noted,thissmallmomentumdifferencepassestoo
many pions into the storage ring, creating back-
where R = ω /ω , a ratio determined in our ex-
a p
ground. If the initial pion momentum is set to
periment.
5.32 GeV/c, then the backward decay muons are
Ineachrunningyear,multipleanalysesofboth
produced at 3.094 GeV/c as desired. The mis-
the precession frequency and the magnetic field
match in momentum between the pion capture
data were carried out independently. Reports to
section and the muon momentum selection sec-
the collaborationwerealwaysmade witha secret
tion is so great that no pions can pass through
offset so that no one person could compute a .
µ
the K3/K4 slits shown in Fig. 2. This implies
After all results were final and all systematic un-
that the entire hadronic flash will be eliminated–
certainties established, the offsets were removed
a key improvement allowing the detectors to be
and a was computed. Figure 4 illustrates the
µ
gated onmuch earlierafter injection and permit-
consistency of the results from eachrunning year
ting the physics fits to start shortly thereafter.
beginning with 1998 and Table 2 gives all of the
Simulations show that the muons are still highly
numeric results.
polarized (albeit, the direction is reversed) and
A precision measurement depends on control
of the systematic uncertainties. Table ?? lists the flux is at or higher than the level obtained
in the current forward-decay scheme. To cre-
all the principle uncertainties for the last three
ate the backward-decaybeam, severalnew front-
high-statistics running periods. The categories
endmagneticelementsmustbebuiltbecausenot
areseparatedbytheindependentω andω anal-
a p
all of the present magnets can be ramped up by
yses. The trend to reduce the uncertainties in
the momentum ratio factor 5.32/3.15. New mag-
each year is evident, except for the CBO effect,
net designs are being pursued and new front-end
whichwasonlyfullyunderstoodpriortothefinal
tunes are being developed by our team.
2001runsothatrunningparameterscouldbead-
Beamtransportstudiesofthepion-to-muonde-
justedtominimizeitseffect. Thegoalforthenew
cay section indicate that improved transmission
experimentistolimitthefieldandtheprecession
canbe obtainedby doubling ortripling the num-
systematic uncertainties each to 0.1 ppm. New
berofquadrupoleelementsintheline. Currently,
data taking operation modes of the storage ring
the 80 mlong FODO sectionhas 20 magnets but
are being planned to reduce some of the beam-
ample room exists for up to four times as many.
dynamics related uncertainties such as CBO and
Forboththeforward-decayorthenewbackward-
muon loss.
decay kinematics, the decay muons are captured
with a wide angular divergence compared to the
pion source. The increased quadrupole density
3. The New BNL Experiment: E969
maintains the lateral extent of the secondary
In September, 2004, the BNL Program Advi- muon beam within the magnet bore, thus avoid-
sory Committee gave the proposal A (g-2) Ex- inglossesthatpresentlyexist. Againinratebya
µ
periment to ±0.2 ppm Precision its highest sci- factor of 2 is expected from this straight-forward
entific endorsement, thus officially launching ex- improvement.
periment E969 [20]. The central idea is to use Themuonbeamentersthestorageringthrough
the existing BNL storage ring largely as is but asuperconductinginflector[21]. Theinflectorhas
to develop a means to increase the stored muon coils thatessentiallyblock both the entranceand
rate, reduce the background, and to maintain or exit openings. Muons lose energy and scatter as
reduce individual systematic uncertainties. they pass through these coils and approximately
6
1997 1998/1999 2000
m] 4 m] 4 m] 4
c c c
y [ y [ y [
2 2 2
0 0 0
−2 −2 −2
−4 −4 −4
−5−4−3−2−1 0 1 2 3 4 5 −5−4−3−2−1 0 1 2 3 4 5 −5−4−3−2−1 0 1 2 3 4 5
x [cm] x [cm] x [cm]
Figure 3. Sequence of improvements to the magnetic field profiles since the original commissioning of
the storage ring. The contours are averagedover azimuth and interpolated using a multipole expansion.
The circle indicates the storage aperture. The contour lines are separated by 1 ppm deviations from the
centralaverage. Fromleft to right,these maps representthe field variationsfor the 1997,1998/1999and
2000 time periods, respectively. The 2001 map, with reversed polarity field, was slightly more uniform
than the 2000 map.
