Study of the process e e with FSR

Study of the process e e with FSR G. V. Fedotovich Budker Institute of Nuclear Physics Novosibirsk

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.

CMD-2 detector at VEPP-2 M 1 – vacuum chamber; 2 – drift chamber; 3 – Z-chamber; 4 – main solenoid; 5 – compensating solenoid; 6 – BGO calorimeter; 7 – Cs. I calorimeter; 8 – muon range system; 9 – yoke; 10 – quadrupoles ( ) 0. 002 rad, ( ) 0. 001 rad,

Luminosity measurement Bhabha scattering events at large angles are preferable. Many reasons are. L= Nee e e ( ) How does get number of Nee ee , Select collinear events in tracking system Separate e e events by energy deposition in Cs. I 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%

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%.

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

Cross section e e with FSR Some parameters used for select collinear events

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 calorimeter. Reject 0 events

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 Me. V is preferable.

Cross section e e with FSR Selection criteria for collinear events : 1. | | < 0. 25 rad, where = 1 + 2 - , (Eph ~ 200 Me. V) 2. | | < 0. 15 rad, where = | 1 - 2| - 3. 1. 1 < aver < - 1. 1, where aver = ( 1 - 2 + )/2 4. p > 90 Me. V/c 5. Hit numbers on each track > 6 (good quality track) 6. One photon detected in Cs. I 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 Me. V²/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 Cs. I calorimeter.

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.

Cross section e e with FSR event separation procedure - simulation Mass square invariant for electrons, muons and pions pairs. Condition M² > 10 000 additional rejects electron and muon events by a factor of 1. 5. About 1% pion events are lost.

Cross section e e with FSR event separation procedure - simulation Two dimensional plot on W - M² variables. Density population is clear seen.

Cross section e e with FSR Two dimensional distribution for CMD-2 experimental events

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.

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.

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.

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 Me. V 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. 5. The main conclusion is: For photon energy up to pion’s mass 6. we can tread the pion like a pseudoscalar pointlike particle.