Huaizhang Deng

Yale University

Muon g-2

experimental results & theoretical developments

University of Pennsylvania

Collaboration

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

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

g - 2 0 for the muon

Largest contribution : 800

1

2

a

Some of other contributions :

QED hadronic weak

New physics ?

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

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

Muon storage ring

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

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).

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)

Uniformity of the B field

The B field variation at thecenter of the storage region. <B>1.45 T

The B field averagedover azimuth.

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.

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.

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

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

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

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

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

History of the experimental measurements

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 :

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 *

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

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

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

Evaluation of R

M. Davier et al., hep-ph/0208177

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

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

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

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

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

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

Beyond standard model

• extra dimensions, or extra particles,• compositeness for leptons or gauge bosons.

particularly supersymmetric particles

tan100

1013)( 10

susym

GeVSUSYa

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.