Status of Compton Analysis

1. Status of Compton Analysis Yelena Prok PrimEx Collaboration meeting December 17, 2006

2. Outline • Changes in basic analysis • Absolute Cross Section Results • Yield Stability in time • Differential Cross Section Results • Radiative Corrections • Summary / What remains to be done

3. Basic Analysis • Starting with raw (not skim) files • Applying cuts used to create skim files • (e1+e2)>3.5 GeV (for 4.9<e0<5.5 GeV) • |px1+px2|<0.025 GeV • |py1+py2|<0.025 GeV • Choose first recorded bit 2 per event to give HyCal time • Look for photons within 10 ns window of HyCal • Choose the one “closest” in time to Hycal • Form all possible combinations of clusters in events with at least 2 clusters, with emin=0.5 GeV

4. Some Basic Distributions Multiplicity of TAGM photons Multiplicity of bit 2 Multiplicity of clusters Cluster energies, no cuts Cut on 0.5 GeV

5. Geometric Cuts • Central opening of Hycal and the adjacent layer of modules are cut out by eliminating events with their coordinates within the square of |x0|<2*2.077 cm and |y0|<2*2.075 cm • Optional cut on the vertical strip (|x0|<2*2.077 cm)

6. Pair Contamination VETO Cut Pairs of e+e- are difficult to distinguish kinematically from e pairs Eliminating cluster pairs where both clusters are charged cleans up distributions but efficiency of this cut is unknown. Solution in the present analysis is to cut out contaminated region

7. Event Selection (Be) Reconstruct the vertex of Compton reaction Z=(x2+y2)0.5[/(E/e-1)]0.5 Apply kinematic constraints: energy and momentum conservation Reconstruct Z again Z (cm) 2<100 removes most of the background PS exit window Z (cm) Z (cm)

8. Calculation of Efficiency • Efficiency () is defined as the fraction of Compton events generated over 4 reconstructed by HyCal using standard PrimEx software • To obtain , use gkprim package and ‘prim_ana’-type reconstruction code • This efficiency includes geometric acceptance, radiative losses in the target, as well as the detection and reconstruction inefficiency. (please see the note for more details)

9. Total Efficiency Carbon target, 7 groups of runs Beryllium target Efficiency (by tcounter) is evaluated separately for every group of runs with similar conditions as the HyCal gains, beam alignment parameters and target material affect the result.

10. Counting Events 9Be, MC 12C, MC 12C, data 9Be, data Reconstructed vertex z is fitted with a double gaussian (target signal), single gaussian (He bag window signal) + second order polynomial ( combinatorial background)

11. Absolute Cross Section,1 Total Cross Section (per electron) • T=N/(L*F*A*) • N=nevents • L=luminosity=*t*NA/ • t=target thickness • =target density • NA=Avogadro’s Number • =atomic mass • =efficiency (from MC) • A=atomic number • F=photon flux • Error bars are statistical only • Radiative corrections are not applied 9Be 12C Klein-Nishina (4) NIST (KN+radiative corr.+double Compton)

12. Absolute Cross Section,2

13. Normalized Yield • For every run of sufficient statistics we calculate the normalized yield defined as : R=N/F/L/tc=1tc=11[tckn*tc*ftc] ftc=Ftotal/Ftc tc – eff. by tc F – total flux Ftc – flux per TC L – luminosity N – experimental yield tckn – KN for tc 9Be All TC 12C All TC

14. Normalized Yield vs Run #

15. Differential Cross Section,1 • d/d or d/de • Can sum over the two distributions ! don’t need to distinguish between electrons and photons • Total cross section in a bin of  , i ,is (i)=sminmax[[d/d]2 sind+[d/de]2 sin ede]

16. Angular Efficiency Angular efficiency , tc() is calculated by finding the ratio of generated events in a given angular bin after cuts and the initially generated ones

17. Differential Cross Section,2 <>=0.7± <>=0.7± 12C • Compare theory with experiment • Theory: kn()=tc[ftc*tckn()] • Experiment:exp()=N()/L/F/A £tc[ftc/tc] 9Be

18. Differential Cross Section,3

19. Radiative Corrections • Virtual: possibility of emission and re-absorption of virtual photon by an electron during the scattering process • Double Compton scattering • Soft: secondary photon of energy k<<kmax, not accessible to the experiment • Hard: secondary photon of energy k>kmax, accessible to the experiment

20. ‘Virtual and Soft’ Correction, SV • Virtual corrections alone do not have a physical meaning because they contain an infrared divergence, which is a consequence of the fact that it is impossible to distinguish experimentally between virtual and real photons of very low energy. For this reason virtual corrections are considered simultaneously with the soft double compton process, which contains an infrared divergence as well. The divergencies cancel out in every order in , giving a physically meaningful cross section that corresponds to the probability for the Compton process to occur and no other free photons emitted. • Cross section reduces to the Born term times a factor: d = d0[1+SV] • SV – function of one variable (energy or angle of the scattered photon), makes a negative contribution

21. ‘Double Hard’ Correction, dh • Another class of corrections to consider is the double Compton scattering where both final photons are accessible to the experiment • Differential cross section for an incident photon of energy k striking an electron at rest to produce one photon with energy k1 emitted into an element of solid angle d1 in the direction 1, and a second photon with energy k2 to be emitted into an element of solid angle d2 in the direction 2,  , is a function of 4 independent variables (besides the initial beam energy): d(k; k1,1,2,)=f(k1,1,2,) Possible to integrate over d2 to obtain the total correction d = d0[1+SV+dh]

22. Radiative Corrections, cont • Numeric integrations carried out using code from M. Konchatnyi (see more details in the note) • To make the result relevant to a particular experiment need to consider: • Detector resolution,  E or/and  • Minimum detected energy,  E • How many particles are detected • Some reasonable values (approximation only)  E=50 MeV,  = 0.002 rad,  E = 500 MeV, lower limit of integration determined by the minimum registered angle (set =0.00476 rad (3.5 cm on HyCal), and maximum determined by the minimum registered energy on the calorimeter. This method also assumes that we can distinguish within our defined resolution between events with 2 particles in the final state from events with 3 particles in the final state

23. RC to diff. xs,  E

24. RC to diff. xs. ,

25. RC to diff. xs.,  E +

26. RC to integrated xs, 1 part.

27. RC to integrated xs., 2 part.

28. Summary • Analyzed » 90 % of carbon and all of beryllium data with the initial beam energy of 4.9-5.5 GeV • We observe agreement with KN prediction in both total and differential cross sections at the level of » 2 %. Systematic error in the present result is estimated to be about 3 %. • We do not observe any systematic shifts over the entire run period: no major changes in the tagging ratios? • Work in progress • RC generator (hope to complete by next month) • Analysis of tcounters 30-42: would be good to have more accurate tagging ratios, currently they are all 0.95 • Systematic error evaluation