PoS(SPIN2018)089 https://pos.sissa.it/ ring envisioned by the CPEDM Collaboration. B ~ × E ~ ∗ [email protected] [email protected] [email protected] [email protected] Speaker. We review the General Relativity inducedrings precession in of terrestrial a environment. spin Besides of thein relativistic clasical focusing particles geodetic fields effect in needed there storage to emerges compensate a forboth spin the effects rotation Earth have a gravity structure force of acting the on spin-orbit storedpoint interaction particles. is in a The the Earth vindication gravitational of field. the Our 2012EDM major Orlov-Flanagan-Semertzidis signal derivation in of the the GR all-electric induced frozen-spinwould false rings. serve as The an experimental observation important of indicatorthe the GR of GR effect a in signal performance a of hybrid a storage ring. We also comment on ∗ Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). 23rd International Spin Physics Symposium -10-14 SPIN2018 September, 2018 - Ferrara, Italy for the JEDI Collaboration A. Saleev Institut f. Kernphysik, FZJ, 52415 Juelich,E-mail: Germany. A. Silenko N.N. Bogolyubov Laboratory for Theoretical Physics,Belarusian JINR, State 141980 University, Dubna, 220030 Russia Minsk, and Belarus. E-mail: F. Rathmann Institut f. Kernphysik, FZJ, 52415 Juelich,E-mail: Germany. N.N. Nikolaev L.D. Landau Institute for Theoretical Physics,Institute 142432 of Chernogolovka, Physics Russia and and Technology, 141701 Moscow E-mail: Dolgoprudny, Russia Gravity and Spin Dynamics for theExperiments EDM Search PoS(SPIN2018)089 ]. 2 (2.1) (2.3) (2.2) quan- in situ N.N. Nikolaev ] what lead to 5 . rad accuracy [ 2 is the magnetic µ /     ) } ]) ]. In this writeup we 2 3 B ~ − × g β ~ = ( + [ {z G E ~ EDM ( EDM η 1 2 | defines its EDM in units of the nuclear , + , ] } m E ~ S ~ q ] 2 EDM × × η 12 s β ~ , , 1 Ω ~ EDM  m ] on the celebrated 1/2 factor in the spin-orbit inter- η 11 G 9 = [ ]). The basic aim of this writeup is a clarification of = 7 S ~ − 1) [ dt d d 1 {z = MDM − c 2 ]. Here we only single out an important first ever 1 and mass = ]. With allowance for the EDM contribution to spin rotations β 1 ¯ h q  10 + ] and Frenkel [ B ~ 8 G |     q m ], but in 2017 it has been challenged by T. Morishima et al [ − 4 = ], see also more recent [ s 6 Ω ~ The Schroedinger equation for spin dynamics in electromagnetic fields is with us since the Systematic background is a bane of high precision searches for the Electric Dipole Moment anomaly of a particle of charge magneton action in atoms. It hasBargmann, been Michel put and in Telegdi the [ widely used modern form appropriate for storage rings by It describes rotation ofspin the precession spin and w.r.t. cyclotron precession the angular particle velocities. momentum Here and gives a dfference of the true classical works by Thomas [ some of the issues in spinand dynamics a in vindication curved of space-time the of O-F-Sreadily relevence result. be to A storage separated critical ring from point experiments is theFurthermore, that true the the EDM GR GR signal provides induced a with false unique EDM counterrotating reference signal beams signal can in for an a crosscheck all-electric of ring. 2. the ring FT-BMT performance. equation the FT-BMT equation reads (here tification of the false EDM signalimperfection from magnetic the fields rotation in of the thesubstantial, magnetic ring the dipole stable - moment spin while (MDM) angular the in orientationSuch the at imperfections an COSY evil proper magnetic can were imperfection be fields found determined willto to to be advertise a absent be here in quite the that all-electric based storagehas on rings. been the It formed JEDI is proper aiming achievements at afocus a new international construction on of CPEDM still the Collaboration another all-electric magneticRelativity ring (GR) in imperfection