BOSTONUNIVERSITY
Ultra High Precisionwith a
Muon StorageRingThe Muon
Experiment
at Brookhaven National Laboratory
B. Lee Roberts
robert [email protected] http: //g2pc1.b u.edu/˜ r oberts/
Department of Physics
Boston University
B. Lee Roberts, EPAC02, 4 June 2002 – p.1/44
BOSTONUNIVERSITY
BNL AGSE821:
A New Precision Measurement of theMuon
Valueat the level of 0.35 ppm
Boston University, Brookhaven NationalLaboratory, Budker Institute of Nuclear Physics -Novosibirsk, Cornell University, FairfieldUniversity, KEK, KVI and Rijksuniversiteit -Groningen, University of Heidelberg,University of Illinois, University ofMinnesota, Tokyo Institute of Technology,
Yale University
B. Lee Roberts, EPAC02, 4 June 2002 – p.2/44
BOSTONUNIVERSITY
E821Collaboration(4/02)R.M. Carey, X. Huang, A. Lam-Ng, I. Logashenko, J.P. Miller, J. Paley, B.L. Roberts,
-
BU G. Bennett, H.N. Brown, G. Bunce,
G.T. Danby, Y.Y. Lee, W. Meng, W.M. Morse,
D. Nikas, C. Özben, R. Prigl, Y.K. Semertzidis - BNL Y. Orlov - Cornell D. Winn
- Fairfield K. Jungmann, KVI G. zu Putlitz Heidelber g P.T. Debevec, F. Gray D.W.
Hertzog, C. Onderwater, C. Polly, M. Sossong - UIUC A. Yamamoto - KEK B. Bous-
quet, P. Cushman, R. McNabb, T. Qian, P. Shagin - Minnesota V.P. Druzhinin, G.V.
Fedotovich, B.I. Khazin, N.M. Ryskulov, Yu.M. Shatunov, E. Solodov - BINP M. Iwasaki
- TyTech H. Deng, M. Deile, S.K. Dhawan, F.J.M. Farley, V.W. Hughes,
S.I. Redin, E.
Sichtermann - Yale
Co-Spokesmen,
Resident Spokesman,
Project Manager
B. Lee Roberts, EPAC02, 4 June 2002 – p.3/44
BOSTONUNIVERSITY
Outlineof theTalk
Brief Introduction to
,the Motivation and Theory Overview of the Experimental Technique The Precision Storage Ring Magnet Beam Dynamics in the
Storage Ring. Summary and Conclusions
B. Lee Roberts, EPAC02, 4 June 2002 – p.4/44
BOSTONUNIVERSITY
Muon: (2
generation lepton)
(1) ! " #(2)
(3) $&% '( )* + , " ,-/. )0 1 ) 0 2(4)
Parity Violating Decay Polarized Muons
3 4 5 36 * " , ) ,-/. 7. (5)
B. Lee Roberts, EPAC02, 4 June 2002 – p.5/44
BOSTONUNIVERSITY
Magnetic Moments, -Factors,etc. 8" 9 9 ) 8;:(6)8" - magnetic moment; - gyromagnetic ratio8;: is the spin.
Dirac Equation Predicts <
In nature radiative corrections make
.
γ
µαπg = 2 +
γ
µγ
Dirac
+ ...
Kusch and Foley,Schwinger, 1947
B. Lee Roberts, EPAC02, 4 June 2002 – p.6/44
BOSTONUNIVERSITY
MagneticMoments:DefinitionsandValues
" 0 ) = > ? @ 0
(7)
" 7 ) = 7 A BDC @ 5 C EF 3 @ G # CH *
(8)
" ) = A " I ! ! ) = I
(9) I !KJ J J
(10)B. Lee Roberts, EPAC02, 4 June 2002 – p.7/44
BOSTONUNIVERSITY
Theoretical Valuefor L
Electron: To the level of the experimentalerror,
ppb
0 7 MON 3 H PQ3 @ P C P R 0 7 S > GN ?UTWV )
Contribution of virtual" , , etc. is
ppb. Muon: The Relative Contribution of heavierthings: X 7 X V
Which is easy to understand from theuncertainty principle.
