# Presentation: 694903

## Precise measurement of (g-2) 

- 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-2

- For the proton :   *a**p****1.8* because the proton is
-                             composite particle.

##  g - 2  0 for the muon

- Other standard model contributions :

- 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.

## Principle of the measurement

- When* *=29.3 (p=3.09 Gev/c),
***a* is independent of *E*.

## How to measure B

*B* is determined by measuring the proton nuclear
- magnetic resonance (NMR) frequency ***p *in the
- magnetic field.

- /p=3.183 345 39(10),
- W. Liu *et al., *Phys. Rev. Lett. **82**, 711 (1999).

## How to measure a

## Muon storage ring

## Some numbers about the experiment

- 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

- 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)

## Trolley measurement

- The *B* field variation at the
- center of the storage region.
-              <B>1.45 T

- The *B* field averaged
- Over azimuth.

## Fixed probe measurements

- Calibration of the fixed
- probe system with respect
- to the trolley measurements

- The magnetic field
- measured by the fixed
- probe system during
- 2000 run.

## Systematic errors for p

| Source of errors | Size [ppm]
2000         1999 |  |
| --- | --- | --- |
| Absolute calibration of standard probe | 0.05 | 0.05 |
| Calibration of trolley probe | 0.15 | 0.20 |
| Trolley measurements of B0 | 0.10 | 0.10 |
| Interpolation with fixed probes | 0.10 | 0.15 |
| Inflector fringe field | -- | 0.20 |
| Uncertainty from muon distribution | 0.03 | 0.12 |
| Others† | 0.10 | 0.15 |
| Total | 0.24 | 0.4 |

- † higher multipoles, trolley temperature and voltage response,
- eddy currents from the kickers, and time-varying stray fields.

## 2000 a data

## Coherent betatron oscillation (cbo)

- kick

## CBO effect on ωa

## Cancellation of cbo around the ring

- CBO effect shown on
- the average energy of *e**+*

- Cancellation of cbo effect
- after summing all detector
- together.

## Error for a

| Source of errors | Size [ppm]
2000        1999 |  |
| --- | --- | --- |
| Coherent betatron oscillation | 0.21 | 0.05 |
| Pileup | 0.13 | 0.13 |
| Gain changes | 0.13 | 0.02 |
| Lost muons | 0.10 | 0.10 |
| Binning and fitting procedure | 0.06 | 0.07 |
| AGS background |  | 0.10 |
| Others† | 0.06 |  |
| Total systematic error | 0.31 | 0.3 |
| Statistical 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 magnetic
- moment was evaluated,

*a***=11 659 204(7)(5) 10-10

## Standard model calculation of a

*a***(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 calculated
- to high accuracy.
- The accuracy of *a***(had) is about 0.6 ppm.

## Hadronic contribution (LO)

## Evaluation of R

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

## Comparison between e+e- and 

## Experimental and theoretical values

## Beyond standard model

-  extra dimensions, or extra particles,

-  compositeness for leptons or gauge bosons.

## Muon electric dipole moment

- Vertical profile of decay positrons oscillates
-   with frequency of *g-2*
-   with phase 90o different from *g-2* phase
-   with amplitude proportional to dμ

## 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.

-           +         +

- s

- p

## Half ring effect due to cbo

## Pileup correction

- real pileup :
-         |***t|<2.9 ns*

- constructed pileup :
-         |***t-10|<2.9 ns*

- raw

- corrected

- raw
- corrected
- later time

## Muon loss

- Absolute normalization is determined by fit.

## Evaluation of R (low energy region)

- Evaluation of R (low energy region)

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

## a(had,1)

## Higher order hadronic contributions

*a***(had,lbl)=8.6(3.5)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.