Table 2
Summary of E821 Results
Year Polarity a ×1010 Precision [ppm] Reference
µ
1997 µ+ 11659251(150) 13 [3]
1998 µ+ 11659191(59) 5 [4]
1999 µ+ 11659202(15) 1.3 [5]
2000 µ+ 11659204(9) 0.7 [6]
2001 µ− 11659214(9) 0.7 [7]
Average 11659208(6) 0.5
half of those muons are lost. A closed-ended in- and time of arrival. Each 14 cm high by 23 cm
flectorisshowninthephotographinFig.5a. The wide calorimeteris12.5X deep(15cm)andthe
0
full inflector was built with this coil design be- fiber direction is radial. Four lightguides trans-
causeitrepresentedapracticalchoiceforreliabil- port the light to individual PMTs, located be-
ity reasons at the time of production. However, low the storage ring midplane to avoid being di-
theoppositeendoftheinflectorprototypehadan rectly struck during the hadronic flash. Wave-
open end (see Fig. 5b), which performed as well form digitizers sample the summed PMT signals
asthe closedendinmagnetictests. We intendto every 2.5 ns. A sequence of these samples is the
build a new full-scale inflector following this de- recordofagivenevent. Theserecordsarescanned
sign having both ends open to regain the factor for electron pulses and fit to determine energy
of 2 in lost muons. and time. Pileup occurs when two pulses strike
the detector within the resolvingtime of the sys-
tem (typically < 5 ns). Pileup events can be re-
3.2. Electron detection and data collection
moved, on average, by a procedure that uses the
E821has24lead-scintillatingfiberelectromag-
leading and trailing samples around a triggered
netic calorimeters [22] to detect electron energy
7
nt
e 11659260
m
o
M
c 11659230
eti
n
g
a
M 11659200
s
u
o
al 11659170
m
o
n
A
11659140
1998 1999 2000 2001 A2v0e0ra2ge
Running Year
Figure4. Compilationofresults fromE821from1998-2001runningperiods, togetherwiththe average.
electronpulse, however,asystematic uncertainty (15X ). The individually read-out modules are
0
remains from incomplete pileup subtraction and stacked in a 4 high by 5 wide array. Laminated
frompulsestoolowinenergytobeaccountedfor thinacrylicsheetsarebundledandbentat90de-
properly. Because the rates will increase by ap- greestowardtheinsideoftheringtopipethelight
proximatelyfivefoldinE969,pileupwilldominate to 20 PMTs. A sketch is shown in Fig. 6, where
thesystematicuncertaintiesifleftunimproved. A the geometrical constraints are evident.
new calorimeter will be built and a new parallel
data-takingmethodisbeingdevelopedtoaddress
theanticipatedhigherrates. Additionally,amore
finely sampling waveform digitizer will be used
and the fivefold vertical segmentation of the ex-
isting front scintillator detector hodoscopes will
be increased by at least a factor of 2.
The new calorimeter will be dense and fast
and it will be segmented transversely with re-
spect to the incoming electrons. Readout of in-
dividual segments will occur on the downstream
side where space is severely limited by existing
vacuum chamber flanges. GEANT studies show
that pileup events can be recognized 4 out of
5 times—which is the goal to reduce this sys-
tematic uncertainty—if the Moliere radius is re-
strictedtolessthan1.7cm. Wehavedevelopeda
Figure 6. Plan view of new calorimeter in the
preliminary design using tungsten and scintillat-
region of the bellows between vacuum chambers
ing fiber ribbons that meets these requirements.
where the available space for lightguides is quite
The calorimeter will be subdivided into twenty
restricted.
