The performance of the CMS electromagnetic calorimeter has been studied with the test beam data recorded with a fully equipped barrel super-module. An efficient method for signal amplitude reconstruction has been implemented and tested on these data. Results on energy resolution and electronics noise show excellent performance of the apparatus. Effects associated to shower containment in crystal arrays were investigated and a set of corrections has been formulated and used to provide results on energy resolution

Zabi, Alexandre

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Available on CMS information server CMS CR 2006/067CMS Conference ReportAugust 2006Test beam results on the performance of theCMS electromagnetic calorimeterAlexandre ZabiImperial College, London, UK.On behalf of the CMS ECAL groupAbstractThe performance of the CMS electromagnetic calorimeter has been studied with the test beam datarecorded with a fully equipped barrel supermodule. An efcient method for signal amplitude recon-struction has been implemented and tested on these data. Results on energy resolution and electronicsnoise show excellent performance of the apparatus. Effects attributed to shower containment in crystalarrays were investigated and a set of corrections has been formulated and used to provide results onenergy resolution.Presented at:XII International conference on calorimetry in high energy physics, June 5-9 2006, Chicago, USA.1 Introduction1.1 CMS electromagnetic calorimeterThe Compact Muon Solenoid (CMS) [1] detector is a general purpose detector to be installed at the 14 TeVproton-proton collider, LHC, under construction at CERN and due to start operation in 2007. The CMS elec-tromagnetic calorimeter (ECAL) [2] is a hermetic homogeneous calorimeter made of 61,200 scintillating leadtungstate (PbWO   ) crystals [3] mounted in the central barrel part, closed by 7,324 crystals in each of the two end-caps. The barrel consists of 36 supermodules, each covering half the barrel length and 20in azimuth, containing1700 crystals together with the associated front end electronics.1.2 Test beam experimental set-upTest beam data taken in the H4 beam line at CERN in October and November 2004 using electron beams witha range of momenta between 20 and 250 GeV/c, have been used to investigate the performance of the ECAL. Asupermodule fully equipped with the nal readout electronics [4] was installed on a movable table which allowedthe beam to be directed at any part of it. Electrons were incident at an angle of  3  to the direction of the crystalaxis in both transverse directions reproducing the average incident angle of particles emerging from the collisionregion in LHC running. Plastic scintillator counters were used to trigger the readout. The trigger denes an areaof 20  20 mm. This area is only slightly smaller than the transverse section of the crystals which have a frontsection of  22  22 mmand a rear section of  25  25 mm. The position of the incident electrons in thetransverse directions was determined by four planes of scintillating bre hodoscopes.1.3 Readout electronicsThe electrical signal from the photodetectors is shaped by a preamplier and amplied by a multi-gain amplier(MGPA) before digitization by ADCs at a frequency of 40 MHz [5]. It provides a dynamic range from about35 MeV to saturation at 1.7 TeV in the barrel. The data read out consists of a series of 10 consecutive digitizations,corresponding to a sequence of samplings of the signal at 40 MHz. The signal amplitude must be reconstructedusing these samplings.2 Reconstruction of the signal amplitude2.1 The weights methodThe method used to reconstruct the amplitude from the digitized samples is based on a digital ltering technique.The signal amplitude,, is computed from a linear combination of discrete time samples (see Equation 1).	 (1)whereare the weights, the time sample values in ADC counts and  is the number of samples used in theltering with the index,  , running over the time samples. The weightsare obtained by minimizing the varianceof [6]. When considering the simplest case (no noise correlations between time samples) the optimal weightsare given by the formula	ﬀﬀ , whereis the value of the function,ﬂﬁﬃ! , describing the timedevelopment of the signal pulse in time,ﬃ, at the timeﬃof sample  . A form of the function,ﬂﬁ"ﬃ! , that provides agood description of the electronics signal is a digital representation (prole histogram) directly built from the testbeam data (see Fig. 1). The determination of the optimum function to be used is addressed in Section 2.3.Various implementations of the weights method have been tested using test beam data and their ability to reducethe noise contribution is used to discriminate between them.2.2 Measurement of the electronics noiseIn the following, we compare the nal electronics noise obtained when implementing a 5-weights and a 3+5-weights method. The 5-weights method uses the sample on the peak, the one before and the 3 after while the 3+5-weights also uses the 3 pre-samples (before any signal appears). The rst implementation requires the pedestal to2Time (ADC clocks)0 1 2 3 4 5 6 7 8 9 10Amplitude (ADC)05001000150020002500MaxTAPFigure 1: Prole of the signal pulse from a crystal of the supermodule using an electron beam of 120 GeV. Thepeaking time #$&%(' , the pedestal ) and the amplitude of the signal * are shown.be determined independently and subtracted prior to reconstruction, while the second allows a subtraction of thepedestal on an event by event basis (the so-called pedestal subtracting weights). For completeness, a 3+1 weightspedestal-subtracting implementation has also been studied. The single weight is then applied to the sample on thepeak. This allows the demonstration of the impact of dynamic baseline subtraction in its simplest form. Table 1summarizes the ECAL noise measured by examining the variation of the reconstructed amplitude for data takenwith random triggers, when no signal is present.Table 1: Noise in ADC counts measured in a single channel and arrays of 3 + 3 and 5 + 5 channels for three differentimplementations of the amplitude reconstruction method, and for a single sampling. 1 ADC count , 37 MeV.Method Noise (ADC counts)1 + 1 3 + 3 5 + 5Single sampling 1.20 - 0.01 3.7 - 0.04 6.5 - 0.15-weights 1.11 - 0.02 3.8 - 0.1 6.7 - 0.13+1 Pedestal subtracting weights 1.13 - 0.03 3.4 - 0.1 5.7 - 0.13+5 Pedestal subtracting weights 1.07 - 0.02 3.2 - 0.1 5.4 - 0.1The results given in the table show that the lowest noise is achieved by the pedestal-subtracting weights. Thisimplies the presence of low frequency noise which is removed by the dynamic pedestal subtraction. Comparingthe noise seen in a single channel with that seen in sums of 3 + 3 and 5 + 5 channels shows a small contribution ofnoise correlations between channels. This is entirely removed by the use of the pedestal subtracting weights. Thisimplementation is used for reconstructing the signal amplitude. Using ve samples in the signal, rather than one,results in a slightly lower value of noise as compared to the 3+1 weights.2.3 Implementation of the reconstruction methodAs mentioned in Section 2.1, the determination of the weights requires knowledge of a signal representation .ﬂ/0!1 .The impact of the choice of this function on the energy resolution has been studied with test beam data. Twoparameters characterize .ﬂ/0!1 : the signal timing #2$&%!' and the parameter C which represents the width of the pulse.In the test beam the scintillation signals have a random phase with respect to the 25 ns ADC clock interval, whileduring LHC operation the ADC clock will be synchronous with the bunch crossing. The relevance of the choiceof .ﬂ/"0!1 has been investigated in both cases. To simulate synchronous running, test beam data have been analyzed3taking only events in a single 1 ns bin of phase. Figure 2 shows the energy resolution measured when the weightsused to reconstruct the amplitude are derived from signal representations with peaking times and widths whichdiffer from those of the actual signal. (ns)Max T∆−3 −2 −1 0 1 2 3Resolution (  /E%)0.350.40.450.50.550.60.650.70.75All phase binsOne phase binσC (arbitrary unit)−0.2 −0.1 −0 0.1 0.2Resolution (  /E%)0.30.40.50.60.70.80.91All phase binsOne phase binσFigure 2: Left: Energy resolution in a 3  3 matrix of crystals measured with a 120 GeV electron beam, as afunction of the timing difference ( 35476&8(9 ). Right: Energy resolution as a function of the contraction factor, C( ﬃ;: ﬃ&<=  ﬁ"ﬃ?