Transcript Final result of muon g-2

Muon g-2
experimental results & theoretical developments
Huaizhang Deng
Yale University
University of Pennsylvania
Collaboration
Outline
 Overview of (g-2)
 Measure (g-2)μ in experiment
• Principle of and experimental setup.
• Analyses and results
• Compare (g-2)+ and (g-2)−
 Calculate (g-2) in theory
• QED contribution
• Weak contribution
• Hadronic contribution
 Conclusion
Magnetic dipole moment
The magnetic moment of a particle is related to its spin



e

S
g
2mc


For Dirac pointlike particle :
g=2
Anomalous magnetic moment
g 2
a
2
For the proton : ap1.8 because the proton is
composite particle.
g - 2  0 for the muon
Largest contribution :

1
a 

2 800
Some of other contributions :
QED
hadronic
New physics ?
weak
Why muon?
• The muon is a point particle, so far.
(Hadrons, like p and n, are composite particles.)
• The effects from heavy particles are generally
proportional to m2.  m / me  2  40,000
• The muon lives long enough for us to measure.
Principle of the measurement



a  s  c
e   
1   

a B   a  2    E 
m c 
 1


When =29.3 (p=3.09 Gev/c),
a is independent of E.
a 
a
e
B
m c
Muon storage ring
Some numbers about the experiment
Magnetic field : 1.45 T
p : 61.79MHz
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
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
How to measure B
B is determined by measuring the proton nuclear
magnetic resonance (NMR) frequency p in the
magnetic field.
a /  p
a
a
a
a 



(1  a )
e
e  p 4  p  /  p
B
m c
m c 2 p g 2 p

a /  p
a 
 /  p  a /  p
+/p=3.183 345 39(10)
W. Liu et al., Phys. Rev. Lett. 82, 711 (1999).
NMR trolley
378 fixed probes
around the ring
17 trolley probes
The NMR system is
calibrated against a
standard probe† of a
spherical water sample.
† X. Fei, V.W. Hughes, R. Prigl,
NIM A394 349 (1997)
Uniformity of the B field
The B field variation at the
center of the storage region.
<B>1.45 T
The B field averaged
over azimuth.
Stability of the B field
Calibration of the fixed
probe system with respect
to the trolley measurements
The magnetic field
measured by the fixed
probe system during
μ− run in 2001.
Systematic errors for p
Source of errors
Size [ppm]
μ+
μ−
Absolute calibration of standard probe
Calibration of trolley probe
Trolley measurements of B0
0.05
0.15
0.10
0.05
0.09
0.05
Interpolation with fixed probes
Uncertainty from muon distribution
Others†
Total
0.10
0.03
0.10
0.24
0.07
0.03
0.10
0.17
† higher multipoles, trolley temperature and voltage response,
eddy currents from the kickers, and time-varying stray fields.
How to measure a
In the parity violated decay   e e , e+ are emitted
preferentially along the muon spin direction in muon rest
frame. And e+ emitted along the muon momentum
direction get large Lorentz boost and have high energy in
laboratory frame. Hence, a is determined by counting
the high energy e+ .
a data
N(t)=Ne-t/[1-Acos(ωat+φ)]
Divide N(t) into four independent
sets N1, N2, N3 and N4
r (t ) 
N1 t   a / 2  N 2 t   a / 2  N 3 (t )  N 4 (t )
N1 t   a / 2  N 2 t   a / 2  N 3 (t )  N 4 (t )
r(t)=Acos(ωat+φ)+(a/16)2
Slow effects are largely
cancelled in the ratio method.
Coherent Betatron Oscillation
n=0.142
Cause :
Phase space not filled
Observation :
• Beam centroid and
beam width oscillate

• CBO  1  1  n
n=0.122

c
• CBO phase varies from
0 to 2π around the ring
Solution :
• Sum all detectors to
reduce the CBO effect
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
0.11
† AGS background, timing shifts, E field and vertical oscillations,
beam debunching/randomization.
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 magnetic
moment was evaluated,
a=11 659 214(8)(3) 10-10
History of the experimental measurements
Compare μ+ and μ− to test CPT
a /  p
a 
 /  p  a /  p

R  a / p
CPT test :

