Huaizhang Deng Yale University Precise measurement of (g-2) University of Pennsylvania.
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Huaizhang Deng
Yale University
Precise measurement of (g-2)
University of Pennsylvania
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Collaboration
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Prof. Vernon W. Hughes (1921 2003)
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Outline
•What is (g-2) and why we measure it ?
•Preliminary result of muon electric dipole moment.
•Analysis and result from the 2000 run.
•Principle of and experimental setup for the measurement.
•Theory of (g-2) and its new development.
•Conclusions.
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What is g-2The magnetic moment of a particle is related to its spin
g Smce
2
For Dirac pointlike particle :
g=2
For the proton : ap1.8 because the proton is composite particle.
Anomalous magnetic moment2
2
ga
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g - 2 0 for the muon
Largest contribution : 800
12
a
Other standard model contributions :
QED hadronic weak
Contribution from new physics : a(exp)-a(SM)=a(new physics)
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Why muon?
• The muon is a point particle, so far.
(Hadrons, like p and n, are composite particles.)
• The muon lives long enough for us to measure.
• The effects from heavy particles are generally proportional to m2. 000,40/ 2 emm
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Principle of the measurement
When =29.3 (p=3.09 Gev/c),a is independent of E.
cme
a
a
B
EaBacm
e
1
12
csa
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How to measure B
B is determined by measuring the proton nuclearmagnetic resonance (NMR) frequency p in the magnetic field.
)1(//
24
2
a
gcmeB
cmea
p
pa
p
p
a
p
p
aa
pap
paa
//
/
/p=3.183 345 39(10), W. Liu et al., Phys. Rev. Lett. 82, 711 (1999).
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How to measure a
In the parity violated decay , e+ are emittedpreferentially along the muon spin direction in muon restframe. And e+ emitted along the muon momentumdirection get large Lorentz boost and have high energy in laboratory frame. Hence, a is determined by countingthe high energy e+ .
ee
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Muon storage ring
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Some numbers about the experiment
Time scales :149.2 ns cyclotron (or fast rotation) period c , 4.4 s g-2 period a , what we want to measure 64.4 s dilated muon lifetime
Experimental sequence :t =0 beam injection
Magnetic field : 1.45 T p : 61.79MHz
35 — 500 ns beam kicked onto orbit 0 — 15 s beam scraping 5 — 40 s calorimeters gated on
45 — 1000 s g-2 measurement 33 ms beam injection repeats (12 times)
3 s circle repeats 3 day field measurement by trolley 1 year data-taking repeats
20 year whole experiment repeats
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NMR trolley
17 trolley probes
378 fixed probesaround the ring
The NMR system iscalibrated against a standard probe† of aspherical water sample.
† X. Fei, V.W. Hughes, R. Prigl,NIM A394 349 (1997)
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Trolley measurement
The B field variation at thecenter of the storage region. <B>1.45 T
The B field averagedOver azimuth.
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Fixed probe measurements
Calibration of the fixedprobe system with respectto the trolley measurements
The magnetic fieldmeasured by the fixedprobe system during2000 run.
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Systematic errors for p
Source of errors Size [ppm]2000 1999
Absolute calibration of standard probe 0.05 0.05Calibration of trolley probe 0.15 0.20Trolley measurements of B0 0.10 0.10Interpolation with fixed probes 0.10 0.15Inflector fringe field -- 0.20Uncertainty from muon distribution 0.03 0.12Others† 0.10 0.15Total 0.24 0.4
† higher multipoles, trolley temperature and voltage response,eddy currents from the kickers, and time-varying stray fields.
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2000 a data
))(cos()(1)()( /0 EtEAeENtN a
t
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Coherent betatron oscillation (cbo)
nccbo 11
kick
)]cos(1)[()( ,/
,00 Ncbocbot
Ncbo teAENEN cbo 01.0, NcboA)]cos(1)[()( ,
/, Acbocbo
tAcbo teAEAEA cbo 001.0, AcboA
)]cos(1)[()( ,/
,
cbocbot
cbo teAEE cbo 001.0, cboA
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CBO effect on ωa
)2/()2( acboacbo
a
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Cancellation of cbo around the ring
CBO effect shown onthe average energy of e+
Cancellation of cbo effectafter summing all detectortogether.
