Muon g-2 experimental results & theoretical developments
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Transcript of Muon g-2 experimental results & theoretical developments
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Huaizhang Deng
Yale University
Muon g-2
experimental results & theoretical developments
University of Pennsylvania
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Collaboration
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Outline
Overview of (g-2)
• Analyses and results
• Principle of and experimental setup.
Calculate (g-2) in theory
Conclusion
• Compare (g-2)+ and (g-2)−
Measure (g-2)μ in experiment
• Weak contribution
• QED contribution
• Hadronic contribution
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Magnetic dipole moment
The magnetic moment of a particle is related to its spin
g Smc
e 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
1
2
a
Some of other contributions :
QED hadronic weak
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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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 15 — 40 s calorimeters gated on
15 — 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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How to measure B
B is determined by measuring the proton nuclearmagnetic resonance (NMR) frequency p in the magnetic field.
)1(/
/
2
4
2
a
gcmeB
cme
ap
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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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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Uniformity of the B field
The B field variation at thecenter of the storage region. <B>1.45 T
The B field averagedover azimuth.
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Stability of the B field
Calibration of the fixedprobe system with respectto the trolley measurements
The magnetic fieldmeasured by the fixedprobe system duringμ− run in 2001.
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Systematic errors for p
Source of errors Size [ppm]
μ+ μ−
Absolute calibration of standard probe 0.05 0.05
Calibration of trolley probe 0.15 0.09
Trolley measurements of B0 0.10 0.05
Interpolation with fixed probes 0.10 0.07
Uncertainty from muon distribution 0.03 0.03
Others† 0.10 0.10
Total 0.24 0.17
† higher multipoles, trolley temperature and voltage response,eddy currents from the kickers, and time-varying stray fields.
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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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a data
N(t)=Ne-t/[1-Acos(ωat+φ)]
)()(2/2/
)()(2/2/)(
4321
4321
tNtNtNtN
tNtNtNtNtr
aa
aa
r(t)=Acos(ωat+φ)+(a/16)2
Slow effects are largelycancelled in the ratio method.
Divide N(t) into four independentsets N1, N2, N3 and N4
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n=0.142
n=0.122
Coherent Betatron Oscillation
Cause : Phase space not filled
Observation :• Beam centroid and beam width oscillate
•
• CBO phase varies from 0 to 2π around the ring
cCBO n 11
Solution :• Sum all detectors to
reduce the CBO effect
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Error for a
Source of errors Size [ppm]
μ+ μ-
Coherent betatron oscillation 0.21 0.07
Pileup 0.13 0.08
Gain changes 0.13 0.12
Lost muons 0.10 0.09
Binning and fitting procedure 0.06
Others† 0.06
Total systematic error 0.31 0.21
Statistical error 0.62 0.66
† AGS background, timing shifts, E field and vertical oscillations,beam debunching/randomization.
0.11
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Blind analysis and result
After two analyses of p had been completed,
p /2π = 61 791 400(11) Hz (0.2ppm),
and four analyses of a had been completed,
a /2π = 229 073.59(15)(5) Hz (0.7ppm),
separately and independently, the anomalous magneticmoment was evaluated,
a=11 659 214(8)(3) 10-10
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History of the experimental measurements
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Compare μ+ and μ− to test CPT
Combined result : a=11 659 208(6) 10-10
pap
paa
//
/
Rμ− = 0.003 707 208 3(2 6)
Rμ+ = 0.003 707 204 8(2 5)
paR /
710)7.94.9(2/)(
RR
RRCPT test :
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Standard model calculation of a
a(SM)= a(QED) + a(weak) + a(had)*
a(QED)=11 658 472.07(0.04)(0.1)10-10
a(weak)=15.1(0.1)(0.2)10-10
*The exact value and error of hadronic contribution are still under studies by
many groups.
a(had,lo)=692.4(6.2)(3.6)10-10 *
a(had,nlo)=−98(0.1)10-10 *
a(had,lbl)=12(3.5)10-10 *
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QED contribution
2a
2
2765857376.0
3
205050898.24
5
2930
4
20.126
a(QED)=11 658 470.6(0.3)10-10a(QED)=11 658 472.07(0.04)(0.1)10-10
4
20.131
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Electroweak Contributions
223.0/1sin GeV,10)1(16637.124
108.194sin413
1
3
5
28
2225
2
2
112
2
2
222
2
21,
zww
w
Hww
loopEW
mmm
gG
m
mO
m
mO
mGa
11,2,
11,2,
10)8.1(0.6
10)0.1(7.34
NLLloopEW
LLloopEW
a
a
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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 indirectly in decay.