B. Lee Roberts, EPAC02, 4 June 2002 – p.8/44
BOSTONUNIVERSITY
Theoryfor Muon L
0 M 0 S 0 ?3 PU@ CH G 5 0 > 3 4
0 > Y ?6 # G 5 # 0 3 #Z @ P 0 M
B. Lee Roberts, EPAC02, 4 June 2002 – p.9/44
BOSTONUNIVERSITY
TheExperimentalTechnique[ [ [ [[ [ [ [\ \ \ \\ \ \ \] ] ] ] ]] ] ] ] ]] ] ] ] ]] ] ] ] ]^ ^ ^ ^ ^^ ^ ^ ^ ^^ ^ ^ ^ ^^ ^ ^ ^ ^
_ _ _ __ _ _ __ _ _ __ _ _ _` ` ` `` ` ` `` ` ` `` ` ` `
a a a a a aa a a a a ab b b b b bb b b b b bc c cc c cc c cc c cc c cc c cc c c d d dd d dd d dd d dd d dd d dd d d e e e e e e e e ee e e e e e e e ef f f f f f f f f
Ideal Orbit
KickerModules
π + +µ
p = 3.1 GeV/c
Pionsµ ν Inflector
Injection Orbit
Storage Ring
TargetProtons
from AGS
= 77 mm~
= 10 mradβ ~
B dl = 0.1 Tm~
β
B. Lee Roberts, EPAC02, 4 June 2002 – p.10/44
BOSTONUNIVERSITY
InflectorGeometry
µ
B. Lee Roberts, EPAC02, 4 June 2002 – p.11/44
BOSTONUNIVERSITY
InflectorExit Geometry
µ
ρ =
B. Lee Roberts, EPAC02, 4 June 2002 – p.12/44
BOSTONUNIVERSITY
SpinandMomentumPrecession
gih ) T gij ) T )T
g 8$ @ R3N Glk N C 8;m gon gij gih )
+−e
information
The highest energycarry the spin = ω µ
Momentum Spin
B. Lee Roberts, EPAC02, 4 June 2002 – p.13/44
BOSTONUNIVERSITY
Theneedfor vertical focusing In
we store for X4000 turns. Magnetic focusing conflicts with the need toknow to 0.1ppm. Can we use an electric field?
Spin Motion in
8
and
8-fields:
8gn pq ) 0 8 0 T 8r 8
sutv T wx y 0 T
B. Lee Roberts, EPAC02, 4 June 2002 – p.14/44
BOSTONUNIVERSITY
TheRing Layout
Q4
Q1
Q2
Q3
inflector
trolleydrive
tracebackchambersFBM
garagetrolley
FBM
quadscover43% ofthe ring
K2K3
K1
cryo pump
B. Lee Roberts, EPAC02, 4 June 2002 – p.15/44
BOSTONUNIVERSITY
TheRing Lfunction
0
2.5
5
7.5
10
12.5
15
17.5
20
0 50 100 150 200 250 300 350
β
β
β(m
eter
s)
φ (degrees)
B. Lee Roberts, EPAC02, 4 June 2002 – p.16/44
BOSTONUNIVERSITY
TheKickerPlates
B. Lee Roberts, EPAC02, 4 June 2002 – p.17/44
BOSTONUNIVERSITY
TheKickerCurrentPulse
x
vacuum
T
CT
1:85
1000 pf
SCR
PowerSupply
~1500 V
"charge"
µ
11.5
20MM
80M10nf
Ω
Ω
Ω"charge now"
300 f
In air In oil
In
4
0
2
Kicker Current
Beam
200 400 600 800 1000time (ns)
Kic
ker
Cur
rent
(kA
)
B. Lee Roberts, EPAC02, 4 June 2002 – p.18/44
BOSTONUNIVERSITY
A Kicker Modulator
B. Lee Roberts, EPAC02, 4 June 2002 – p.19/44
BOSTONUNIVERSITY
MagneticCircuits
z" ? E | # R3 >
µ ∼106
steel
µ = 1air
I Biron yoke
void in yoke
air gaps
pole piece
pole piece
field regionhigh quality
B. Lee Roberts, EPAC02, 4 June 2002 – p.20/44
BOSTONUNIVERSITY
Schematicof theMagnet
thermal
pole piece
polebump
wedge
current sheet
g−2 Magnet in Cross Section
dipole correction coil
beamregion
fixed
probesNMR
YOKE
inner coil
inner coil
programmable
An array of 17NMR probes on the
trolley maps the B Field in the storage region
= 7112 mmρ
insulation
outercoils
B. Lee Roberts, EPAC02, 4 June 2002 – p.21/44
BOSTONUNIVERSITY
Installation of aPolePiece
B. Lee Roberts, EPAC02, 4 June 2002 – p.22/44
BOSTONUNIVERSITY
TheNudeStorageRing
B. Lee Roberts, EPAC02, 4 June 2002 – p.23/44
BOSTONUNIVERSITY
StorageRing Parameters
Parameter Value Comments
(g-2) Frequency
~ Hz ~ s
Muon kinematics GeV/c s
Cyclotron Period ns
Central Radius mm
¡
T Storage Aperture
cm circle
In one lifetime: 432 revolutions around ring
14.7 (g-2) periods
B. Lee Roberts, EPAC02, 4 June 2002 – p.24/44
BOSTONUNIVERSITY
Mappingthe
¢
field.