effects. Europe induced [ The in presented all-electricthe material CPEDM storage is project. rings part A by of correct a theSemertzidis treatment JEDI General of in activity the 2012 related GR [ to effects discussions hasquite of been an given active by dicussion Orlov, of Flanagan the and by GR Lee effect (a Roberts fairly [ complete summary of this discussion was given (EDM) of charged particles in storage ringring experiments. in The Juelich JEDI collaboration had working recentlyvance at to COSY obtained search outstanding for the experimental EDM results signalresults at on and all-magnetic spin their storage implications rings. dynamics for A ofby comprehensive the rele- F. review future Rathmann of at all-electric these this storage conference rings [ was given in the plenary talk EDM in Gravity Field 1. Introduction PoS(SPIN2018)089 is g ~ (2.4) (3.1) (2.5) ]. The ). Bear in units ] y v 17 ~ e ~ × of a particle. N.N. Nikolaev x e , pure horizon- ~ L ~ y e ~ = [ B z e ~ = B ~ is a radius-vector from r ~ is fully reminiscent of the one ] is the particle velocity LS , where z 13 Ω ~ r e ~ ~ β ∝ g = ~ . ] E β ~ ~ g ~ q ]. A gyroscope precession test of GR was . × m β 14 ~ G 2 [ EDM 1 1 η + 1 1 2 0, where + − + gives rise to an orbital momentum γ ] γ = = 2 r ~ ) = 2 B ~ × = β · FS EDM β ~ LS [ β ~ Ω ~ Ω ~ form a right-handed coordinate system, } ) = ( z should not be confused with the magnetic g-factor. Because e E ~ ] and references therein). In the calssification of Khriplovich and ,~ ]. Schiff’s predictions have been fully confirmed by the satellite g · ~ y e 16 β ~ 15 ,~ ( x e ~ { and x e ~ E = of light ( E ~ c As far as the Earth gravity is concerned, is suffices to invoke the weak field approximation. The central idea is to eliminate the MDM effect altogether first by going to the all-electric ring, Now we recall that our storage rings rest on the terrestial surface and stored particles are The first discussion of precession of gyroscopes in gravitational fields by de Sitter, often re- 0, and next operating at the frozen-spin (FS) magic energy [ = The geodetic effect does not depend on the magnetic anomaly. the Earth center, and the cross product proportional to a gradient of the gravitationalfrom field, LS this result interaction for familiar from atomic physics. Indeed, Then the spin dynamics willthe boil angular down velocity to a pure EDM driven rotation around the radial axis with Kh-P relativistic extension of the spin precession angluar velocity from the geodetic effect reads The vector free fall acceleration suggested by Schiff in 1960Garvity [ Probe-B experiment ([ Pomeransky, the geodetic effect is but a spin-orbit interaction in a gravitational field [ B of the velocity in mind that the above canonical formnetic of confinement the of FT-BMT particles equation in only holds a for ring. the pure electromag- subject to gravitational field of thea Earth. major While role in in the traps neutron for EDM ultracoldof experiments neutrons, charged the for particles a gravity in good plays reason storage noposition rings. one such has A that ever point cared the about is gravitational a thatA free force the gravity fall is induced beam cancelled shift automatically for of finds the by the stable a equilibrium orbit Lorentz is force absolutely from insignicant focusing for all fields. 