1. BESIII Cell-type EMC Photon Position Measurement Zhe Wang Mar. 2004

2. Contents:  Introduction to Belle’s method  Introduction to BaBar’s methods  Other methods …  A MC prototype ‘Matrix’  Analysis and understanding  Conclusion

3. Introduction to Belle’s method  Corrected center of gravity  Formula  Position correction By a detailed calibrated complicated function. By a detailed calibrated complicated function. And few dependence on θ and energy is found. And few dependence on θ and energy is found.  For correction only a few dependence on energy and theta is found.

4. Introduction to BaBar’s methods  Center of gravity  Logarithmic weight method usually a≈4 usually a≈4 Some points will be dropped. Some points will be dropped.  A mixing of these two methods  Now we can only check its result from its original tests.

5. Others (E852)  A weighted mean:  Comparison done by E852 Optimization is done. But correction maybe not. Optimization is done. But correction maybe not.

6. Others (BaBar’s method comes from here.) NIM A311 (1992) 130

7. Others (GAMS) one-dimension  Shower profile  Methods: 1. corrected center of gravity 1. corrected center of gravity 2. 2. The ith cell = center cell The ith cell = center cell 3. 3.

8. Others (GAMS) two-dimension  Shower profile  Method

9. Others (GAMS-200)  Direct Access  Method: Four crystals are concerned: Four crystals are concerned: the Max. the Max. biggest horizontal neighbor biggest horizontal neighbor biggest vertical neighbor biggest vertical neighbor the fourth to form a box the fourth to form a box

10. A MC prototype ‘Matrix’

11.  A 7×7 CsI crystal matrix in air  Each cell: 5cm ×5cm ×28cm  Gun: 100Mev—1.2GeV photon at (x,y,-1)m (x,y  [0,2.5] flat distribution) at (x,y,-1)m (x,y  [0,2.5] flat distribution) along direction of z axis along direction of z axis

12. Analysis and understanding  Shower lateral profile: and  Shower lateral profile: MACRO and micro Ratios of two counters: i: coordinate index for column or row 1. Clear target (relationship between signal ratios and position) 2. And easy realization. Density function: 1. Care more details. (cell structure, wrapping) 2. Analogous to heat dispersion in a plane. 3. Integration and fit need more CPU time.

13. Analysis and understanding Three kinds of methods: Weighted mean Guess a usable weight Fit Fitting based on 2- dimension distribution Experiment calibrated formula Directly find the relationship between the ratio of two signals and x from experiment

14. Analysis and understanding (MC)

17. Linear weight and logarithmic weight

18. Conclusion  After some rough comparison and study, three easy methods will be realized first. They are: They are:  Linear weighted mean  Logarithmic weighted mean  Experiment calibrated function