NMR trolley, 17 probes to map the field.
366 fixed NMR probes monitor field stability.
B. Lee Roberts, EPAC02, 4 June 2002 – p.25/44
BOSTONUNIVERSITY
£ £ in 1999o = 0θ
o90
o180
o270
-2000
200 (ppm)BB- φ
B. Lee Roberts, EPAC02, 4 June 2002 – p.26/44
BOSTONUNIVERSITY
¤ ¥ £ ¥ £ ¥ ¥
¦ §;¨ª© « ¬® ¯°± ² ¨
°³;´ °µ¶· ¸ «º¹ » °· ¼¾½ ¸ « ¿
x
y
xθr
One slice in azimuth.
Muon Distribution (V À ÁT Â ( 5 C # À Ã Â ( # GH À Ä
B. Lee Roberts, EPAC02, 4 June 2002 – p.27/44
BOSTONUNIVERSITY
And is:
1ppm field contours
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5 -4 -3 -2 -1 0 1 2 3 4 5x [cm ]
y [c
m]
2000
−1
+1
00
0
−1
+1
x (cm)-4 -3 -2 -1 0 1 2 3 4
y (c
m)
-4
-3
-2
-1
0
1
2
3
4
Multipole expansion of B field in 1999
0 ppm
1
1
0 0
-1 -2
2 3
2 3
-3 -4
Multipoles (ppm)
normal skew
Quad -2.23 2.17
Sext -1.15 2.52
Octu -1.33 1.85
Decu 0.92 0.95
B. Lee Roberts, EPAC02, 4 June 2002 – p.28/44
BOSTONUNIVERSITY
ExperimentalSignalis Decay
e+
e+
Highest energy are along muon spin
momentum
spin
The Muon Rest Frame
µ +
νe
νµ
The electron carries the muon spin
B. Lee Roberts, EPAC02, 4 June 2002 – p.29/44
BOSTONUNIVERSITY
The Å Energy SpectrumN
umbe
r of
Pul
ses
0.9 GeV
hardwarethreshold
softwarethreshold1.8 GeV
ÆÈÇ É ÆËÊDÌÊDÌ É ÍÍlÎ Ì ÏÑÐ ÒÓ
Ô Õ ÖØ× ÙÚÛÜÙÝ Ô Þß à Õ Ö Þß àá ß
Pulse finding
threshold
250 MeV
2NA
A
N (E)
x
B. Lee Roberts, EPAC02, 4 June 2002 – p.30/44
BOSTONUNIVERSITY
TheDetectorGeometry
â ââ ââ ââ ââ âã ãã ãã ãã ãã ãmuon momentum
muon spin
e
Sci−Fi Calorimetermodule
p
spin backward, lesshigh energy e
spin forward, morehigh energy e
Measures Energyand time
digitizer400 MHz
B. Lee Roberts, EPAC02, 4 June 2002 – p.31/44
BOSTONUNIVERSITY
Time Spectrum,
äå GeV
æèç éëê ì í î ïðòñOó ôõö æ ÷ùø ç éú1,394.5 million e + (1999 data)
time, µs
Ne+ /14
9.185
ns
600-6
99
500-5
99
400-4
99
300-3
99
200-2
99
100-1
99
25-99
µs
B. Lee Roberts, EPAC02, 4 June 2002 – p.32/44
BOSTONUNIVERSITY
TheMuonDistribution+e Time Spectrum: t = 6 sµ
+e Time Spectrum: t = 36 sµ
datasimulation
The distribution ofequilibrium radii
B. Lee Roberts, EPAC02, 4 June 2002 – p.33/44
BOSTONUNIVERSITY
û Fitting FunctionNature gives us 5 parameters:æèç éëê ì í î ïðñOó ôõö æ ÷oø ç éúStorage ring plus bunched beam gives more:
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.5 1 1.5 2 2.5üýÿþC
BO
-(g-
2)G
ain
chan
ge CB
O
CB
O+
(g-2
)
Dou
ble
CB
O
Ver
tical
wai
st
Fla
shle
ts
Fourier Transform of
the residuals from a5−parameter fit
(from 1 detector).
