Response Uniformity of the ATLAS Liquid Argon Electromagnetic Calorimeter
M. Aharrouche, J. Colas, L. Di Ciaccio, M. El Kacimi, O. Gaumer, M. Gouanere, D. Goujdami, R. Lafaye, S. Laplace, C. Le Maner, L. Neukermans, P. Perrodo, L. Poggioli, D. Prieur, H. Przysiezniak, G. Sauvage, I. Wingerter-Seez, R. Zitoun, F. Lanni, L. Lu, H. Ma, S. Rajago palan, H. Takai, A. Belymam, D. Benchekroun, M. Hakimi, A. Hoummada, Y. Gao, R. Stroynowsk i, M. Aleksa, T. Carli, P. Fassnacht, F. Gianotti, L. Hervas, W. Lampl, J. Collot, J. Y. Ho stachy, F. Ledroit-Guillon, F. Malek, P. Martin, S. Viret, M. Leltchouk, J. A. Parsons, S. Simion, F. Barreiro, J. Del Peso, L. Labarga, C. Oliver, S. Rodier, P. Barrillon, C. Bench ouk, F. Djama, F. Hubaut, E. Monnier, P. Pralavorio, D. Sauvage, C. Serfon, S. Tisserant, J. Toth, D. Banfi, L. Carminati, D. Cavalli, G. Costa, M. Delmastro, M. Fanti, L. Mandell i, M. Mazzanti, G. F. Tartarelli, K. Kotov, A. Maslennikov, G. Pospelov, Yu. Tikhonov, C. Bourdarios, L. Fayard, D. Fournier, L. Iconomidou-Fayard, M. Kado, G. Parrour, P. Puzo, D. Rousseau, R. Sacco, L. Serin, G. Unal, D. Zerwas, B. Dekhissi, J. Derkaoui, A. El Kharrim, F. Maaroufi, W. Cleland, D. Lacour, B. Laforge, I. Nikolic-Audit, Ph. Schwemling, H. Gha zlane, R. Cherkaoui El Moursli, A. Idrissi Fakhr-Eddine, M. Boonekamp, N. Kerschen, B. Man soulie, P. Meyer, et al. (2 additional authors not shown)
aa r X i v : . [ phy s i c s . i n s - d e t ] S e p Response Uniformity of the ATLAS LiquidArgon Electromagnetic Calorimeter
M. Aharrouche a , , J. Colas a , L. Di Ciaccio a , M. El Kacimi a , ,O. Gaumer a , , M. Gouan`ere a , D. Goujdami a , , R. Lafaye a ,S. Laplace a , C. Le Maner a , , L. Neukermans a , , P. Perrodo a ,L. Poggioli a , , D. Prieur a , , H. Przysiezniak a , G. Sauvage a ,I. Wingerter-Seez a , R. Zitoun a , F. Lanni b , L. Lu b , H. Ma b ,S. Rajagopalan b , H. Takai b , A. Belymam c , D. Benchekroun c ,M. Hakimi c , A. Hoummada c , Y. Gao d , R. Stroynowski d ,M. Aleksa e , T. Carli e , P. Fassnacht e , F. Gianotti e , L. Hervas e ,W. Lampl e , J. Collot f , J.Y. Hostachy f , F. Ledroit-Guillon f ,F. Malek f , P. Martin f , S. Viret f , M. Leltchouk g ,J.A. Parsons g , S. Simion g , F. Barreiro h , J. Del Peso h ,L. Labarga h , C. Oliver h , S. Rodier h , P. Barrillon i , ,C. Benchouk i , , F. Djama i , F. Hubaut i , E. Monnier i ,P. Pralavorio i , D. Sauvage i , , C. Serfon