Energy Calibration for the Forward Detector at WASA-at-COSY

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Leo Berge
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1 Energy Calibration for the Forward Detector at WASA-at-COSY Kay Demmich Westfälische Wilhelms-Universität Münster, Institut für Kernphysik DPG Spring Meeting (HK 42.7) 5. März 23 K. Demmich (WWU) Calibration for the WASA Forward Detector 5. März 23 / 4

2 Experimental setup WASA-at-COSY One physics topic: Studies on meson production cross sections e.g. of p + d 3 He + η Pellet Strahl Pelletstrahl SEC Solenoid MDC EDDA FTH FWC FRI PAX Absorber FPC FVH COSY Strahl PSB FRH Zentraldetektor K. Demmich (WWU) Vorwärtsdetektor Calibration for the WASA Forward Detector 5. März 23 2 / 4

The Forward Range Hodoscope Scattering angle + energy losses four momentum A: digitalised ADC value E: energy loss Only projections on the beam axis are comparable: E z = E cos ϑ A z = A cos ϑ f NU,

3 The Forward Range Hodoscope Scattering angle + energy losses four momentum A: digitalised ADC value E: energy loss Only projections on the beam axis are comparable: E z = E cos ϑ A z = A cos ϑ f NU, f NL : 3rd order polynomials 8 parameters To be determined for each detector element, partly correlated Energy reconstruction ( E z rec = =f f Az NL f NU (ϑ) ) K. Demmich (WWU) Calibration for the WASA Forward Detector 5. März 23 3 / 4

4 Non uniformity angular dependence E rec z = f NL ( Az f NU (ϑ) ) MIPs have identical energy losses Pure angular effects Plot A cos(ϑ) vs. ϑ Fit f NU as 3rd order polynomial A z LS method mean method Gauss method ϑ MIP spectrum with differently fitted polynomials Layer 4 element 23 K. Demmich (WWU) Calibration for the WASA Forward Detector 5. März 23 4 / 4

5 Non uniformity fitting algorihms Least Square method (LS) Minimize χ 2 χ 2 = N δ 2 i = δi 2 i= ( ) yi f (x i ) 2 σ i dn/da z Mean and Gauss method Projections along A z axis Mean value or mean of Gaussian fit A z K. Demmich (WWU) Calibration for the WASA Forward Detector 5. März 23 5 / 4

6 Non uniformity fitting algorihms Least Square method (LS) Minimize χ 2 χ 2 = N δ 2 i = δi 2 i= ( ) yi f (x i ) 2 σ i Mean and Gauss method Projections along A z axis Mean value or mean of Gaussian fit Least Trimmed Square method (LTS) Iteratively minimisation of χ 2 = h (δ 2 ) i:n i= (δ 2 ) i:n : ordered residuals h < N predefined value,e.g., h/n = 6 % K. Demmich (WWU) Calibration for the WASA Forward Detector 5. März 23 6 / 4

7 Non uniformity angular dependence E rec z = f NL ( Az f NU (ϑ) ) MIPs have identical energy losses Pure angular effects Plot A cos(ϑ) vs. ϑ Fit f NU as 3rd order polynomial Best results with Least Trimmed Squares method (LTS) A z LS method mean method Gauss method LTS method ϑ MIP spectrum with differently fitted polynomials Layer 4 element 23 K. Demmich (WWU) Calibration for the WASA Forward Detector 5. März 23 7 / 4

8 Non uniformity results A 8 6 A /f NU (ϑ) Uncalibrated data A 2 5 A 2 /f NU (ϑ) After non uniformity calibration K. Demmich (WWU) Calibration for the WASA Forward Detector 5. März 23 8 / 4

9 Non linearity energy dependence K. Demmich (WWU) Calibration for the WASA Forward Detector 5. März 23 9 / 4

10 Non linearity energy dependence K. Demmich (WWU) Calibration for the WASA Forward Detector 5. März 23 / 4

11 Bounded sum of the square of the errors Usual least square approach: N χ 2 = δi 2 i= ( ) δi 2 yi f (x i ) 2 = σ i Bounded least squares: N Q 2 = qi 2 i= ( ) qi 2 = min δi 2 ; δmax 2 E / GeV E 2 / GeV K. Demmich (WWU) Calibration for the WASA Forward Detector 5. März 23 / 4

12 Check non uniformity parameters E / GeV.3 3 < ϑ < ϑ 7 7 < ϑ < ϑ.2. < ϑ 3 3 < ϑ < ϑ < ϑ < ϑ E 2 / GeV K. Demmich (WWU) Calibration for the WASA Forward Detector 5. März 23 2 / 4

13 Corrected non uniformity parameters E / GeV.3 3 < ϑ < ϑ 7 7 < ϑ < ϑ.2. < ϑ 3 3 < ϑ < ϑ < ϑ < ϑ E 2 / GeV K. Demmich (WWU) Calibration for the WASA Forward Detector 5. März 23 3 / 4

14 Conclusion Software with graphical user interface Powerful tool for FRH energy calibration Non uniformity calibration and fine calibration without user interactions Non linearity parameters can be found and controlled quickly by the use of the GUI and fit Complete detector calibration within a few days possible Significant calibration speed up Suitable for all possible reactions p + p p + p + X, p + d 3 He + X and d + d 4 He + X Suitable for other detector components K. Demmich (WWU) Calibration for the WASA Forward Detector 5. März 23 4 / 4

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