B. Lee Roberts, EPAC02, 4 June 2002 – p.34/44
BOSTONUNIVERSITY
WeakFocussing
ê electric quadrupole gradient; ó
ì æó é ê í ê
ê ê ó
Detector acceptance depends on . The beammoves radially relative to one detector with the“Coherent Betatron Frequency”
ê ê æó ó é
which amplitude modulates the í
signal.B. Lee Roberts, EPAC02, 4 June 2002 – p.35/44
BOSTONUNIVERSITY
TheTunePlane
ν − 4ν = −12ν = 1
2ν −
2ν =
13ν
− 2
ν =
2ν − 2ν = 0
ν + ν = 1
3ν +ν = 34ν + ν = 4
ν = 1
5ν = 2
3ν = 1
ν − 3ν = 0
2ν − 3ν = 1
0.90 0.95 1.000.850.25
0.80
0.50
0.30
0.35
0.40
0.45
ν
ν
n = 0.137n = 0.142
n = 0.122
B. Lee Roberts, EPAC02, 4 June 2002 – p.36/44
BOSTONUNIVERSITY
Frequenciesin the ring.
Quantity Expression Frequency Period
ø ! "# û%$ 0.23 MHz 4.37 &s
# '! (*) 6.7 MHz 149 ns
ó # 6.23 MHz 160 ns
# 2.48 MHz 402 ns
# 0.477 MHz 2.10 &s
+, # 1.74 MHz 0.574 &s
B. Lee Roberts, EPAC02, 4 June 2002 – p.37/44
BOSTONUNIVERSITY
FiberBeamMonitors
x monitor y monitor
calibrate
calibrate
B. Lee Roberts, EPAC02, 4 June 2002 – p.38/44
BOSTONUNIVERSITY
Measuring theTunewith FBM
Harp 1 (Horizontal), Fiber 4 ns
a.u.
Harp 2 (Vertical), Fiber 4 ns
a.u.
0
1
2
3
4
5
6
7
8
9
2000 3000 4000 5000 6000 7000 8000 9000 10000
0
10
20
30
40
50
60
2000 3000 4000 5000 6000 7000 8000 9000 10000
x fiber
y fiber
B. Lee Roberts, EPAC02, 4 June 2002 – p.39/44
BOSTONUNIVERSITY
BeamCentroid andScraping
nsec
Bea
m C
entr
oid
Pos
ition
(cm
)
No Scraping, f β = 472 kHz
7 kV Scraping, f β = 416 kHz
-1.5
-1
-0.5
0
0.5
1
1.5
1000 2000 3000 4000 5000 6000 7000
cbo − traceback
frequency (MHz)
fc(1 - 2√n)
fc(1 - √n)
Muon Fast Rotation Frequency
Proton Fast Rotation Frequency
0
1000
2000
3000
4000
5000
6000
7000
8000
0 1 2 3 4 5 6 7 8
FFT − fiber harpscbo − fiber harps
B. Lee Roberts, EPAC02, 4 June 2002 – p.40/44
BOSTONUNIVERSITY
û í &
Remove offsets and divide to determine
ê ÷ø ÷.-From û%$ ê /
/ê & $&-
Add corrections for radial
0
-field and vertical
“pitching motion”. ( 1 2ó 2
ppm)
B. Lee Roberts, EPAC02, 4 June 2002 – p.41/44
BOSTONUNIVERSITY
Agreementwith SM?
Experiment −
Theory = + 1.6 σ+µ
µ+
µ−
µ+
µ+
a µ
(5 ppm)
(13 ppm) E821 (97)
E821 (98)
(9.4 ppm)
(10 ppm)CERN
CERN
E821 (99)(1.3 ppm)
The
ory
B. Lee Roberts, EPAC02, 4 June 2002 – p.42/44
BOSTONUNIVERSITY
Agreementwith SM?
