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

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 ) in storage ring.

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

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  1. Generalized Bargmann-Michel-Telegdi Equation @ Osaka U. Nov. 23 2013 Takeshi Fukuyama Osaka U. RCNP with Alexander Silenko (Belarus)

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

  3. Contents of my talk • Introduction What is the implication of electric dipole moment (EDM) in BSM physics ? • EDMs of charged particles in storage ring. • The derivation of generalized Thomas-Bargmann-Michael-Telegdi Eq. • Pitch corrections if we have time.

  4. Methodological uniqueness in general EDM searches. Fukuyama review (2012) Experimental side 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.

  5. Searches for BSM physics (with muon). Anomalous MDM/EDM E821(BNL) (four loop) from YbF (Hinds et al. 2011)

  6. Setup for EDM measurement Magnetic shield Heater Solenoid coil Probe laser Photoelastic Modulator (PEM) Pumping laser

  7. 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) Surface muon Super Precision Magnetic Field (3T, ~1ppm local precision) Ultra Cold m+ Source Muon storage Resonant Laser Ionization of Muonium (~106m+/s) Muon LINAC (300 MeV/c) New Muon g-2/EDM Experiment at J-PARC with Ultra-Cold Muon Beam 7

  8. Expected time spectrum of me+nn decay Muon spin precesses with time.  number of high energy e+ changes with time by the frequency : Saito-Mibe　（J-PARC） p>200 MeV/c 0.1ppm statistical uncertainty w 8 e+ decay time (sec)

  9. 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 asi.e. either dµ is of order 10–22e cm, or the CP phase is strongly suppressed! 3.0 29.7 x J.L. Feng, K.T. Matchev, Y. ShadmiTheoretical Expectations for the Muon's Electric Dipole Moment,Nucl. Phys. B 613 (2001) 366 9 Klaus Kirch (Nufact08)

  10. 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.

  11. Let us start with non-relativistic case for MDM only

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

  13. Now let us consider the relativistic case.

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

  15. 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

  16. Then Thus we obtain This is the Thomas-Bargmann-Michel-Telegdi (T-BMT) equation added by the EDM terms.

  17. The spatial part of this equation is presented by with.

  18. Tedious but simple calculations result in

  19. One usually considers the spin motion relative to the beam direction. Let us introduce Magic number was adopted at BNL Measured oscilation is

  20. 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)

  21. The orbit is stabilized in the z directin by

  22. where

  23. So

  24. where

  25. where

  26. 5. Summary

  27. Back Up

  28. Muon storage magnet and detector Iron yoke Cryogenics Muon storage orbit 2900 mm Radial tracking vanes (Silicon strip) Super conducting coils e+ tracking detector Positron track μ decay vertex 666 mm 34 34 34 p(e+) > 200 MeV/c 34

  29. where

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