Study of the process e  e        with FSR

1. Study of the process ee   with FSR G.V.Fedotovich Budker Institute of Nuclear Physics Novosibirsk

2. Outline • Motivation why is it necessary to study this process? • Some ideas how to extract events with FSR. • Experimental run and data taking. • Kinematics selection criteria for the events . • Event separation procedure to extract events  with FSR. • Comparison of the simulation result with CMD-2 data. • Conclusion.

3. CMD-2 detector at VEPP-2M 1 – vacuum chamber; 2 – drift chamber; 3 – Z-chamber; 4 – main solenoid; 5 – compensating solenoid; 6 – BGO calorimeter; 7 – CsI calorimeter; 8 – muon range system; 9 – yoke; 10 – quadrupoles ()  0.002rad, ()  0.001 rad,   

4. Nee L= ee  ee() Bhabha scattering events at large angles are preferable. Many reasons are. Luminosity measurement How does get number of Nee ee Select collinear events in tracking system Separate ee events by energy deposition in CsI calorimeter  Crude separation – number of events in red box More precise separation – unbinned fit of energy distribution ,  About 30 million Bhabha events at large angles were detected Systematic error of separation techniques is about 0.2% - 0.4%

5. ee  ee cross section calculation 1. Vacuum polarization by leptons and hadrons is included. 2. Matrix element due to one photon emission at large angle is treated with O() corrections exactly. 3. Photon “jets” emission inside narrow cones along initial or final particles ( < 0) is described by SF function –D(z). 4. All enhanced terms proportional to [(ln(s/m²)]n comes from collinear regions are included in SF. 5. Interference due to soft photons radiation by initial and final particles is taken into account. 6. Non-leading contribution of the first order of  (so called K-factor) is included. 7. Theoretical accuracy is estimated to be about of  0.2%.

6. ee  ee cross section calculation 2 + + 2 + + 2 + - “compensators” “Compensator” is required to remove from D(z) the part caused by emission of one photon at large angles

7. Cross section ee   with FSR Some parameters used for select collinear events

8. Cross section ee   with FSR  events in CMD-2 Two collinear tracks in DC One cluster in calorimeter (not associated with tracks) No signal in outer muon range system No signal in BGO calorime- ter. Reject 0 events

9. Cross section ee   with FSR Cross section ratio [(ISR + FSR)/ ISR] vs cms energy. Digit upper every curve – threshold of the photon energy to detect. Energy interval 720 – 780 MeV is preferable.

10. Cross section ee   with FSR Selection criteria for collinear events : 1. || < 0.25 rad, where  = 1 + 2 - , (Eph ~ 200 MeV) 2. || < 0.15 rad, where  = |1 - 2| -  3. 1.1 < aver <  - 1.1, where aver = (1 - 2 + )/2 4. p > 90 MeV/c 5. Hit numbers on each track > 6 (good quality track) 6. One photon detected in CsI calorimeter 7. |Zvert| < 6 cm – vertex distance along beam axis (z-coordinate) 8. vert < 1 cm – vertex distance to beam axis in r- plane 9. Missing mass square < 7000 MeV²/c² 10. Angle between photon direction and missing momentum < 1 rad 11. Angle between any tracks and photon direction > 0.2 rad. 1-5 conditions select good quality collinear events . 7-8 conditions select events originated from interaction point. 9-10 conditions suppress multiphoton events. Last condition is required to separate a photon cluster in CsI calorimeter.

11. Cross section ee   with FSR  event separation procedure - simulation Energy deposition (measured in calorimeter) divided on particle momentum (measured in DC). W later 0.4 is preferable. Nevertheless about 1% ee events are under condition W < 0.4.

12. Cross section ee   with FSR  event separation procedure - simulation Mass square invariant for electrons, muons and pions pairs. Condition M² > 10 000 additionalrejects electron and muon events by a factor of 1.5. About 1% pion events are lost.

13. Cross section ee   with FSR  event separation procedure - simulation Two dimensional plot on W - M² variables. Density population is clear seen.

14. Cross section ee   with FSR Two dimensional distribution for CMD-2 experimental events

15. Cross section ee   with FSR Histogram – simulation, points with bar – experiment Normalization – the same number of events in both histograms  events distribution as a function of photon energy emitted by pions. Vertical dotted line separates the field on three zone. Inscription inside zone points the relative abundance of events with FSR.

16. Cross section ee   with FSR Experimental events number in each histogram bin normalized on simulation events number. Fit – table line approximation. Average deviation is (-2.1 ±2.3)%. No hints pointing beyond scalar QED for pions.

17. Cross section ee   with FSR The same plot, but fit is done only for the spectra end (more interesting region) Average deviation is (24 ±18)%. As a result we can conclude: Approach with scalar QED for pions is good enough. Unfortunately a poor data in this energy region does not allowed to check this assumption with higher accuracy.

18. Conclusions • The process ee  with FSR is a powerful and a unique tool to answer on the question – can we tread a pion like a point object. • 1. Analysis is based on the integrated luminosity 1.2 pb-1 collected at 8 energy points (left slope of the  meson). • 2. About 3000  events with photon energy > 50 MeV were selected for analysis. • 3. Simulation of the process ee  with FSR is done using MCGPJ generator. • 4. Comparison simulation results with CMD-2 data (preliminary) • were done. • The main conclusion is: For photon energy up to pion’s mass • we can tread the pion like a pseudoscalar pointlike particle.