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