Fabbietti, L.

Lapidus, K.

Mihaylov, D.

GSI Repository

A data-driven calibration procedurefor the HADES electromagnetic calorimeter∗D. Mihaylov†1, L. Fabbietti1, and K. Lapidus11Excellence Cluster “Universe”, TU Mu¨nchen, Boltzmannstr. 2, 85748 Garching, GermanyIn its present configuration the HADES detector systemis not able to detect photons. The proposed lead-glass elec-tromagnetic calorimeter (EMC) [1] will, besides improv-ing the electron-pion separation, enable the identificationof the neutral pseudoscalar mesons (π0, η) via their decayinto two photons and their Dalitz decay[1]. The exclusivereconstruction of π0 and η is achieved by analyzing the in-variant mass spectrum (IMS) of the detected photons. Theinterpretation of the signal from the EMC is a complex pro-cess, which involves multiple steps. An algorithm, capableof reconstructing the initial photons hitting the EMC, hasbeen developed [1]. Mostly due to energy losses inside theEMC this algorithm delivers systematical errors to the re-constructed momenta of the photons. A calibration proce-dure able to eliminate these systematical effects is, there-fore, required.The analysis of simulated data has shown that for pho-tons the inaccuracy in the energy reconstruction is muchlarger than the errors in the reconstruction of polar and az-imuthal angles [2]. Thus it is sufficient to calibrate onlythe energies of the single photons, in a first step this can beachieved by applying a correction to the energy using theequation:EC = E × f (E, θ, ϕ) , (1)where EC and E are the calibrated and reconstructed ener-gies, respectively, and f is a calibration function. A conve-nient general form of the function f is [2-3]:f(E, θ, ϕ) = exp(n∑i=0Ai lni E), (2)where Ai are calibration coefficients, which need to be de-termined. The summation limit n is usually set to 2 or 3[2]. The coefficients Ai are determined using the likeli-hood function L, which is defined as [3]:L =N∑j=1[lnMγγj − lnmπ0 ]2 . (3)Here the summation is over all photon pairs in the data sam-ple, Mγγj is the invariant mass of the j-th photon pair andmπ0 is the reference mass value, which is the mass of π0.If the summation is performed only over photon pairs withinvariant masses Mγγ in the range Mπ0 ± σMπ0 , then thelikelihood function L should converge towards zero. Thus∗Work supported by the BMBF grant 06MT9156† dimitar.mihaylov@mytum.dethe calibration coefficients Ai can be determined by mini-mizing L with respect to Ai. The minimization of L andcalculation of the coefficients Ai is performed numerically.A distinctive feature of this approach is that no prior knowl-edge of the calorimeter response is required: the calibrationis based solely on measured data. Figure 1 shows the per-formance of the calibration procedure on the IMS of a sim-ulated data sample.Figure 1: Two-photon invariant mass spectra showingπ0-peaks before and after calibration. The data are full-scale simulations of Ni+Ni collisions at 8 AGeV [2].From Fig. 1 follows that the developed calibration pro-cedure is accurate in the mass region of interest for theHADES experiment.The calibration procedure was implemented in a stan-dalone C++ program that uses only standard C++ andROOT libraries [2] and can be, therefore, used for a broadclass of electromagnetic calorimeters.References[1] W. Czyzycki et al., “Electromagnetic Calorimeter forHADES”, arXiv:1109.5550 [nucl-ex].[2] D. Mihaylov, “Calibration Software for the HADES Elec-tromagnetic Calorimeter”, 2012, http://www.e12.ph.tum.de/groups/kcluster/Documents/Publications/Dimitar_Thesis.pdf.[3] D. J. Tanner, “Energy calibration of the BaBar EMC usingthe π0 invariant mass method”, SLAC-R-850.PHN-HSD-EXP-02 GSI SCIENTIFIC REPORT 20128

A data-driven calibration procedure for the HADES electromagnetic calorimeter

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A data-driven calibration procedure for the HADES electromagnetic calorimeter

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