Takeshi Fukuyama

Osaka U. RCNP

with Alexander Silenko (Belarus)

Generalized Bargmann-Michel-Telegdi Equation @ Osaka U. Nov. 23 2013

The aim of this talk is to write down equation for the classical spin vector in a rotating rest frame in which tha particle’s velocity is instaneously at rest.

Our target is to measure both aMDM and EDM of charged particle (especially ) in storage ring.

Contents of my talk

1． Introduction

What is the implication of electric dipole moment (EDM) in BSM physics ?

2. EDMs of charged particles in storage

ring.

3. The derivation of generalized Thomas-Bargmann-Michael-Telegdi Eq.

4. Pitch corrections if we have time.

Methodological uniqueness in general EDM searches.

Fundamental physics parameters (EDMs of elementary particles) are determined from atom and molecule spectroscopies with huge enhancement.

Therfore the collaboration over the wide range of particle physics, atomic and molecular physics is indispensable.

Experimental side

Fundamental breakthrough is possible by desktop experiments.

Theoretical side

Fukuyama review (2012)

Searches for BSM physics (with muon).

Anomalous MDM/EDME821(BNL)

from YbF (Hinds et al. 2011)

(four loop)

Probe laser

Photoelastic Modulator(PEM) Pumping laser

HeaterMagnetic shieldSolenoid coil

7

Resonant Laser Ionization of Muonium (~106 +/s)

Graphite target (20 mm)

3 GeV proton beam ( 333 uA)

Surface muon beam (28 MeV/c, 1-2x108/s)

Muonium Production (300 K ~ 25 meV⇒2.3 keV/c)

Silicon Tracker

66 cm diameter

Super Precision Magnetic Field(3T, ~1ppm local precision)

Expected time spectrum of e+ decay

8

Muon spin precesses with time. number of high energy e+ changes with time by the frequency :

BBa

m

e 2

e+ decay time (sec)

p>200 MeV/c

0.1ppm statistical uncertainty

Saito-Mibe 　（ J-PARC ）

Generic new-physics dipole momentIf one assumes that both non-SM MDM (a

NP) and EDM (dµ)

are manifestations of the same new-physics object:

and

with D a general dipole operator (W. Marciano),

then the Brookhaven measurement can be interpreted as

i.e. either dµ is of order 10–22 e cm,

or the CP phase is strongly suppressed!J.L. Feng, K.T. Matchev, Y. ShadmiTheoretical Expectations for the Muon's Electric Dipole Moment,Nucl. Phys. B 613 (2001) 366

3.029.7 x

9Klaus Kirch (Nufact08)

EDMs cover over huge range of physics and chemistry.

The targets are particles (quarks, leptons, neutron, protons), atoms (paramagnetic and diamagnetic atoms), molecules, ions, solid states etc.

1. Introduction

EDM is P-odd and T-odd, and, therefore CP-odd.

Let us start with non-relativistic case for MDM only

On the other hand, the euation of motion of particles is

Now let us consider the relativistic case.

The relativistic equation of spin motion in electromagnetic field using this 4-pseudovector is given by

In this frame, the equation of spin motion is

Comparing this equation with the previous Eq., we obtain

The value of results from the equation of motion

Then

Thus we obtain

This is the Thomas-Bargmann-Michel-Telegdi (T-BMT) equation added by the EDM terms.

The spatial part of this equation is presented by

with　　　　　　　 .

Tedious but simple calculations result in

One usually considers the spin motion relative to the beam direction. Let us introduce

Magic number was adopted at BNL

Measured oscilation is

4. Pitch correction

The muon momentum is not exactly orthogonal to the external magnetic field , inducing coherent betatron oscillation. 　 (parallel: pitch correction, perpendicular: yaw correction)

The orbit is stabilized in the z directin by

where

So

where

where

5. Summary

Back Up

Muon storage magnet and detector

34

Cryogenics

e+ trackingdetector

29

00 m

m

Muon storage orbit

Iron yoke

Super co

nductin

g co

ils

666 mm

343434

μ decayvertex

Radial tracking vanes (Silicon strip)

Positron

trac

kp(e+) > 200 MeV/c

where