4×4 cm modules, each having a length of 11 cm
8
Table 3
Systematic Errors from the 1999, 2000 and 2001 data sets [5,6,7]. †Higher multipoles, the trolley fre-
quency,temperature,andvoltageresponse,eddycurrentsfromthekickers,andtime-varyingstrayfields
‡In 2001 AGS background, timing shifts, E field and vertical oscillations, beam debunch-
ing/randomization, binning and fitting procedure together equaled 0.11 ppm
σ ω 1999 2000 2001 σ ω 1999 2000 2001
syst p syst a
(ppm) (ppm) (ppm) (ppm) (ppm) (ppm)
Inflector Fringe Field 0.20 - - Pile-Up 0.13 0.13 0.08
Calib. of trolley probes 0.20 0.15 0.09 AGS background 0.10 0.01 ‡
Tracking B with time 0.15 0.10 0.07 Lost Muons 0.10 0.10 0.09
Measurement of B 0.10 0.10 0.05 Timing Shifts 0.10 0.02 ‡
0
µ-distribution 0.12 0.03 0.03 E-field/pitch 0.08 0.03 ‡
Absolute calibration 0.05 0.05 0.05 Fitting/Binning 0.07 0.06 ‡
Others† 0.15 0.10 0.07 CBO 0.05 0.21 0.07
Beam debunching 0.04 0.04 ‡
Gain Changes 0.02 0.13 0.12
Total for ω 0.4 0.24 0.17 Total for ω 0.3 0.31 0.21
p a
3.3. The Q method of data accumulation • Measurementofthefieldchangefromkicker
Thetraditional“T”methodofdataselectionin eddy currents in situ [17],
E821involvesacceptingelectronsonlywhentheir
• Extensivemeasurementswiththe magnetic
energy exceeds a fixed threshold. Such events
field trolley, aiming in particular to better
are sorted into histograms of events versus time
resolve the position of the active NMR vol-
with weight 1 for each event. In contrast, the
umesinsidethetrolleyshellandtomapout
“Q” method does not rely on the separate iden-
the response functions to the level where
tification or isolation of events. It simply his-
corrections canbeapplied,ratherthanlim-
tograms the energy striking the detectors versus
its be set,
time. All electrons that shower in the calorime-
ters areincluded, but theirdecaytime is intrinsi-
• More frequent measurements of the mag-
cally weightedby their energy. The net asymme-
netic field in the storage ring during beam
try is roughly halved compared to the T method
periods,
but itiscompensatedforbythe use ofallevents.
Full GEANT simulations were used to compare • Repair and retuning of a number of fixed
the methods, finding that the Q method is sta- NMRprobestoimprovethesamplingofthe
tistically weaker by about 9 percent. However, storage ring,
it requires no pileup correction. In fact, for the
• Analysis refinements to reduce trolley posi-
Q method, the detectors do not need to be seg-
tion uncertainties.
mented at all because only the integrated energy
depositionis ofinterest. We plantoemploy both
4. Summary
data-taking methods in E969.
Our E821 experiment is complete. The result
3.4. Magnetic field determination at 0.5 ppm precision is statistics limited. This
Themagneticfieldwillbemeasuredtoapprox- brief overview was aimed at illustrating a few of
imately 0.11ppm using the same technique and the technical issues that must be addressed to
apparatus as was used in E821. The uncertainty continue the experiment at higher rates and the
inthe2001runwas0.17ppmandthiswillbeim- same or reduced systematic uncertainties. With
proved. The proposal [20] details the work plan: the full complement of plans realized, we project
9
(a)ClosedEnd (b)OpenEnd
Figure5. Photosofthe closed-andopen-endinflectorprototype. The inflectoristurnedonitsside. The
opening, evident in (b), has an 18 mm width and 57 mm height.
that an overall uncertainty of 0.2 ppm can be lated to the hadronic contributions to the stan-
obtained in one run of roughly 20 weeks, which dardmodelexpectation. Projectingtothefuture,
would follow several years of construction and a webelievethatthetheoreticaluncertaintycanbe
short commissioning run. The Collaboration is reducedto≈ 0.4ppm. Combinedwithanexper-
beginning to do the simulation work necessary imental uncertainty of 0.2 ppm, this will yieldan
and a formal Technical Design Report will be improved sensitivity to new physics by a factor
written for proper costing and time projections. of 2. The current 2.7σ difference between exper-
If the past history of (g − 2) experiments iment and theory is tantalizing, but not defini-
µ
can be used as a guide, then the next genera- tive. An additional resolution by a factor of 2 is
tion effort will certainly reveal exciting physics therefore very exciting to contemplate and we all
results. At this Workshop, we have learned of eagerly anticipate this next step in precision.
the extensive worldwide effort to establish the
standard model a expectation with high preci-
µ
sion. New radiative return data from KLOE [10]
supports the hadronic vacuum polarization de-
termination, which is largely based on the pre- 5. Acknowledgments
cise CMD-II e+e− annihilation measurements.
Additional data are expected from BaBar and The authorexpressesgratitudetothe Guggen-
Belle. Meanwhile,thediscrepancybetweene+e−- heim Foundation for partial support. The (g −
based and hadronic tau-based spectral functions 2) experiment is supported in part by the U.S.
remains. Untilthisisresolved,DavierandHo¨cker Department ofEnergy,the U.S. NationalScience
suggestusingthee+e−-basedresults,whichisre- Foundation, the GermanBundesminister fu¨r Bil-
flected in Table 1. Many contributions to this dungundForschung,theRussianMinistryofSci-
Workshop have helped to clarify the issues re- ence, and the US-Japan Agreement in High En-
ergy Physics.
10
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