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 ring. 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 experiments. 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 indispensable. Searches for BSM physics (with muon). Anomalous MDM/EDM E821(BNL) (four loop) from YbF (Hinds et al. 2011) Magnetic shield Solenoid coil Probe laser Photoelastic Modulator (PEM) Pumping laser Heater 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) 7 Expected time spectrum of me+nn decay Muon spin precesses with time. number of high energy e+ changes with time by the frequency : e w am B B m 2 Saito-Mibe （J-PARC） p>200 MeV/c 0.1ppm statistical uncertainty w 8 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: and with D a general dipole operator (W. Marciano), then the Brookhaven measurement can be interpreted as 3.0 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 9 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 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 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 where So where where 5. Summary Back Up Muon storage magnet and detector 2900 mm e+ tracking detector Super conducting coils Muon storage orbit Radial tracking vanes (Silicon strip) μ decay vertex 34 p(e+) > 200 MeV/c 34 where

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