i , S. Tisserant i ,J. Toth i , , D. Banfi j , L. Carminati j , D. Cavalli j , G. Costa j ,M. Delmastro j , M. Fanti j , L. Mandelli j , M. Mazzanti j ,G. F. Tartarelli j , K. Kotov k , A. Maslennikov k , G. Pospelov k ,Yu. Tikhonov k , C. Bourdarios ℓ , L. Fayard ℓ , D. Fournier ℓ ,L. Iconomidou-Fayard ℓ , M. Kado ℓ, , G. Parrour ℓ , P. Puzo ℓ ,D. Rousseau ℓ , R. Sacco ℓ, , L. Serin ℓ , G. Unal ℓ, , D. Zerwas ℓ ,B. Dekhissi m , J. Derkaoui m , A. El Kharrim m , F. Maaroufi m W. Cleland o , D. Lacour n , B. Laforge n , I. Nikolic-Audit n ,Ph. Schwemling n , H. Ghazlane p , R. Cherkaoui El Moursli q , r ,A. Idrissi Fakhr-Eddine q , M. Boonekamp s , N. Kerschen s ,B. Mansouli´e s , P. Meyer s , J. Schwindling s , B. Lund-Jensen. t a Laboratoire de Physique de Particules (LAPP), Universit´e de Savoie,CNRS/IN2P3, Annecy-le-Vieux Cedex, France. b Brookhaven National Laboratory (BNL), Upton, NY 11973-5000, USA. c Facult´e des Sciences A¨ın Chock, Casablanca, Morocco. d Southern Methodist University, Dallas, Texas 75275-0175, USA.
Preprint submitted to Elsevier Science 22 October 2018
European Laboratory for Particle Physics (CERN), CH-1211 Geneva 23,Switzerland. f Laboratoire de Physique Subatomique et de Cosmologie, Universit´e JosephFourier, IN2P3-CNRS, F-38026 Grenoble, France g Nevis Laboratories, Columbia University, Irvington, NY 10533, USA. h Physics Department, Universidad Aut´onoma de Madrid, Spain. i Centre de Physique des Particules de Marseille, Univ. M´editerran´ee,IN2P3-CNRS, F-13288 Marseille, France. j Dipartimento di Fisica dell’Universit`a di Milano and INFN, I-20133 Milano,Italy. k Budker Institute of Nuclear Physics, RU-630090 Novosibirsk, Russia. ℓ LAL, Univ Paris-Sud, IN2P3/CNRS, Orsay, France. m Laboratoire de Physique Theorique et de Physique des Particules, Universit´eMohammed Premier, Oujda, Morocco. n Universit´es Paris VI et VII, Laboratoire de Physique Nucl´eaire et de HautesEnergies, F-75252 Paris, France. o Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh,PA 15260, USA. p Centre National de l’ ´Energie, des Sciences et Techniques Nucl´eaires, Rabat,Morocco. q Faculty of Science, Mohamed V-Agdal University, Rabat, Morocco. r Hassan II Academy of Sciences and Technology, Morocco. s CEA, DAPNIA/Service de Physique des Particules, CE-Saclay,F-91191 Gif-sur-Yvette Cedex, France. t Royal Institute of Technology, Stockholm, Sweden.
