1. G.V.Fedotovich Budker Institute of Nuclear Physics Novosibirsk MC generators with radiative corrections used in direct e + e - scan experiments

2. Outline 1.MC generators for the processes e  e   e  e  (n  ) Comparison with BHWIDE and BABAYAGA codes 2.MC generators for the processes e  e       (n  ),     (n  ) Comparison with KKMC codes 3. MC generators for the processes e  e       (n  ), K  K  (n  ) Contribution to the cross section coming from FSR effects Comparison with Berends (one hard photon emission) 4.MC generator for the processes : , K L K S (n  ),  0  (n  ),  (n  ),  0 (n  ) without FS 5. “Dressed” and “bare” cross sections for different applications 6.Another approach to calculate a  had.LO 7. Conclusion

3. Luminosity measurement L= L= N ee  vis (e  e   e  e  ) Main sources of systematic errors in previous experiments were Quality of events separation N ee, N xx typical value 0.4 %- 5% Accuracy of beam energy measurement typical value 0.3% - 1% Events detection reconstruction efficiencies typical value 0.2% - 2% Systematic error of RC calculation typical value 0.3% - 1% Very soon accuracy of RC calculation with systematic error less than 0.1% will be required for future forthcoming experiments (for example CMD-3 experiments at VEPP-2000) Bhabha scattering events are preferable for normalize purpose to calculate cross sections with collinear events in FS L= L= N xx  vis (e  e   x  x  )   vis (e  e   x  x  ) = ------ N xx N ee  vis (e  e   e  e  )

4. Cross section construction: include all  corrections and enhanced contributions Vacuum polarization effects by leptons and hadrons should be inserted to each amplitude Enhanced contributions proportional to [(  /  Ln(s  m 2 e )] n ~[1/30] n, n=1,2,..coming from collinear regions are taking into account by means of SF formalism (E.Kuraev, V.Fadin) One photon radiation at large angle out of narrow cones (  >  0, E >  E ) – enough to provide systematic error about 0.1% (no enhanced contributions inside these regions) + 2 + 2 + +  + 2 How to improve the accuracy of cr. sect. calculation for the process e  e   e  e  Yyyyyyy yyyyyyy photon jets in collinear regions

5. Bhabha cross section e  e   e  e  as a function of inner parameters Cross section dependence vs inner parameter  . Cross section dependence vs inner parameter  0. In both cases the cross sections deviations are inside corridor ±0.1%

6. e  e   e  e  cross section vs energy Difference between cross sections calculated by MCGPJ code, BHWIDE and BabaYaga is inside corridor 0.1% Comparison with BHWIDE code, 0.5% (S.Jadach, W.Placzek, B.F.L.Ward) CMD-2 selection criteria for collinear events were applied:  < 0.25 rad,  <0.15 rad, 1.1 <  final <  -1.1 Comparison with BabaYaga code, 0.1% (new version)

7. e  e   e  e  cross section Relative cross sections difference for MCGPJ code and BHWIDE vs acollinearity polar angle. Relative cross sections difference for MCGPJ code and “Berends” vs acollinearity polar angle. CMD-2 cut

8. e  e   e  e  cross section Events number vs acollinearity polar angle  . Solid line – simulation (MCGPJ), histogram – CMD-2 data. All data upper 1040 MeV are collected on this plot. Events number vs acollinearity azimuthal angle  . Solid line – simulation (MCGPJ), histogram – CMD-2 data. All data upper 1040 MeV are collected on this plot. Comparison with experimental distributions

9. e  e   e  e  cross section Relative contribution of photon jets with respect to cross section with radiation of one hard photon, % Radiation two and more photons (enhanced contributions coming from collinear regions) contributes to cross section about 0.25% only !!!

10. Contribution of vacuum polarization to Bhabha cross section as a function of energy, % e  e   e  e  cross section  , 

11. e  e   e  e  cross section Two dimensional plot of simulated events – energy of one photon vs another. Left – MCGPJ code, right – “Berends”. About 0.5% events have total energy E 1 + E 2 < 600 MeV. Cross section strongly depends on the cut for transverse momentum p  

12. e  e   e  e  cross section Relative cross sections difference as a function of cut applied to transverse momentum of both particles. CMD-2 cut

13. e  e   e  e  cross section Crucial point is how to estimate theoretical accuracy of this approach. To quantify the systematic error independent comparison was performed with generator based on “Berends”, where first order  corrections are treated exactly. It was found that the relative cross sections difference is less than 0.2% for   about of 0.25 rad. Comparison with BGWIDE code (0.5%) and BABAYAGA (0.1%) demonstrates very good agreement between different distributions. Conclusion: radiation two and more photons in collinear regions contributes to cross section for amount 0.2% only. Since the accuracy of this contribution is known with error better than 100% therefore theoretical systematic accuracy of the cross section with RC certainly is better than 0.2% for “soft” selection criteria. In order to believe to 0.2% accuracy the different experimental proofs are needed !

