1. Rare decay  0 → e + e - and its implication to muon (g-2) μ A.E. Dorokhov (JINR, Dubna) Introduction Model Independent Approach to  0 →e + e – Decay and KTeV Data Model dependent approaches Other P →l + l – decays Conclusions

2. Introduction Abnormal people are looking for traces of Extraterrestrial Guests Abnormal Educated people are looking for hints of New Physics Cosmology tell us that 95% of matter was not described in text-books yet Two search strategies: 1)High energy physics to excite heavy degrees of freedom. No any evidence till now. Waiting for LHC era. 2) Low energy physics to produce Rare processes in view of huge statistics. There are some rough edges of SM.  (g-2)  is very famous example,  0 →e+e- is in the list of SM test after new exp. and theor. results That’s intriguing

3. Anomalous magnetic moment of muon From BNL E821 experiment (1999-2006) Standard Model predicts the result which is 3.4  below the experiment    h    he     X  

4. Rare Pion Decay  0 →e + e -- from KTeV From KTeV E799-II EXPERIMENT at Fermilab experiment (1997-2007) 97’ set 99-00’ set, The result is based on observation of 794 candidate  0  e+e- events using K L  3  0 as a source of tagged  0 s. The older data used 275 events with the result: PRD (2007) One of the simplest process for THEORY

5. Classical theory of  0 →e+e– decay FF Drell (59’), Berman,Geffen (60’), Quigg,Jackson (68’) Bergstrom,et.al. (82’) dispersion approach Savage, Luke, Wise (92’)  PT The Imaginary part is Model Independent

6. From condition one has the unitary limit KTeV 99-00 Progress in Experiment >7  from UL Still no intrigue

7. Dispersion approach (Bergstrom et.al.(82)) The Real Part is known up to Constant The Constant is the Amplitude in Soft Limit q 2  0 In general it is determined in Model Dependent way

8.  PT approach ( D’Ambrosio,Espriu(86),Savage,Luke,Wise(92)) is unknown LE constant

9. I. The Decay Amplitude in Soft limit q 2  0 The accuracy is of order O(m e  m   2. Thus the amplitude is fully reconstructed! A.D., M.A.Ivanov PRD 07’ The unknown constant is expressed as inverse moment of Pion Transition FF!!! Still no intrigue

10. II. CLEO data and Lower Bound on Branching Use inequality and CLEO data (98’) Intrigue appears

11. III. F  (t,t) general arguments Let then 1. From one has 2. From OPE QCD one has It follows 3.3  below data!! It would required change of s 0 scale by factor more then 10! F(t,0)  F(t,t) reduces to rescaling Now it’s intriguing!

12. A. F  (t,t) QCD sum rules (V.Nesterenko, A.Radyushkin, YaF 83’) one has From and Nicely confirms general arguments!

13. B. F  (t,t) VMD parametrization (M.Knecht, A.Nyffeler, EPJC 01’) Nicely confirms general arguments! Parameters for LbL

14. C. F  (t,t) Quark Models (Bergstrom 82’)

15. D. F  (t,t) Nonlocal Quark Models Nicely confirms general arguments! (A.Dorokhov 06’)

16. Instanton Model and Pion Transition FF

17. CLEO +QCD CLEO 3  diff What is next? It would be very desirable if Others will confirm KTeV result Also, Pion transition FF need to be more accurately measured.

18. 1) Radiative corrections KTeV used in their analysis the results from Bergstrom 83’. A.D.,Kuraev, Bystritsky, Secansky 08’ confirmed Numerics. 2) Mass corrections (tiny) A.D., M.Ivanov 08’ 3) New physics Kahn, Schmidt, Tait 07’ Low mass dark matter particles 4) Experiment wrong Waiting for new results from KLOE, NA48, BESII,… Possible explanations of the effect

19. Radiative Corrections (Bergstrom 83’ A.D.,Kuraev, Bystritsky, Secansky 08’) =-3.4%

21. Other P →l+l– decays

22. The conclusion is that the experimental situation calls for clarification. There are not many places where the Standard Model fails. Hints at such failures deserve particular attention. Possibilities: New Physics Still “dirty” Strong Interaction Or the measurements tend to cluster nearer the prior published averages than the ‘final’ value. (weather forecast style) Much more experimental information is required to disentangle the various possibilities. Perhaps new generation of high precision experiments (KLOE, NA48, BES II) might help to remove the dust. Conclusions

23. Summary of speed of light measurements It is interesting that the series of four measurements from1930-1940 displays a 17km/sec systematic shift from the true value Klein,Roodman Ann.Rev.Nucl.Part.Sci.55:141-163,2005

24. Conclusions The low-energy constant defining the dynamics of the process is expressed as the inverse moment of pion transition FF Data on pion transition form factor provide new bounds on decay branchings essentially improving the unitary ones. QCD constraint further the change of scales in transition from asymmetric to symmetric kinematics of pion FF We found 3  difference between theory and KTeV data If these results are confirmed, then the Standard Model is in conflict with observation in one of those reactions which we thought are best understood.

25. Theory vs KTeV experiment 3.3  effect!!!

26. LO is expressed via Adler function as Leading Order Hadronic Contribution Phenomenological approach    h   From phenomenology one gets 1) Data from low energy s<1Gev are dominant (CMD, KLOE, BaBar) 2) Until CVC puzzle is not solved t data are not used