Abstract
The construction of the ATLAS electromagnetic liquid argon calorimeter modulesis completed and all the modules are assembled and inserted in the cryostats. Duringthe production period four barrel and three endcap modules were exposed to testbeams in order to assess their performance, ascertain the production quality andreproducibility, and to scrutinize the complete energy reconstruction chain fromthe readout and calibration electronics to the signal and energy reconstruction. Itwas also possible to check the full Monte Carlo simulation of the calorimeter. Theanalysis of the uniformity, resolution and extraction of constant term is presented.Typical non-uniformities of 5 / and typical global constant terms of 6 / aremeasured for the barrel and end-cap modules. Key words:
Calorimeters, High Energy Physics, Particle Detectors, EnergyResolution and Uniformity ACS:
INTRODUCTION
The large hadron collider (LHC) will collide 7 TeV proton beams with lu-minosities ranging from 10 to 10 cm − s − . The very high energy and lu-minosity foreseen will allow to investigate the TeV scale in search for newphenomena beyond the Standard Model. Reaching such performance is anoutstanding challenge for both the collider and the detectors.The electromagnetic calorimeter of the ATLAS detector, one of the two multipurpose experiments at LHC, is a lead and liquid argon sampling calorimeterwith accordion shaped absorbers. In its dynamic range covering the few GeVup to the few TeV domain an excellent measurement of the energy of electronsand photons is required in order to resolve potential new particle resonances,and to measure precisely particle masses and couplings.One of the salient benchmark processes that has guided the design of theelectromagnetic ATLAS calorimeter is the Higgs boson production with sub-sequent decay into a pair of photons. This event topology will be observableonly if the Higgs boson mass is smaller than ∼
150 GeV/c . In this channelthe capabilities of the calorimeter in terms of photon pointing resolution and γ / π discrimination are of chief concern. An excellent and uniform measure-ment of the photon energy is essential. Another process involving the Higgsboson where it decays to a pair of Z bosons and subsequently into four elec-trons also requires a uniform measurement of the electron energy over a largedynamic range. Finally, among the processes which will require the most ac- Now at university of Geneva, switzerland. Now at Rutherford Appleton Laboratory (RAL), Chilton, Didcot, OX11 0QX,United Kingdom. Now at university of Toronto, Ontario, Canada. Visitor from LPHEA, FSSM-Marrakech (Morroco). Deceased. Also at KFKI, Budapest, Hungary. Supported by the MAE, France, the HNCfTD(Contract F15-00) and the Hungarian OTKA (Contract T037350). Corresponding author, E-mail: [email protected] Now at Queen Mary, University of London. Now at LAL, Univ Paris-Sud, IN2P3/CNRS, Orsay, France. Now at Facult´e de Physique, Universit´e des Sciences et de la technologie HouariBoumedi`ene, BP 32 El-Alia 16111 Bab Ezzouar, Alger, Alg´erie. Now at CERN, Geneva, Switzerland. ∼ / . For all these processes the constant term b of thethree main resolution elements: σ E E = a √ E ⊕ b ⊕ cE (where c and a are the noise and stochastic terms respectively) plays an im-portant role. It arises from various sources encompassing the calibration andreadout electronics, the amount of material before and in the calorimeter, theenergy reconstruction scheme and its stability in time. The c term comprisesthe electronic noise and the pile-up.Many years of R&D work [1,2,3,4,5] have led to the ATLAS calorimeter designwhose first performance assessments on pre-production modules were reportedin [6,7]. Since then, modifications were made in order to improve the produc-tion, the quality control and the performance of the calorimeter modules.During the three years of module construction, four barrel and three endcapmodules have been exposed to electron beams in the North Area at CERN’sSPS. The primary aim was to assess the quality of the production by mea-suring the response uniformity over the complete acceptance. However, thesemeasurements have led to numerous further improvements of the calibration,signal reconstruction and the simulation of the calorimeter.This paper reports on measurements of the uniformity and a study of thedifferent contributions to the constant term of the electron energy resolutionfor barrel and endcap modules exposed to high energy electron beams. Theactions taken to optimize the electron energy resolution and in particular theuniformity of the response are also described. Finally a review of all sourcesof non-uniformities is presented.The paper is organized as follows. In Sec. 1 the main features of the calorimetermodules are described and the differences with respect to the pre-productionmodules are briefly presented. A description of the readout and calibrationelectronics is then given in Sec. 2. The signal reconstruction, including crosstalk issues is also presented. The beam test setups are described in section 3.Finally the barrel and endcap analysis and results are presented in Sec. 4 andSec. 5. The ATLAS electromagnetic calorimeter is a lead and liquid argon samplingcalorimeter using an accordion geometry for gaps and absorbers. It is com-posed of a cylindrical barrel centered on the beam and two endcaps. The usual4lightly modified polar coordinate system is used, where the z -axis coincideswith the beam axis, φ is the azimuthal angle and the polar angle θ is replacedby the pseudo rapidity η = − ln ( tanθ/ Barrel Modules Description
The ATLAS barrel calorimeter is divided in two half barrels covering the pos-itive and the negative pseudo rapidities, from | η | = 0 to | η | = 1 . , .
