Calibration software for the HADES electromagnetic calorimeter (EMC) Dimitar Mihaylov Excellence Cluster ‘Universe’, TU Munich HADES collaboration meeting XXV GSI, November 2012

Overview  The proposed electromagnetic calorimeter (EMC)  Data analysis  Motivation for a calibration procedure  Calibration procedure – Mathematical model  Calibration procedure – Realization  Summary  Ongoing improvements and outlook 2

Overview of EMC Parameters and benefits: Identification of light neutral pseudoscalar mesons (π 0 and η). Good e/π-separation at high momenta. Six sectors, each containing 163 lead-glass blocks. High refractive index of the lead-glass blocks (n = 1.708). Radiation length (X 0 ) of 2.51 cm. Almost full azimuthal coverage. The polar angle is covered between 12 ˚ and 45 ˚. The energy resolution is Czyzycki et al., arXiv: v2 3

Data analysis Simulation Reconstruction Output data (reconstr. γ) Invariant mass spectrum (IMS) Input data (initial γ) Experiment 4 Unaccounted energy losses. Undetected photons. Reconstruction of a non-existing photon (false signals). Large combinatorial background in the IMS (polynomial part of the fit).

Overview of the calibration procedure Fitting the IMS Calibration of single γ Final IMS ?? The general form of the calibration procedure is: where M is a calibration matrix. 5 A calibration procedure capable of compensating for those inaccuracies is needed. The calibration procedure will be performed on individual photons.

Is only energy calibration enough? The error in the energy is significantly larger compared to the error in the polar and azimuthal angles. Distribution of E S /E Distribution of θ S / θ Distribution of ϕ S /ϕ 6 Only spherical coordinates will be used. Comparison between the initially simulated and reconstructed values of the components of the photon momentum.

Choice of calibration function The general form of the calibration function is: The exact form of the expressions F i can be determined by reconstructing simulated data and analyzing the resulting deviations. D.J. Tanner, MSc thesis, University of Manchester, Oct 1998 The general form of the calibration procedure is: 7

Mathematical model Definition of some variables for photon pairs The calibration is performed by minimizing the function 8

Energy dependence The energy dependence of the calibration function can be well described with function of the type: 9

Result of the calibration procedure The results below are obtained with the following calibration functions: 10

Accuracy Example of the calibration functions f1, f2 and f3 as a function of the energy. Error in the energy of single photons before and after calibration. 11

Accuracy Distribution of the error in the energy before and after calibration. Position of the η peak after calibration. 12

Implementation in C++ The described calibration procedure has been implemented in a standalone C++ program called IMS-expert. Only standard C++ and ROOT libraries have been used. IMS-expert allows the user to perform the calibration with different types of functions. After a calibration has been performed, the calibration parameters are saved and can be used for further calibrations of different data. 13

Summary The presented calibration procedure is able to accurately correct the IMS for invariant masses in the range of the mass of π 0 (135 MeV/c 2 ) and of η (548 MeV/c 2 ). The systematic shift of the IMS is compensated by the calibration procedure but the statistical error, which is mostly related to the energy resolution, remains approximately the same. The error in the energy of individual photons decreases, but it still remains significant. The energy dependence of the calibration function has the biggest influence on the final result. The calibration procedure is implemented in a standalone program called IMS-expert and can be used for any EMC. 14

Ongoing improvements 15 Look-up table approach Analytical angle calibration

Backup slide If not all R i =0, then: For small δR i 17