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R are decay p 0 → e + e - and its implication to muon (g-2) μ

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

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R are decay p 0 → e + e - and its implication to muon (g-2) μ

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  1. Rare decay p0 → e+e- and its implication to muon (g-2)μ A.E. Dorokhov (JINR, Dubna) Introduction Model Independent Approach to p0→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: • 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)m 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 FromBNL E821 experiment (1999-2006) Standard Model predicts the result which is 3.4s below the experiment a3 a2 X   p   e h h     m

  4. Rare Pion Decayp0→e+e--from KTeV PRD (2007) One of the simplest process for THEORY From KTeV E799-II EXPERIMENT at Fermilab experiment (1997-2007) 99-00’ set, The result is based on observation of 794 candidate p0 e+e- events using KL 3p0 as a source of tagged p0s. The older data used 275 events with the result: 97’ set

  5. Classical theory of p0→e+e– decay Drell (59’), Berman,Geffen (60’), Quigg,Jackson (68’) Fp Bergstrom,et.al. (82’) dispersion approach Savage, Luke, Wise (92’) cPT The Imaginary part is Model Independent

  6. one has theunitary limit From condition Progress in Experiment >7s from UL KTeV 99-00 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 q20 In general it is determined in Model Dependent way

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

  9. I. The Decay Amplitude in Soft limit q20 A.D., M.A.Ivanov PRD 07’ The unknown constant is expressed as inverse moment of Pion Transition FF!!! The accuracy is of order O(me/mr)2. Thus the amplitude is fully reconstructed! Still no intrigue

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

  11. III. Fp(t,t) general arguments Let then 1. From one has one has 2. From OPE QCD F(t,0)  F(t,t) reduces to rescaling It follows 3.3s below data!! It would required change of s0 scale by factor more then 10! Now it’s intriguing!

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

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

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

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

  16. Instanton Model and Pion Transition FF

  17. 3s diff CLEO +QCD CLEO 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. Possible explanations of the effect 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,…

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

  20. Other P →l+l– decays

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

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

  23. 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 3s 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.

  24. Theory vs KTeV experiment 3.3s effect!!!

  25. a2 Leading Order Hadronic Contribution  LO is expressed via Adler function as 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

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