> 4 6&8!9  ). The black square points correspond to the summing of all bins in phase as inthe asynchronous data taking (Test beam). The red dots correspond to the synchronous mode (CMS) which isreproduced by selecting a single 1 ns bin in phase.These results suggest that, in the case of synchronous running (such as in CMS operation), the same referencesignal representation can be used to derive a single set of weights to be used for the signal amplitude reconstructionof all channels. The uniformity of the readout electronics allows this important simplication. Reconstructingthe signal pulse amplitude in test beam is sensitive to the individual channel signal timing and shape due to theasynchronous nature of the data taking. When the weights are derived using the signal description specic to eachchannel, the resolution is as good as the one obtained in a single 1 ns bin.3 Shower containment variation with positionThe energy contained in 3  3 and 5  5 matrices of crystals depends on the particle incidence position on the centralcrystal. The variation of the energy containment with respect to this position was studied with electron test beamdata. A correction based on the balance of energy between crystals can be applied to recover a uniform energyresponse [7].3.1 Dependence of the measured energy with the positionFigure 3 displays the reconstructed energy summed in 3  3 and 5  5 arrays of crystals centered on three adjacentcrystals, as a function of the @ coordinate measured by the hodoscope. The maximum response has been normalizedto the beam energy (120 GeV) in each case. The peak to peak variation of the measured energy contained in amatrix decreases from 2.5% for a sum of 9 to 1.6% for a sum of 25 crystals. Similar distributions can be obtainedwhen plotting the energy as a function of A .3.2 Parametrization of the response with positionThe energy balance between crystals can be used to determine the position of incidence. As illustrated by Fig. 4(left), this method uses the ratio of the energy contained in the side rows (or columns) of crystals to the energycontained in the rest of the matrix (including the central row/column).Figure 4 (right) shows the energy variation parametrized as a function of position, measured by the variableBDCﬁ"EGFEIHJ , using test beam data. In order to better determine this parametrization, data have been recorded4Crystal 184Crystal 204Crystal 224η0.16 0.17 0.18 0.19 0.2 0.21Energy (GeV)106108110112114116118120122124η0.16 0.17 0.18 0.19 0.2 0.21Energy (GeV)106108110112114116118120122124 Crystal 184Crystal 204Crystal 224Energy (GeV)Figure 3: Left: Energy in 3  3 matrices centered on crystals 184 (dots), 204 (squares), 224 (triangles) as a functionof @ ; Right: Same for 5  5 matrices. The double arrow shows the extent of a single crystal.with the beam directed on the edge of the centre crystal. These functions are used to correct the energy on an eventby event basis. An asymmetry can be observed between the distributions in the regions close to the two oppositeedges which is due to the 3off-pointing of the crystals. A single correction function was used for all energies andfor all regions in the supermodule.W2 W1 W2 W1E2 E1 E2 E1ηa) b)Φln(E2/E1)-3 -2 -1 0 1 2 3Normalized energy0.960.9650.970.9750.980.9850.990.99511.0051.01L RC1 C2ηC1 C2LRFigure 4: Left: Denition of clustered crystal energy into E1 and E2 in the case where W1 K W2 (a) and W1 L W2(b) (W1 and W2 are the energies of the crystals on either side of the centre crystal). Right: Normalized sum ofenergy measured in 9 crystals versus BDCﬁ"EGFEIHJ in the @ views for crystal 204 ( @ NMPOQHSRUT ). The crystal 204 hasalways the maximum energy. The lines are third order polynomial functions tted to the measured distributions(independently for positive and negative values of BQC ﬁVEWFEXHJ because of the asymmetry mentioned before).4 Energy resolutionResults on energy resolution are given for both electrons in a small region of incidence and for electrons withuniform incidence over the calorimeter surface. The electron-induced shower energy is reconstructed in matricesof 33 crystals centred on the crystal containing the maximum energy. Corrections for variations in the showercontainment are applied in the case of uniform incidence.4.1 Intrinsic energy resolutionAs explained in Section 3, the electron shower energy contained in a crystal matrix depends on the shower position.Investigating the energy resolution in the central incidence region, dened as a limited 44 mmregion aroundthe point of maximum containment, gives a measure of the intrinsic resolution of the calorimeter. In this region,the containment