July 8, 2019 Kimiko Sekiguchi Workshop

1. July 8, 2019 Kimiko Sekiguchi Workshop Are there three-body forces between point particles ? H. Sakai RIKEN Nishina Center

2. Three-Nucleon Force (3NF) H. Miyazawa J. Fujita • Fujita•Miyazawa type 3NF (Prog. Theor. Phys. 17(1957)360.) 2 exchange type N+N’ p n n • Nucleon (finite size) has internal structure • N : essential for the origin of 3NF • My longstanding (20 y) question is : Is there a three-body force between point particles ? Looking for a genuine three-body force.

3. Three point(?) particles • Graviton (mass=0, Q=0, s=2) not found • Photon (mass=0, Q=0, s=1) gauge particle • Neutrino (mass<0.12 eV, Q=0, s=1/2) ferimion, Dirac/Majorana? • Electron/Positron (mass=0.511 MeV, Q=1, s=1/2, ), Muon, Tauon • Three-body force between electron/positron system : • Electro-magnetic three-body force Interactions : Coulomb electron-photon int.  higher order effect(3BF) • Appears as a correction to hyperfine interaction effects (mag-mag-mag) •  three-body effect will be very very small ! •  needs three-body QED calculations. Are there three electron/positron (e- e - e) system ? Yes!(First predicted by John Wheeler in 1946)

4. Positronium and its negative ion • Positronium (Ps) Ps B.E.= 6.80 eV (B.E.(H)=13.6 eV) <r(e-e+)>=2a0 (a0=0.529A) p-Ps : 1S0(J=0),  =125 ps, 2-decay o-Ps : 3S1(J=1),  =142 ns, 3-decay r e+ e+ e+ e- e- e- e- e- Ps- • Positronium negative ion (Ps-) B.E.(e-Ps)= 0.33 eV (B.E.(H-)=0.775 eV) <r(e-Ps)>=5.5a0 (a0=0.529A) Ps- :mainly o-Ps?,  =0.5 ns, 2-decay J=1/2 r • lightest three-body bound state p-Ps o-Ps

5. Positronium negative ion

6. Production of positronium negative ions (Ps-) Cscoated Ps- production rate = 1.25 % !!! E(e+) = thermal W=3 kV E() : Doppler shifted  540 kV

7. Spectroscopy of Ps-(photo ionization)

8. Ps- beam station at KEK PF

9. Muonium negative ion : Mu- (e)e • Negative Muonium (Mu-) + B.E.(e-Mu)= 0.75 eV (B.E.(Mu)=13.54 eV) <r(e-Mu)>=1.005a0 (a0=0.529A) =2.2 s (same as + decay): J=1/2 (or 3/2 ?) e- e- Kuang et al. PRA 39(1989) 6109 Almost H- ion T=0.5 MeV r Mu- production rate = 0.018 % !!!

10. Mu- produced and accelerated at JPARC Kitamura et al., Proc. PASA(2018) 239 (in Japanese) 89 keV Mu- production rate = 0.05 % ???

11. QED corrections in Ps-binding energy e+ e- e- Ps- 2 r23 r12 3 r13 1 rel. QED

12. One photon-decay of Ps-and 3-body force? GSI E(e+)=316keV e+e+e-e++ 3BInteraction? or 3BCorrolation?

13. Effective 3-body forces everywhere Two virtual photon emission 3BF But usually

14. Summary of my dream (may be nonsense !) • Does 3BF among 3 point particles exist or not? • Ps- and Mu- systems, available as a beam. • 3BF under long-range electro-magnetic force (expanded system). Cf. 3NF works in compact nuclear system under short-range nuclear forces. • 3BF effects seems to be very tiny, may be an order of 610-13 . (Cf. 5 calculations are done for g-2) • How to detect such tiny 3BF effects? • B.E. effect? Or scattering effects or …. It sounds impossible. • If observed as an interference effect, it may be possible. (Cf. LIGO, gravitational wave detection, △L/L=10-24) So my dream stays as a ‘dream’ for a while.