24 2
2
)()(3
)lo,had(
m
sRsKs
dsma
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Evaluation of R
M. Davier et al., hep-ph/0208177
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aμ(had, lo) based on e+e− data
5.4537.96±1.02±0.31ω
100.0696.3±6.2±3.6Total
1.429.88±0.11±0.00> 5.0
1.077.44±0.38±0.00J/ψ,ψ’
4.8733.92±1.72±0.032.0 − 5.0
9.0763.18±2.19±0.860.6 − 2.0
5.1335.71±0.84±0.20φ
72.99508.20±5.18±2.742π
%GeV ,s1010 ),lohad,(
a
aμ(had,lo) = 696.15(5.7)(2.4) × 10-10 (HMNT)aμ(had,lo) = 694.8 (8.6) × 10-10 (GJ)
(DEHZ)
S. Eidelman at DAФNE 2004
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Discrepancy between e+e− and data
aμ(had,lo) = 711.0(5.0)(0.8)(2.8)×10-10 (DEHZ)
mode e−e+ Δ(e−e+ − )
π−π+ 508.20±5.18±2.74 520.06±3.36±2.62 -11.9±6.9π−π+ 2π0 16.76±1.31±0.20 21.45±1.33±0.60 -4.7±1.8
2π−2π+ 14.21±0.87±0.23 12.35±0.96±0.40 1.9±2.0
total 539.17±5.41±3.17 553.86±3.74±3.02 -14.7±7.9
M. Davier et al., hep-ph/0208177S. Eidelman at DAФNE 2004
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Possible reasons for discrepancy
• Problem with experimental data
• Difference in mass of ρ mesons (mρ±>mρ0). Current data indicate equality within a few MeV
• Problem with SU(2) breaking corrections
• Non-(V−A) contribution to weak interaction
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Comparsion between CMD-2 and KLOE
)GeV(2M
Kloe
CMD-2
only statisticalonly statistical
errors are shownerrors are shown
(375.6 0.8stat 4.9syst+theo) 10-10 (1.3%)KLOE
(378.6 2.7stat 2.3syst+theo) 10-10(0.9%)
CMD-2
2
22
)(
3)
(
ee
MM
F
)93.037.0( 222 GeVMGeVa
• Two measurements are in agreement
Radiative return is another way tomeasure hadronic contributions
F. Nguyen at DAФNE 2004
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a(had,lbl)=8.6(3.5)10-10
Higher order hadronic contributions
a(had,nlo)=10.0(0.6)10-10 a(had,lbl)=13.6(2.5)10-10a(had,lbl)=12.0(3.5)10-10
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Comparison of SM and experiment
e+e− : aμ = 11 659 184.1 (7.2had,lo)(3.5lbl)(0.3QED+EW) × 10-10
: aμ = 11 659 200.4 (5.8had,lo)(3.5lbl)(0.3QED+EW) × 10-10
experimental result : a=11 659 208(6) 10-10
e+e− : Δaμ = 23.9 (7.2had,lo)(3.5lbl)(6exp) × 10-10 (2.4 σ): Δaμ = 7.6 (5.8had,lo)(3.5lbl)(6exp) × 10-10 (0.9 σ)
…including KLOE result
F. Nguyen at DAФNE 2004
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Beyond standard model
• extra dimensions, or extra particles,• compositeness for leptons or gauge bosons.
particularly supersymmetric particles
tan100
1013)( 10
susym
GeVSUSYa
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Conclusions
• Measurement of a−=11 659 214 (8)(3)×10-10(0.7 ppm)
• The combined result a=11 659 208(6) ×10-10(0.5 ppm)
• a− and a+ agree with each other as expected by CPT
• a(exp)−a(SM) is 2.4σ (e+e−) or 0.9σ ()
• The discrepancy between e+e− and data is confirmed by KLOE
• Efforts on solving discrepancy between e+e− and , and attempts to calculate a(had) from lattice QCD
• Upgraded muon g-2 experiment is expected to reduce the experimental error to 0.2 ppm.