Rμ+ = 0.003 707 204 8(2 5)
Rμ− = 0.003 707 208 3(2 6)
R   R 
( R   R  ) / 2
 ( 9.4  9.7)  107
Combined result :
a=11 659 208(6) 10-10
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
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 *
*The exact value and error of hadronic contribution are still under studies by
many groups.
QED contribution

a 
2
 
 0.765857376
 
 2 
 
 24.05050898
 
 2 
2
3
 
 131
126.0 
 2 
 
 930 
 2 
5
-10
a(QED)=11 658 472.07(0.04)(0.1)10
470.6(0.3)10-10
4
Electroweak Contributions
EW ,1loop
a
2
2



G m2  5 1
m
m
2


2







1

4
sin


O

O

w
 m2 
 m2
8 2 2  3 3
 w
 H
g2
5
G 

1
.
16637
(
1
)

10
GeV,
2
4 2mw

  194.8  1011


sin 2  w  1  mw2 / mz2  0.223
aEW , 2loop,LL  34.7(1.0)  1011
aEW , 2loop, NLL  6.0(1.8)  1011
Hadronic contribution (LO)
Cannot be calculated from pQCD alone
because it involves low energy scales
near the muon mass.
However, by dispersion theory,
this a(had,1) can be related to
(e  e   hadrons)
R
(e e      )
measured in e+e- collision
or indirectly in  decay.
 m 
a ( had , lo)  

 3 
2


4 m2
ds
K ( s) R( s)
2
s
Evaluation of R
M. Davier et al., hep-ph/0208177
aμ(had, lo) based on e+e− data
s , GeV
2π
ω
φ
0.6 − 2.0
2.0 − 5.0
J/ψ,ψ’
> 5.0
Total
a (had,lo),1010
508.20±5.18±2.74
37.96±1.02±0.31
35.71±0.84±0.20
63.18±2.19±0.86
33.92±1.72±0.03
7.44±0.38±0.00
9.88±0.11±0.00
696.3±6.2±3.6
%
72.99
5.45
5.13
9.07
4.87
1.07
1.42
100.0 (DEHZ)
aμ(had,lo) = 696.15(5.7)(2.4) × 10-10 (HMNT)
aμ(had,lo) = 694.8 (8.6)
× 10-10 (GJ)
S. Eidelman at DAФNE 2004
Discrepancy between e+e− and  data
mode
π−π+
e −e +

Δ(e−e+ − )
508.20±5.18±2.74 520.06±3.36±2.62
-11.9±6.9
π−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
539.17±5.41±3.17 553.86±3.74±3.02
-14.7±7.9
total
aμ(had,lo) = 711.0(5.0)(0.8)(2.8)×10-10 (DEHZ)
M. Davier
S. Eidelman
et al., athep-ph/0208177
DAФNE 2004
Possible reasons for discrepancy
• Problem with experimental data
• Problem with SU(2) breaking corrections
• Non-(V−A) contribution to weak interaction
• Difference in mass of ρ mesons (mρ±>mρ0).
Current data indicate equality within a few MeV
Comparsion between CMD-2 and KLOE
CMD-2
2
(378.6  2.7stat  2.3syst+theo)  10-10(0.9%)
 2
KLOE
(375.6  0.8stat  4.9syst+theo)  10-10 (1.3%)
Kloe
CMD-2
F ( M  ) 
2
a (0.37GeV 2  M
 0.93GeV 2 ) 
2
 (e e      )
3M 
Radiative return is another way to
measure hadronic contributions
• Two measurements are in agreement
2
M
(GeV)
F. Nguyen at DAФNE 2004
Higher order hadronic contributions
a(had,nlo)=10.0(0.6)10-10
-10-10
a(had,lbl)=8.6(3.5)10
(had,lbl)=13.6(2.5)10
(had,lbl)=12.0(3.5)10
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
…including result : a=11 659 208(6) 10-10
experimental
KLOE result
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)
F. Nguyen at DAФNE 2004
Beyond standard model
• compositeness for leptons or gauge bosons.
• extra dimensions, or extra particles,
particularly supersymmetric particles
10
a ( SUSY)  13 10
100GeV
tan 
msusy
Conclusions
• Measurement of a−=11 659 214 (8)(3)×10-10(0.7 ppm)
• a− and a+ agree with each other as expected by CPT
• The combined result a=11 659 208(6) ×10-10(0.5 ppm)
• a(exp)−a(SM) is 2.4σ (e+e−) or 0.9σ ()
• The discrepancy between e+e− and  data is confirmed by
KLOE
• Upgraded muon g-2 experiment is expected to reduce the
experimental error to 0.2 ppm.
• Efforts on solving discrepancy between e+e− and , and
attempts to calculate a(had) from lattice QCD