Oleg Teryaev JINR, Dubna

1. Equivalence Principle and Partition of Angular Momenta in The Nucleon SPIN-2006 Kyoto, October 6 2006 Oleg Teryaev JINR, Dubna

2. Outline • Equivalence principle and spin • Spin structure of nucleon (Plenary Talk of X. Ji) and Gravity Formfactors • Tests of Post-Newtonian Equivalence Principle • Extended Equivalence Principle and Exact Equipartition of momenta and total angular momenta fof quarks and gluons and NP QCD • Relation to Sivers functions, Burkardt SR and Brodsky/Gardner conjecture

3. Equivalence principle • Newtonian – “Falling elevator” – well known and checked • Post-Newtonian – gravity action on SPIN – known since 1962 (Kobzarev and Okun’) – not yet checked • Anomalous gravitomagnetic moment iz ZERO or • Classical and QUANTUM rotators behave in the SAME way

4. Electromagnetism vs Gravity • Interaction – field vs metric deviation • Static limit • Mass as charge – equivalence principle

5. Gravitational fromfactors • Conservation laws - zero Anomalous Gravitomagnetic Moment : (g=2) • Moments of GPD’s (X. Ji)- may be extracted from high-energy experiments/NPQCD calculations • Describe the partition of angular momentum between quarks and gluons • Describe also interaction with TeV gravity – similar t-dependence to EM FF (CNI-like spin effects-O.Selugin, O.T, in progress) • Anapole term analogous to EM case may be added

6. Gravitomagnetism • Gravitomagnetic field – action on spin – ½ from spin dragging twice smaller than EM • Lorentz force – similar to EM case: factor ½ cancelled with 2 from Larmor frequency same as EM • Orbital and Spin momenta dragging – the same - Equivalence principle

7. Helicity • EM – conserved: velocity dragging is the same as that of spin • Gravity – not conserved BUT the same as required by conservation in LOCAL INERTIAL frame • Helicity is not flipped by the scattering in gravitomagnetic field – another form of Post-Newtonian EP

8. Equivalence principle for moving particles • Compare gravity and acceleration: gravity provides EXTRA space components of metrics • Matrix elements DIFFER • Ratio of accelerations: - confirmed by explicit solution of Dirac equation (Silenko, O.T.)

9. Gravity and acceleration for spin dragging • Helicity – not affected by space components of metric – the same angular velocity • Spin dragging – differ by factor 3

10. Spin rotation or spin-gravity coupling? • Scale of Earth ROTATION effects – much higher than Earth gravitomagnetic field : order ( achievable by level crossing – L. Stodolsky) vs eV • Suggestion – use flippers (Mashhon et al.,98) • New option- - GRANIT–transitions

11. Rotating spin-flipper for existing interferometer at ILL • Magnetic field H: about 30 Gs • Volume about • Frequency of rotation about 10 KHz • Not affect significuntly the other beam at the distance about 3 cm • Suggestion: TWO rotating flippers: many true qnd false signals – like for double spin asymmetries BUT – measurement in INERTIAL frame

12. Other tests of the equivalence principle • Coupling to Earth rotation at storage rings a la g-2 experiment and Coupling to acceleration a la EDM experiments (A. Silenko, O.T., in progress); RECENT claim (hep-ex/0609055) that Gravity-Rotation coupling is ALREADY seen in EDM experiment! • Space experiments (of Probe-B type) with spin instead of classical rotator?

13. Generalization of Equivalence principle • Various arguments: AGM 0 separately for quarks and gluons – most clear from the lattice (LHPC/SESAM)

14. Extended Equivalence Principle=Exact EquiPartition • In pQCD – violated • Reason – in the case of EEP- no smooth transition for zero fermion mass limit (Milton, 73) • Conjecture (O.T., 2001 – prior to lattice data) – valid in NP QCD – zero quark mass limit is safe due to chiral symmetry breaking

15. Another arguments in favour of EEP • J=1/2 -> J=1. QCD SR calculation of Rho’s AMM gives g close to 2. Maybe because of similarity of moments. Gluons momentum fraction sizable. Direct calculation for AGM are desired! • “Valence” Parametrization of E (GPV) – remarakble relations between valence quantities - physical input – EQUIPARTITION • Relation: E -> Sivers; EP -> Burkardt SR; EEP -> Brodsky/Gardner conjecture (talk of F.Bradamante) • See also talk of M. Wakamatsu

16. Another relation of Spin Structure and NP QCD (first reported at 1992: hep-ph/9303228) • BELINFANTE (relocalization) invariance : smoothness in momentum space • Leads to absence of massless pole in singlet channel – U_A(1) • Related to equipartition by QCD evolution • May explain relation of Sivers function to orbital momentum: L -> gT -> f(Sivers)

17. Conclusions • Post-Newtonian EP – important fundamental property yet to be checked • Accelerator and Neutron tests seem to be possible • TeV gravity studies require the use of gravitational formfactors • Equipartition of momentum and total angular momentum – interesting relation between Spin structure (interrelated, including Sivers function), gravity and NP QCD