14. Vacuum polarization effects by leptons and hadrons are inserted to each diagram. Only one hard photon radiation out of narrow cone. One hard photon for FSR + interference terms. Photon jets radiation along initial particles. + 2 +    2 + 2   BUT this cross section is very important to perform cross check of the theoretical accuracy of the cross sections with RC. For example double ratio of can serve as a powerful tool for it e  e       cross section calculation ( ten times smaller than Bhabha cross section) ~90% ~5% ~0.3% Cross section accuracy with RC  0.2 % is expected for MCGPJ. Second and so on…photons radiation inside narrow cones - enhanced contributions

15. e  e       cross section Relative contribution of FSR to cross section with ONLY one hard photon emission, %. CMD-2 selection criteria were used. BUT, as it was elucidated by Smith and Voloshin that all parametrically enhanced contributions proportional to  ² increase cross section close to threshold region only at the level 0.02% and these contributions fall down with energy. Main conclusion was done: It is enough to take into account only first order radiative corrections O (  ) to provide cross section systematic error with FSR better than 0.1%.

16.   0.17 % Difference with KKMC code with FSR, % Difference with KKMC code without FSR, %   0.06 % Vacuum polarization effects switch off in both generators MCGPJ code comparison with KKMC (0.1%) (S.Jadach, B.F.L.Ward, Z.Was)

17. e  e       cross section Number of selected muon pairs to electrons ones divided on the ratio of theoretical cross sections. Average deviation is: –1.7% ± 1.4% st ± 0.7% syst. For low energies CMD-2 momentum resolution is enough to separates e, ,  It is practically the first direct exami- nation of the theoretical accuracy of the cross section with RC at ~1% level CMD-2 data

18. e  e       (K + K - ) cross section calculation Vacuum polarization effects by leptons and hadrons are included in shape of resonance and removed from RC:“dressed” cross section Pions were treated as point like objects and scalar QED was applied to calculate RC. Clear evidences are needed to believe this approach + + + 2      22 Photon jets radiation along initial particles inside narrow cones “Dress” cross section

19. e  e       cross section Comparison with “Berends” code taking into account ONLY one hard photon radiation. Practically all previous experiments used it!!! Deviations around  -meson amount to ± 1% and for energies upper  -meson the difference rapidly increase Relative cross section difference vs acollinearity polar angle  . Beam energy 450 MeV

20. e  e       cross section (low energies) CMD-2 spatial resolution is enough to separate e/  /  events for low energy Momentum and angle resolutions, decays on flight and interaction with detector matter were smeared with simulated events kinematics parameters Enveloping curve describes three peaks and long “tails” very well Bad  ² if we used MC generator with radiation of one photon E = 185 MeV

21. Two collinear tracks in DC One cluster in calorimeter (not associated with tracks) No signal in outer muon range system No signal in endcap BGO calorim. - reject      0 events Cross section ratio  ISR + FSR /  ISR vs energy Digit upper every curve – threshold of the photon energy to detect Energy interval 2*360  2*390 MeV is preferable The process e  e        with FSR is a unique tool to answer on question – can we tread a pion like a point object

22. Selection      events with FSR Two dimensional plot for x  x   events Variables on axis: vertical - W = p/E, horizontal - M² Density population      events is clear seen inside region W < 0.4 and 1000 < M² < 40000 MeV². Analysis is based on the integrated luminosity  1.2 pb -1 collected at 8 energy points (left slope of the  meson). experiment (CMD-2)simulation

23. Spectrum of      events with FSR as a function of the emitted photon energy About 3000      events with ph. en. > 50 MeV were selected for analysis Inscriptions inside zone point the relative part of      events with FSR The main conclusion is: For photons with energies up to pion’s mass we can tread the pion as a pointlike object and scalar QED can be applied Histogram – simulation (MCGPJ), bar points – CMD-2 data average div. ~ (2.1 ± 2.3)%

24. Processes with neutral particles in FS (only initial state radiation are considered: e  e    (n  ), K L K S (n  ),  0  (n  ),  (n  ),  ’  (n  ),  0 (n  ) Cross section accuracy with RC is estimated to be at ~0.2% Very important channel e  e    : Large cross section (2.5 times) – independent way to measure luminosity, clean QED process and no Feynman’s graphs with vacuum polarization effects. aver. diff. ~0.25% Relative cr. sect. difference (    jet  /  jet vs energy Relative cr. sect. difference (    jet  /  jet vs angle  , rad CMD-2 cut

25. What is R(s) required? Definition of R(s) depends on the application  Bare (s)=  Dress (s)|1-P(s)|²[1+(  /  )   (s)]f CI (s) In order to keep systematic error of the “bare” cross section at the same level as “dress” has VP effects should be calculated with syst. accuracy better than 0.1% AND cross sections with radiation of one photon in final state should be obtained. Today it is done for the processes: e+e-  e  e  ,     , K + K - ,  +  - ,     . Indeed at the current systematic accuracy it is enough to do only for two channels: e+e-       and K + K -  - give dominant contributions to a µ. Hadron spectroscopy (used to get meson’s mass, width, …): vacuum polariz. effects is the part of the “Dress” cross-section. Final state radiation (FSR) and Coulomb interaction (CI) are not and must be removed (they are in RC). “Bare” cross-section used in R: vice versa – FSR and CI are the part of the cross-section, VP is not and must be removed from all hadr. cross sections:

