1. Search for Lepton Flavor Violation (LFV) in e+e– interaction (review of experimental results) M.N. Achasov International Workshop on e+e– collisions from Phi to Psi

2. Introduction Fundamental fermionsProcesses with flavor violation udud cscs tbtb Quarks decays e   Neutrino oscillations e  Never been observed The charged LFV is strongly suppressed in Standard Model (SM) due to small neutrino mass: Observation of LFV process would be a signal of physics beyond SM Estimation, SM + neutrino oscillationsPresent limit, CL=90% Br(  →e  ) < 10 -40 < 1.2 ×10 -11 Br(  →  ) < 10 -40 < 4.4 ×10 -8

3. Processes with LFV (   and   ) decays, for example  →e   eee,  →  meson (K,B,D,  ) decays, for example   →e  ;  → e conversion on nucleuses; e+e− interaction e + e − →e , e + e − →e , e + e − →  The diagrams of the e+e– → e  process. V denotes vector meson or Z-boson

4. Some theoretical constraints The limits on the Br(V→e  ) and Br(V→  l) were obtained from present experimental bounds on Br(  →3e)<10 -12, Br(  →ll´l´)<10 -8 and e-  conversion data.  and  decays [1]e-  conversion [2] Br(  →e  ) <4 × 10 -24 Br(  →e  ) <6 × 10 -27 Br(  →e  ) <4 × 10 -17 <1× 10 -21 Br(J/  →e  ) <4 × 10 -13 Br(  →e  ) <2 × 10 -9 <4 × 10 -6 Br(Z→e  ) <5 × 10 -13 <8 × 10 -15 Br(J/  →  l) <6 × 10 -9 Br(  →  l) <1 × 10 -4 Br(Z→  l) <3 × 10 -8 [1] S.Nussinov, R.D. Peccei and X.M. Zhang, Phys. Rev. D,63,015003 (2000) [2] Thomas Gutsche, Juan C. Helo, Sergey Kovalenko and Valery E. Lyubovitskij. Phys. Rev. D 81, 037702 (2010); arXiv:1103.1317v2 [hep-ph] 16Jun 2011 The most of estimates are below achievable experimental accuracy. The e + e – →ll´ processes are less sensitive to LFV than leptons decays and not expected.

5. Reasons to search for LFV in e + e – →e , e ,  processes. Not expected process exists due to some kind of «miracle»; The processes have clear signal in detector and easy for analysis; Such studies demonstrate understanding of detector performance and backgrounds; The collider experiments are rather expensive, so the number of studies should be as much as possible.

6. Approach to data analysis e+e → ee+e → e Two collinear charged particles with opposite charges electron candidate: produce electromagnetic shower in calorimeter with beam energy, do not hit muon system muon candidate pass through detector like minimal ionizing particle, has beam momentum and hit muon system. e + e  → e(  electron (muon) candidate  decay of  with clear signature, for example  →e, , , ,a 1

7. Search for LFV below 2 GeV e + e  → e   studies at √s=984 – 1060 MeV with SND at VEPP-2M, IL=8.5 pb -1  e  < 11 pb CL=90% B(  → e  ) < 2×10 -6 CL=90% Search for  →e  and  →e  in process e + e  → e   is difficult due to huge e + e  →  +  – background. At VEPP-2000 it is possible to search for e + e  →  e  at 2 GeV (?)

8. Search for LFV in  -charm energy region. J/  →e , e ,  studies with BES-II at BEPC were based on 58 × 10 6 J/  events. Upper limit, 90% CLCandidates number Estimation from ,  decays Br(J/  →e  ) < 1.1×10 -6 4 <10 -13 Br(J/  →e  ),  →  < 8.3×10 -6 1 <10 -9 Br(J/  →  ), t→e < 2.0×10 -6 0 In experiments with BES-III at BEPC-II (  charm factory) it is expected to have upper limits 10 -8 – 10 -9. Huge data sample is collected at  ´,  (3770),  (4040) also. Super c –  factory can provide upper limits 10 -10 – 10 -11 (?).

9. Search for LFV in bottomonium energy region. CLEO-III  (nS)→ ,  →e n=1,2 and 3 BABAR  (nS)→e ,  → ,  ± ,  ±  (nS)→ ,  →e,  ± ,  ±  n=2,3 Upper limit, 95% CL (CLEO) Upper limit, 90% CL (BABAR) IL, fb-1 (CLEO) IL,fb-1 (BABAR) Br(  S  →  ) < 6.0 × 10 -6 – 1.1 Br(  S  →e  ) – < 3.2 × 10 -6 1.313.6 Br(  S  →  ) < 14.4 × 10 -6 < 3.3 × 10 -6 Br(  S  →e  ) – < 4.2 × 10 -6 1.426.8 Br(  S  →  ) < 20.3 × 10 -6 < 3.1 × 10 -6 BABAR  √s=10.58 GeV, IL=211 fb -1 e + e –  → e +  –,  +  –,  →  –,  –  +  –  e  <9.2 fb CL=90%   <3.8 fb CL=90% Upper limits at Super b-factory can be 10 -7 – 10 -8 (?) Estimation from  decays: Br(  →  l) <10 -4

10. Search for LFV at LEP e + e − →e , e , , 189<√s<209 GeV (OPAL) OPALL3DELPHIALEPH Estimations from  and  decays Br(Z→ e  ), 10 -6, 95% CL < 1.7< 6< 2.5< 26< 10 -15 – 10 -13 Br(Z→ e  ), 10 -6, 95% CL < 9.8< 13< 22.0< 120 < 3 × 10 -8 Br(Z→  ), 10 -6, 95% CL < 17.0< 19< 12.0< 100 Number of Z-bosons, 10 6 41.53.9 √s, GeVIL, pb -1  e , fb, CL=95%  e , fb, CL=95%  , fb, CL=95% 1891755895115 192 – 19610462144116 200 – 209322227864

11. Conclusion Upper limits on branching ratios of vector mesons and Z- boson to LFV final state. ee ee φ2×10 -6 J/  10 -6 8×10 -6 2×10 -6  3×10 -6 Z2×10 -6 10×10 -6 12×10 -6 Experimental upper limits are much higher, then those expected from  and  LFV decays, except  -meson case.