3. the practical Gyroscope purposes. in a gravitational field ferred to as the geodetic effect, goes back to 1916 [ EDM in Gravity Field and we consider a reference closedtal orbit electric with field a pure vertical magnetic field and a slow build upsignal of of EDM. the The vertical in-plane polarization polarizatonat of from any a fixed the particle angle can initially w.r.t. be longitidinal therise frozen one momentum. either to along is the In its EDM a the momentum signal, sought latter or whilea case for the comagnetometer the readily to longitidinal measureable maintain polarization sideways the would component frozen-spin would give condition. serve as sort of ~ PoS(SPIN2018)089 (4.6) (4.1) (4.4) (4.5) (4.3) (4.2) N.N. Nikolaev ] g ~ . × ] v g ~ ~ [ . } ] × ) . g ) is of pure academic interest as in all- ~ v 1 ~ . g [ ~ r ) × g q ~ − m e 4.3 ~ 1 v ~ 2 m · [ G γ − 1 1 q m 2 c 2 √ ( · | − γ γ − γ g γ 2 ~ 2 G 2 1 2 | 3 c ( γ γ 2 + 2 − 2 G v = 2 1 ]. As a heavy juggling by GR formalism it is not an γ − γ { − = 4 2 2 1 g OFS gE = v 1 F ~ γ g = Ω ~ = E ~ g − B ~ = OST gE Ω ~ ST gM shall emerge as an extra in the FT-BMT equation. Ω ~ . One can say that the GR effects do always amount to generation of ] r g ~ B ~ × v ~ [ ∝ ]. It is furnished by the radial magnetic field 18 Silenko and Teryaev were the first to discuss this compensation in the all-magnetic ring as The first treatmet of the GR effect on the EDM in all-electric frozen spin rings was given in The case of all-electric storage ring was revisited in 2016 by Obukhov, Silenko and Teryaev Although of apparent electromagnetic origin, a net effect of this GR correction to spin preces- The Kh-P relativistic formula for a geodetic effect describes a spin precession in the free fall ]. In this case the free fall is compensated for by a vertical focusing electric field 19 the radial magnetic imperfection fields.GR When induced combined angular with velocity the of geodetic spin effect, rotation it around gives the the radial total axis early as in 2005 [ 2012 by Orlov, Flanagan and Semertzidis [ needs to be compensateddependence by of this a gravity Lorentz force is forceis dictated somewhat from by different the the for spin-2 focusing the natureGR of all-magnetic fields effects gravitons. we and in The prefer all-electric the rest to fields. follow of ring. a the In historic story route. the The further energy discussion of the magnetic rings it is an absolutely negligible and basically unobservable effect. In a generic ring runningradial at magnetic a field non-magic energy this vertical electric field amounts to a motional [ The S-T effect was a first instance offrom an the interplay of point the geodetic of and view focusing field of effects, although the EDM the S-T formula ( easy reading and a separation ofin the there. geodetic and The free-fall O-F-S compensation final effects result might reads look (hereafter elusive the velocity of light c is in) sion is of precisely theprecession same becomes form as the geodetic effect. The combined GR contribution to spin motion. In particle physics wenetic deal fields. with charged Here particles we confined ask for inforce a a closed ring orbit by in static a electromag- ring placed on the terrestial surface and the gravity EDM in Gravity Field 4. The S-T, O-S-T and O-F-S effects Upon this compensation the cyclotron rotation willfield, be but exactly the the focusing same field as in a pure vertical driving PoS(SPIN2018)089 · e 701 29 . (5.1) (5.2) − 0 10 ≈ ], the term 4 ∼ p d N.N. Nikolaev 7 MV/m are considered feasible. ∼ the GR signal would take over. ) p d gM 0 Ω ~ κ < . + G g g gE E vB Ω ~ 4 ( = κ κ 1 + . At still smaller ring for 1 B ~ cm = · × e g 28 E Ω ~ ~ − 10 · 0 the frozen spin condition can be met only in a hybrid ring with 4 < ≈ p G d . Its observation would become a very important and uniqe confirmation of 1 at ) is imposed in the O-S-T generic equation, the O-S-T result becomes identical the GR effect would become an indispensable calibration check. i.e., 2.4 , cm 14 · − e 10 29 · − 4 10 ≈ On the theoretical side, the issue of GR induced false EDM signal has been closed. However, While a clearcut separation of the EDM and GR effects was commented on already by Orlov et al. [ We also reiterate that unlike the true EDM signal the false EDM-like contribution from the While the true EDM signal is identical for the clockwise (CW) and counterclockwise (CCW) For deuterons with Remarkably, the GR effect does not depend on the electric field in the ring. Go back to the all-electric frozen-spin ring storing protons with magic momentum of 1 ∼ , then the gravity signal will be seen in full glory and, as it has become a folklore, can be taken η p "standard candle" can, apparently, be attributed to R. Talman. one should not viewexperimental this side a false senisitivity GR to the signal proton EDM as will ever a be systematic boosted to error. the level of Quite to the contary, if on the GR signal does notrequire depend impracticaly on expensive a the comparison of radialconfining results confining E-fileds from and two field. different magic radii. energy However, rings testing with different this property would 7. Conclusions cm for a standard candle spin dynamics of relativistic particles in General Relativity. beams, a false GRtwo signals effects are can of readily be opposite separated. sign.d Furthermore, in Hence experiments aiming in at a an ring ultimate sensitivity with CW and CCW beams the crossed electric and magnetic fields.energy 45 The MeV protons. same is Inon true a the relative hybrid of contribution ring the of the the prototype GR magnetic frozen-spin and correction ring electric to focusing for the fields low spin to precession the would Lorentz force depend This new parameter is not fixed bying the fields. frozen-spin Then condition the of GR vanishing induced MDM false rotation EDM in confin- signal would be 5. GR effects in the combined EDM in Gravity Field At first sight, the O-S-T formula mightspin look quite condition different ( from the O-F-S one,to but the once the O-F-S frozen- one. GeV/c. The electrostatic deflectors sustainingThen electric the fields false of signal from theat GR induced MDM rotation would become equal to the EDM signal 6. When does the false GR signal take over the EDM signal? PoS(SPIN2018)089 , 1055 N.N. Nikolaev 43 , 492 (1959) 2 , no. 7, 072801 (2017) [Phys. Rev. , no. 4, 044019 (2016) , 839 (1998) [Zh. Eksp. Teor. Fiz. 20 94 86 , no. 8, 089201 (2018) , 2822 (2018) , 435 (1959) 2018 2 A376 , no. 17, 175003 (2018) [arXiv:1803.01395 , 1350147 (2013) , 064016 (2005) [gr-qc/0407015]. 35 5 71 , no.11, 115116 (2016) A28 87 , 155 (1916). , 221101 (2011) 77 106 , 215 (1960) 4 , 1129 (2000)]. , 514 (1926) 43 117 , 243 (1926) 37 , 072801 (2017)] , “Feasibility Study for an EDM Storage Ring,” arXiv:1812.08535 [physics.acc-ph]. [JEDI Collaboration], Phys. Rev. Accel. Beams 20 et al. et al. , 1537 (1998)]; A. A. Pomeransky, R. A. Senkov and I. B. Khriplovich, Phys. Usp. [gr-qc]]. 113 (2000) [Usp. Fiz. Nauk September, 2018, to be published in PoS. Ferrara, Italy Accel. Beams. The authors wish to acknowledge a support of the JEDI collaboration by the European Re- [1] F. Rathmann, Plenary talk at the 23rd International Spin Physics Symposium -[2] SPIN2018, 10-14 A. Saleev [8] L.H. Thomas, Nature [9] J. Frenkel. Z.Phys. [6] J.P. Miller and B.L. Roberts, arXiv:1805.01944 [hep-ph]. [7] A. Laszlo and Z. Zimboras, Class. Quant. Grav. [4] Y. Orlov, Y. Flanagan and Y. Senetrzidis, Phys. Lett. [3] F. Abusaif [5] T. Morishima, T. Futamase and H. M. Shimizu, PTEP [15] L.I. Schiff, Phys. Rev. Lett. [16] C.W.F. Everitt et al. Phys. Rev. Lett. [17] I. B. Khriplovich and A. A. Pomeransky, J. Exp. Theor. Phys. [19] Y. N. Obukhov, A. J. Silenko and O. V. Teryaev, Phys. Rev. D [12] T. Fukuyama, A.J. Silenko, Int.J.Mod.Phys. [14] W. de Sitter, Mon. Not. R. Astron. Soc. [18] A. J. Silenko and O. V. Teryaev, Phys. Rev. D [13] V. Anastassopoulos et al., Rev.Sci.Instrum. search Council via the ERC Advancedof Grant the "srEDM" Russian (No. State program 694340). 0033-2019-0005. The work of NNN is aReferences part EDM in Gravity Field 8. Acknowledgemens [11] D.F. Nelson, A.A. Schupp, R.W. Pidd, H.R. Crane, Phys.Rev.Lett. [10] V. Bargmann, L. Michel, V.L. Telegdi, Phys.Rev.Lett.