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Error for a
Source of errors Size [ppm]2000 1999
Coherent betatron oscillation 0.21 0.05Pileup 0.13 0.13Gain changes 0.13 0.02Lost muons 0.10 0.10Binning and fitting procedure 0.06 0.07AGS background 0.10Others† 0.06Total systematic error 0.31 0.3Statistical error 0.62 1.3
† Timing shifts, E field and vertical oscillations, beam debunching/randomization.
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Blind analysis and result
After two analyses of p had been completed,
p=61 791 595(15) Hz (0.2ppm),
and four analyses of a had been completed,
a=229 074.11(14)(7) Hz (0.7ppm),
separately and independently, the anomalous magneticmoment was evaluated,
a=11 659 204(7)(5) 10-10
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Standard model calculation of aa(SM)= a(QED)+ a(had)+ a(weak)
a(QED)=11 658 470.57(0.29)10-10 (0.025 ppm)
a(weak)=15.1(0.4)10-10 (0.03 ppm)
Both QED and weak contribution has been calculatedto high accuracy.
The accuracy of a(had) is about 0.6 ppm.
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Cannot be calculated from pQCD alonebecause it involves low energy scalesnear the muon mass.
Hadronic contribution (LO)
However, by dispersion theory,this a(had,1) can be related to
)(e)(
e
hadronseeR
measured in e+e- collisionor tau decay.
24 2
2
)()(3
)1,(
m
sRsKsdsm
hada
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Evaluation of R
M. Davier et al., hep-ph/0208177
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Comparison between e+e- and
M. Davier et al., hep-ph/0308213M. Davier et al., hep-ph/0208177
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Experimental and theoretical values
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Beyond standard model
• extra dimensions, or extra particles,
• compositeness for leptons or gauge bosons.
particularly supersymmetric particles
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Muon electric dipole moment
Bacm
eaobs
s
ωobs
ωedm
ωa
δ 115 )(109.8
2 cmed
af
Vertical profile of decay positrons oscillates • with frequency of g-2• with phase 90o different from g-2 phase• with amplitude proportional to dμ
cmefd
4
where
Bfedm
21
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Amplitude with CBO frequency [μm]
Am
plitu
de w
ith g
-2 fr
eque
ncy
[μm
]
Preliminary result of muon EDM
dμ=(−0.1±1.4)×10-19e·cm
dμ< 2.8×10-19e·cm (95% CL)
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Conclusions
•Improve the accuracy of a to 0.7 ppm
•The discrepancy between a(exp) and a(SM) is 0.7-1.9, depending on theory.
•Uncertainty is about half the size of the weak contribution.
•We are analyzing the data for negative muons, a test of CPT.•Factor 3.75 improvement on the upper limit of muon electric dipole moment.
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Superconducting inflector
The radial phase space allowed by the inflector aperture(green) is smaller than that allowed by the storage ring (red).
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Photo of the storage ring
inflector kickers
Detectors
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Magnet
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Muon distribution
Radial muon distribution determined by the Fourier trans-formation of cyclotron periods when beam is debunching.Vertical muon distribution is symmetric.
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Residual after fit with ideal function
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Detectors and positron signals
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Polarized muons
Parity violated decay
produces longitudinally polarized muons.
+ +sp
: spin 0: left handed
: left handed
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Half ring effect due to cbo
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Pileup correction
real pileup : |t|<2.9 ns
constructed pileup : |t-10|<2.9 ns
rawcorrected
rawcorrectedlater time
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Muon loss
Absolute normalization is determined by fit.
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Evaluation of R (low energy region)
M. Davier et al., hep-ph/0208177
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a(had,1)
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a(had,lbl)=8.6(3.5)10-10
Higher order hadronic contributions
a(had,2)=10.1(0.6)10-10
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Near future
• Analysis of 2001 data on with reduced systematic error and roughly the same statistical error.• Test CPT. Assuming CPT, reduce the total statistical error.• Measurement of muon electric dipole moment.• Muon life time measurement.• Sidereal day variation of a.
• Theoretical evaluation continues to be scrutinized.• Radiative return data from KLOE and B factory.• Lattice QCD calculation.