26. Factors determining systematic accuracy RC calculation Unaccounted corrections more higher orders: 1. Weak interactions contribute to cross sections later than 0.1% at energies 2E < 3 GeV and we can omitted in our approach. 2. NLO corrections which proportional to  ²ln(s/m²) ~ 10 -4 fortunately small with respect to 0.1% level. 3. The uncertainty of about 0.1% is related to experimental systematic errors for hadronic cross sections. For example, 1% error changes “bare” cross sections at scale 0.03%. 4.Fourth source uncertainty due to theoretical models which are used to describe hadronic cross sections energy dependence. 5. In paper Smith and Voloshin was done very important for us conclusion: For FSR (except electrons) the combine effect of all parametrically enhanced O(  ²) corrections is limited by 210 -4 and it is beyond the accuracy 0.1%  0.2%. Considering the uncertainty sours as independent  total systematic error of the cross sections with RC better than 0.2% MUST BE!!!

27. Another way of a µ calculation Special experiment - it is necessary to measure cross sections of the THREE QED PROCESSES ONLY: e + e -  , for luminosity measurement (no VP effects, accuracy < 0.1%) BUT special calorimeter is required to detects photons (CMD-3) e + e -   +  - direct cross section measurement to extract product |1 +  (s)|² (accuracy < 0.1%) VP effects must be removed from RC Effects of FSR and CI must be included into RC e + e -  e + e - to extract the value  (-q²) in spacelike region (accuracy <0.1%) SCAN EXPERIMENT: Luminosity ~ 10 32 cm -2 s -1, ~ 100 energy points with number of muon events 10 8 /per year (statistical accuracy about 0.1% in every point) Cross section has practically isotropic distribution vs polar angle

28. Contribution to a µ Time-like regionSpace-like region Red lines – resonance contributionsx < 0.7 analytical approximation Cross section of all three QED processes can be measured in one direct scan experiment. Accuracy of RC calculation will not contribute to final systematic error  (-q²) We hope to achieve experimental systematic error 0.5% about with CMD-3 at VEPP-2000. Of course, if stars on the sky will in favour for us.

29. Conclusions MC generators to simulate different processes were done : e  e   e  e , BHWIDE (0.5%), MCGPJ (0.2%?!) and BabaYaga (0.1%) e  e      ,    -, KKMC (0.1%), MCGPJ (0.2%?!) e  e       and K + K -, MCGPJ (0.2%?!) that is all unfortunately We can state now that pions can tread as point like object (at 1% accuracy) and sQED applied to describe FSR e  e   , K l K s,  0 , ,  ’ ,  0, MCGPJ (0.2%?!) that is all unfortunately. Neutral particles in final state – ISR is taking into account only Good agreement between CMD-2 data and distributions for  ,   produced by MCGPJ code is observed. Total statistic for Bhabha scattering events is collected ( 2E > 1040 MeV) Muon cross section – deviation from QED prediction is about –1.7% ± 1.4% ± 0.7%.

30. Conclusions Common description of three “peaks” for e/  /  events at low energies is impossible without photon jets (bad  ²) “Dressed” cross sections for dynamic studies, “bare” cross sections for dispersion relations New experiments are needed extremely to cross check the theoretical accuracy of the cross sections with RC. Forthcoming CMD-3 results can solve some problems Very interesting to see KLOE result for double ratio (N  /Nee)/(   /  ee ) around  -meson energy region (direct scan). KLOE has statistic more than 100 times exceeds CMD-2!!! Very interesting to see KLOE result for the same double ratio in a broad energy region to find out the syst. accuracy of the ISR approach Necessary study and develope another approach to estimate hadronic contribution to a µ using data in spacelike region

31. Conclusions Rough theoretical estimation of the main systematic errors: 1. Weak interactions contribute less than 0.1% for 2E < 3 GeV 2. Next leading order RC proportional to  ²Ln(s/m²) ~ 10 -4 are fortunately small with respect to 0.1%. 3. Soft or virtual photon emission simultaneously with one hard photon emission and so on. If we assume that coefficient before these terms will be of order of ten nevertheless their contribution can not exceed 0.1%. 4. Fourth source of uncertainty is due to vacuum polarization effects and currently they are calculated with systematic error later than 0.1%. 5. Next source of uncertainty is mainly driven by collinear approximation approach – several terms proportional to  )  0 ² and (  0  ² were omitted. Indeed photons inside jet have angular distribution. Numerical estimations show that a contribution of these factors is about of 0.1%. 6. It is enough to take into account only first order radiative corrections O (  ) to provide cross section systematic error with FSR better than 0.1%. (B.Smith and M.Voloshin) Considering the uncertainties sources as independent the total systematic error of the cr. sect. with RC smaller than 0.2% we must expect!!!