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