2σ +−
− 1 σ + 5.5 σto
requiring that
2000 answer
agree with ’99
result to
gives the range
of values
SM agreement
+µ
µ+
µ−
µ+
µ+
a µ
(5 ppm)
(13 ppm) E821 (97)
E821 (98)
(9.4 ppm)
(10 ppm)CERN
CERN
E821 (99)(1.3 ppm)
The
ory
B. Lee Roberts, EPAC02, 4 June 2002 – p.42/44
BOSTONUNIVERSITY
ConclusionsandOutlook
3 The storage ring, kicker, quadrupoles, allmeet their specifications in the
æ54 éexperiment.
Beam dynamics is quite important inunderstanding the data.
Two data sets are being analyzed:ppm from 2000 run.
ppm from 2001 run
B. Lee Roberts, EPAC02, 4 June 2002 – p.43/44
BOSTONUNIVERSITY
ConclusionsandOutlook
3 The storage ring, kicker, quadrupoles, allmeet their specifications in the
æ54 éexperiment.
3 Beam dynamics is quite important inunderstanding the data.
Two data sets are being analyzed:ppm from 2000 run.
ppm from 2001 run
B. Lee Roberts, EPAC02, 4 June 2002 – p.43/44
BOSTONUNIVERSITY
ConclusionsandOutlook
3 The storage ring, kicker, quadrupoles, allmeet their specifications in the
æ54 éexperiment.
3 Beam dynamics is quite important inunderstanding the data.
3 Two data sets are being analyzed:1
ppm & 6from 2000 run.1 2
ppm & î from 2001 run
B. Lee Roberts, EPAC02, 4 June 2002 – p.43/44
BOSTONUNIVERSITY
ConclusionsandOutlook, ctd.3 Historically muon
æ54 é
has developed as adialog between experiment and theory.
It still is!
Whatever the final answer, it will provide animportant constraint on new theories.
There is a window for discovery.
This is clearly a work in progress! Both theoryand experiment will be refined in the nearfuture.
Stay tuned!
B. Lee Roberts, EPAC02, 4 June 2002 – p.44/44
BOSTONUNIVERSITY
ConclusionsandOutlook, ctd.3 Historically muon
æ54 é
has developed as adialog between experiment and theory.
3 It still is!
Whatever the final answer, it will provide animportant constraint on new theories.
There is a window for discovery.
This is clearly a work in progress! Both theoryand experiment will be refined in the nearfuture.
Stay tuned!
B. Lee Roberts, EPAC02, 4 June 2002 – p.44/44
BOSTONUNIVERSITY
ConclusionsandOutlook, ctd.3 Historically muon
æ54 é
has developed as adialog between experiment and theory.
3 It still is!
3 Whatever the final answer, it will provide animportant constraint on new theories.
There is a window for discovery.
This is clearly a work in progress! Both theoryand experiment will be refined in the nearfuture.
Stay tuned!
B. Lee Roberts, EPAC02, 4 June 2002 – p.44/44
BOSTONUNIVERSITY
ConclusionsandOutlook, ctd.3 Historically muon
æ54 é
has developed as adialog between experiment and theory.
3 It still is!
3 Whatever the final answer, it will provide animportant constraint on new theories.
3 There is a window for discovery.
This is clearly a work in progress! Both theoryand experiment will be refined in the nearfuture.
Stay tuned!
B. Lee Roberts, EPAC02, 4 June 2002 – p.44/44
BOSTONUNIVERSITY
ConclusionsandOutlook, ctd.3 Historically muon
æ54 é
has developed as adialog between experiment and theory.
3 It still is!
3 Whatever the final answer, it will provide animportant constraint on new theories.
3 There is a window for discovery.
3 This is clearly a work in progress! Both theoryand experiment will be refined in the nearfuture.
Stay tuned!
B. Lee Roberts, EPAC02, 4 June 2002 – p.44/44
BOSTONUNIVERSITY
ConclusionsandOutlook, ctd.3 Historically muon
æ54 é
has developed as adialog between experiment and theory.
3 It still is!
3 Whatever the final answer, it will provide animportant constraint on new theories.
3 There is a window for discovery.
3 This is clearly a work in progress! Both theoryand experiment will be refined in the nearfuture.
3 Stay tuned!B. Lee Roberts, EPAC02, 4 June 2002 – p.44/44