is almost constant.In the following, results are given for runs with 30 000 events taken in crystal 704, located at pseudorapidity@YMPO ZUF. The energy spectra for 120 GeV electrons reconstructed in a 33 matrix centred on crystal 704 isshown in Fig. 5 (left). The energy scale in these plots is obtained by normalizing the mean signal amplitude to thebeam momentum. The crystals were intercalibrated with constants determined directly from the test beam data.5The energy dependence of the resolution is studied for data taken at a series of beam energies: 20, 30, 50, 80, 120,180 and 250 GeV. The energy dependence is tted by the following functional form :[\]_^a`b]_c<d`]c<fe(2)where  is the stochastic term,  the noise andethe constant term (E is in GeV). The t is performed with thenoise term xed at its measured value. The energy resolution values for a 3  3 matrix centred on crystal 704 isshown in Fig. 5, together with the tted resolution function.Energy (GeV)114 116 118 120 122 124 126Events020406080100CMS ECALe 120 GeV 0.01 %±/E =0.39 σResolution 3x3crystal 704E (GeV)0 50 100 150 200 250(E)/E (%)σ00.20.40.60.811.21.4CMS ECALResolution in 3x3crystal 704S= 2.83 +/- 0.3 (%)N=124 (MeV)C= 0.26 +/- 0.04 (%)Figure 5: Left: Distribution of energy reconstructed in a 3  3 crystal matrix centered on crystal 704 for electronsat 120 GeV. Right: Resolution as a function of the energy reconstructed by summing for the same matrix afterhodoscope cuts of 4  4 mm.4.2 Energy resolution for uniform impactFigure 6 shows the effect of shower containment corrections summing data from many runs where the incidentbeam is impacting at many locations on an array of 9 crystals. This conguration reproduces quite well a uniformcoverage of an array of 9 crystals. The measured relative resolution at 120 GeV is 0.50%.Energy (GeV)114 116 118 120 122 124Number of events020004000600080001000012000140001600018000 Fit results:m =   120.0 GeV =    0.60 GeVσ / m =   0.50 %σWithout correctionWith correction3 crystals×3Figure 6: Distribution of energy before (unshaded) and after shower containment corrections (shaded) when theincident beam is centered at many locations of an array of 3 g 3 crystals as shown by the black crosses on the rightside of the Figure.65 ConclusionTest beam data taken in 2004 allowed exhaustive performance studies to be made on one CMS ECAL supermodule.Reconstruction of the signal amplitude in the CMS ECAL can be performed by a digital ltering technique. Animplementation with dynamic pedestal subtraction gives a noise in a single channel of 40 MeV, and coherent noisebetween channels is effectively removed. In synchronous running, as will be the case at LHC, a single set ofweights can be used to reconstruct the amplitude in all channels.Consistent energy resolution is obtained for electrons with central incidence in different areas of the calorimeter.The resolution obtained using the energy reconstructed in a matrix of 3  3 crystals is 0.40 h 0.01% for electrons of120 GeV. A typical energy dependent resolution for central incidence gives a stochastic term of 2.8% and a constantterm of 0.3%. For a uniform incidence, shower containment can be effectively corrected to give a resolution betterthan 0.5% for electrons of energy greater than 100 GeV. The resolution measured for the supermodule is compatiblewith design expectations.References[1] CMS Collaboration, The Compact Muon Solenoid Technical Proposal, CERN/LHCC 94-38, 1994[2] CMS Collaboration, The Electromagnetic Calorimeter Technical Design Report, CERN/LHCC 1997-033,1997[3] A.A. Annenkov, P. Lecoq and M.V. Korzhik, Lead Tungstate scintillation material, Nucl. Instr. and Meth.A490 (2002) 30[4] CMS Collaboration, CMS Physics Technical Design Report Vol. 1, CERN/LHCC 2006-001 (February2006) 547pp[5] Raymond, M. et al., The MGPA Electromagnetic Calorimeter Readout Chip for CMS, Proceedings of the9th Workshop on Electronics for the LHC Experiments, CERN-LHCC-2003-055, 2003[6] CMS ECAL Group, Reconstruction of the signal amplitude of the CMS electromagnetic calorimeter, TheEuropean Physical Journal C, Vol 46, Sup 1, 2006, pp:2335[7] J. Descamps and P. Jarry, Performance of the cluster containment correction for the CMS electromagneticcalorimeter barrel, CMS Note 2006/045.7

Test Beam Results on the Performance of the CMS Electromagnetic Calorimeter

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