Generalized Bargmann-Michel-Telegdi Equation
@ Osaka U. Nov. 23 2013
Takeshi Fukuyama
Osaka U. RCNP
with Alexander Silenko (Belarus)
Our target is to measure both aMDM
and EDM of charged particle (especially
storage ring.
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.
) in
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
3. The derivation of generalized ThomasBargmann-Michael-Telegdi Eq.
4. Pitch corrections if we have time.
Methodological uniqueness in
general EDM searches.
Experimental side
Fukuyama review (2012)
Fundamental breakthrough is possible by desktop
Theoretical side
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
Searches for BSM physics (with muon).
Anomalous MDM/EDM
(four loop)
from YbF (Hinds et al. 2011)
Magnetic shield
Solenoid coil
Probe laser
Photoelastic Modulator
Pumping laser
3 GeV proton beam
( 333 uA)
Graphite target
(20 mm)
Silicon Tracker
Surface muon beam
(28 MeV/c, 1-2x108/s)
66 cm diameter
Muonium Production
(300 K ~ 25 meV⇒2.3 keV/c)
Super Precision Magnetic Field
(3T, ~1ppm local precision)
Resonant Laser Ionization of Muonium
(~106 m+/s)
Expected time spectrum of me+nn decay
Muon spin precesses with time.
 number of high energy e+ changes with time by the frequency :
e    
w    am B    B 
p>200 MeV/c
e+ decay time (sec)
Generic new-physics dipole moment
If one assumes that both non-SM MDM (amNP) and EDM (dµ)
are manifestations of the same new-physics object:
with D a general dipole operator (W. Marciano),
then the Brookhaven measurement can be interpreted as
29.7 x
i.e. either dµ is of order 10–22 e cm,
or the CP phase is strongly suppressed!
Klaus Kirch (Nufact08)
J.L. Feng, K.T. Matchev, Y. Shadmi
Theoretical Expectations for the Muon's
Electric Dipole Moment,
Nucl. Phys. B 613 (2001) 366
1. Introduction
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.
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
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
Tedious but simple calculations result in
One usually considers the spin motion relative to the
beam direction. Let us introduce
Magic number
Measured oscilation is
was adopted at BNL
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
5. Summary
Back Up
Muon storage magnet and detector
2900 mm
e+ tracking
Super conducting coils
Muon storage orbit
Radial tracking vanes (Silicon strip)
μ decay
p(e+) > 200 MeV/c

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