1. ° status report analysis details: overview; “where we are”; plans: before finalizing result..
I.Larin 02/13/2009

2. Data sample selection
Carbon data have been rerun on new Linux OS (ifarms) with updated flux counting
(all flux corrections are incorporated)
Some of “end run files” look suspicious and were excluded with negligible statistics losses
Total flux accounted for carbon target for this analysis 1.396×1012
Lead target rerun is in progress

3. ° yield VS flux ratio stability
“tail”

4. Data sample for Carbon
List of runs used:
some “end run files” were excluded

5. Event selection M > 80 MeV E > 0.5GeV
|tdif| < 4.5ns (after additional alignment)
“best-in-time” beam candidate only
PWO-only region (except shielded central square)

6. Event reconstruction Variables to be analyzed after event selection:
R – elasticity (all p0s in analysis supposed to be elastic with known beam energy (properly tagged). Deviation of parameter R from 1 comes from energy resolution or misidentified beam
M – invariant mass of two clusters (any deviations from (6)MeV are from Hycal resolution
q – production angle. This variable allows to separate different p0 production mechanisms and extract Primakoff part of cross-section M R q

7. ° yield extraction
First split events on variable q (production angle)
Then fit Mc (invariant mass) distributions for each q bin
q is a function of reconstructed gammas coordinates and energies q = q(x1,y1,x2,y2,e1,e2) :
e1, e2 – could be corrected using mass and elasticity constraint:
MC distributions before and after constraint e1 e2

8. Reconstruction efficiency convoluted with resolution
θ-reconstructed distribution obtained from MC for each E-channel energy and for each θ-actual bin.
This insures correct calculation with non-gaussian resolution shape.
actual   measured transition
matrix normalized to resolution

9. Correction to efficiency for background: first approximation
Corrections to reconstructed number of °s for MC,
(i.e. efficiency correction bin by bin)
MC data
Bg simulated according to polynomial fit
of the data for the given  bin

10. Further correction to efficiency for background
More close agreement between MC distributions and the data could be useful:
Use of the same ° shape parameters in MC as in the data fit
Use of more close to the data background shape in MC:
Use of empty target data (increase stat. by picking up adjacent theta bin – factor of 3 for Carbon)
Background simulation for empty target and non-elastic °s

11. Applying theory functions
Theory function  use of transition matrix bin by bin  function to fit data

12. List of correction factors applied to MC efficiency
Br ratio
Hycal resp. function
Carbon data:
Accidentals correction (|tdif|<4.5ns )
Best-in-time beam selection
Target impurity
Lead data
Best-in-time beam selection
Target absorption (VS carbon)

13. Invariant mass fit: free shape of ° peak
Inv. mass distribution for “first”  bin (0 – 0.02deg)
Elasticity and mass constraint
applied for 
No constraint for 

14. dN/d yield extraction: effect of using different E energies for 
0.02 binning -> 7.65eV
0.02 binning -> 7.86eV
Elasticity and mass constraint
applied for 
No constraint for 

15. Fit with the fixed shape of signal
Inv. mass distribution for ALL  bins (0 – 2.50deg)

16. Invariant mass fit: fixed shape of ° peak
Inv. mass distribution for “first”  bin (0 – 0.02deg)
Peak parameters fixed for each
0.5deg. bins individually
No constraint for 
Elasticity and mass constraint
applied for 

17. dN/d yield extraction: effect of using different E energies for 
0.02 binning -> 7.63eV
0.02 binning -> 7.68eV
Elasticity and mass constraint
applied for 
No constraint for 

18. Invariant mass fit: fixed shape of ° peak
Inv. mass distribution for “first”  bin (0 – 0.02deg)
Peak parameters the same for all
 bins
Elasticity and mass constraint
applied for 
No constraint for 

19. dN/d yield extraction: effect of using different E energies for 
0.02 binning -> 7.83eV
0.02 binning -> 7.86eV
Elasticity and mass constraint
applied for 
No constraint for 

20. dN/d yield extraction: effect of different binning
0.02 binning -> 7.86eV
0.05 binning -> 7.91eV
Elasticity and mass constraint
applied for 
Elasticity and mass constraint
applied for 

21. Invariant mass fit: possible ways to cross check
Check of ° inv. mass shape with increased statistics
(include more stat. from less “reliable” runs)
Out-of-target (“empty target”) background simulation (understanding the origin)
Apply this background to MC (add adjacent bins for carbon to increase “empty” statistics)
Add “empty” statistics to lead to double effect of background presence
Unbinned M fit
Try “hybrid mass” cut
Check with unconstrained analysis

22. dN/d fit: applying to Dustin’s cross section
Comparing extracted yield fit with yield renormalized to
Dustin’s cross section
(no constraint on  applied)
Renormalized fit: 0.9% higher 

23. Error budget [%] Target properties 0.07 Photon beam flux 0.97
p Branching Ratio
0.03
Beam parameters uncertainty
0.34
Trigger efficiency
0.1
Hycal response function
0.45
Production angle resolution
0.25
Setup acceptance
0.51
Event selection
0.33
Yield extraction
0.9 ? 1.5
Accidentals correction
w and r background subtraction
0.24
Theoretical uncertainties
Total
0.15
1.6 ? 2.0

24. Conclusion
With increasing of precision, number of details needed be taken into account grows geometrically
Stat. VS Syst. error: available statistics applies certain limitation for precision with what we can know some of systematical error items

25. Things to be done to finalize result (a short plan)
More detailed study of M fit systematics
Background simulation
Fit systematics study with empty target data
Update Lead analysis
Use of Lead Glass part of Hycal
Look at unconstrained yield extraction
Finalize theory issues
Review HyCal reconstruction code