Huaizhang Deng

Yale University

Precise measurement of (g-2)

University of Pennsylvania

Collaboration

Prof. Vernon W. Hughes (1921 2003)

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.

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

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)

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

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).

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

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 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

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)

Trolley measurement

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

The B field averagedOver azimuth.

Fixed probe measurements

Calibration of the fixedprobe system with respectto the trolley measurements

The magnetic fieldmeasured by the fixedprobe system during2000 run.

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.

2000 a data

))(cos()(1)()( /0 EtEAeENtN a

t

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

CBO effect on ωa

)2/()2( acboacbo

a

Cancellation of cbo around the ring

CBO effect shown onthe average energy of e+

Cancellation of cbo effectafter summing all detectortogether.

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.

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

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.

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

Evaluation of R

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

Comparison between e+e- and

M. Davier et al., hep-ph/0308213M. Davier et al., hep-ph/0208177

Experimental and theoretical values

Beyond standard model

• extra dimensions, or extra particles,

• compositeness for leptons or gauge bosons.

particularly supersymmetric particles

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

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)

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.

Superconducting inflector

The radial phase space allowed by the inflector aperture(green) is smaller than that allowed by the storage ring (red).

Photo of the storage ring

inflector kickers

Detectors

Magnet

Muon distribution

Radial muon distribution determined by the Fourier trans-formation of cyclotron periods when beam is debunching.Vertical muon distribution is symmetric.

Residual after fit with ideal function

Detectors and positron signals

Polarized muons

Parity violated decay

produces longitudinally polarized muons.

+ +sp

: spin 0: left handed

: left handed

Half ring effect due to cbo

Pileup correction

real pileup : |t|<2.9 ns

constructed pileup : |t-10|<2.9 ns

rawcorrected

rawcorrectedlater time

Muon loss

Absolute normalization is determined by fit.

Evaluation of R (low energy region)

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

a(had,1)

a(had,lbl)=8.6(3.5)10-10

Higher order hadronic contributions

a(had,2)=10.1(0.6)10-10

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.