8] and [0 . , . | η | < . | η | > . η , ends after 4 radiations lengths ( X ), while the second stopsafter 22 X . The total thickness of the module varies as a function of η be-tween 22 and 33 X . Summing boards, plugged on the electrodes, perform thesignal summation in φ : 16 adjacent electrodes are summed for a strip celland 4 electrodes for middle and back cells. The granularity of the differentcompartments are shown in Table 1 for | η | < . | η | from 0 to 1.52 and covers a region of ∆ φ = 0 .
2. The signal issampled in a thin active layer of 11 mm of liquid argon with a readout cellgranularity of ∆ η × ∆ φ = ∼ . × . η × ∆ φ =0.2 × .2 Endcap Modules Description
The ATLAS electromagnetic endcap calorimeter (EMEC) covers the rapid-ity region from 1.375 up to 3.2 and consists of 2 wheels, one on each sideof the electromagnetic barrel. Each wheel, divided into eight wedge-shapedmodules, is 63 cm thick with internal and external radii of about 30 cm and2 m. For technical reasons, it is divided in one outer (1 . < | η | < .
5) andone inner (2 . < | η | < .
2) wheel, both projective in η . The crack betweenthe wheels is about 3 mm wide and is mainly filled with low density material.In φ , one outer (inner) wheel module is made of 96 (32) accordion shapedabsorbers interleaved with readout electrodes, covering a range of ∆ φ = 2 π/ η ) : liquid argon gap, sampling fraction, accor-dion wave amplitudes or folding angles. A continuously varying high voltagesetting along η , would partially compensate for this and imply an almost η -independent detector response. However, the high voltage is set by steps. Theouter (inner) wheel is divided into seven (two) high voltage sectors. In each ofthem a residual η -dependence of the response will need to be corrected.In the region devoted to precision physics, where the tracking information isavailable (1 . < | η | < . φ -sectors of 24 (4) electrodes in the outer (inner) wheel,independently on each side.Three endcap modules where exposed to the H6 beam line namely ECC0,ECC1 and ECC5. Design modifications
Following the construction and the beam tests of the prototype modules 0 [6,7],a few design modifications have been implemented : • The high voltage is distributed on the electrodes by resistors made of resis-tive paint silkscreened on the outer copper layer of the electrodes. The roleof these resistors is also to limit the current flowing through the readoutelectronics in case of an unexpected discharge of the calorimeter cell. Someof these resistors located near the electrode bends were displaced in order6 odules η range Front Middle Back[0.0,0.8]& [0.8,1.35] 0 . × . . × .
025 0 . × . . × . . × .
025 -[1.4,1.475] 0 . × . . × .
025 -[1.375,1.425] 0 . × . . × .
025 –[1.425,1.5] 0 . × . . × .
025 –EC [1.5,1.8] ∼ . × . . × .
025 0 . × . ∼ . × . . × .
025 0 . × . ∼ . × . . × .
025 0 . × . . × . . × .
025 0 . × . . × . . × . Granularity ( ∆ η × ∆ φ ) of calorimeter cells in the electrodes A and B ofthe barrel modules and the outer and inner wheels of the endcaps (EC). to avoid breaking during the bending process. This lead to a change of thebending process of the barrel electrodes [10]. • On the prototype, an increased cross talk and pulse shape deformation wasobserved every 8 (4) channels in the barrel (endcap). This effect was tracedback to the absence of ground on one side of some signal output electrodeconnectors. These missing contacts were added in the production electrodecircuits. • Summing and motherboards of the endcap were redesigned to reduce theinductive cross talk to an acceptable level ( < • Precise calibration resistors (0.1 % accuracy) are located on the motherboard. It appears that if an accidental HV discharge occurs, a large fractionof the energy released could damage these resistors, thus preventing anycalibration of the cell. Diodes were added on the signal path to protect theseresistors for the middle and back cells where the detector capacitances arethe largest. For the strips section such a protection scheme [14] could not beinstalled, but the smaller detector capacitances reduce the risk of damage. • Finally for the endcap construction, the cleanliness and humidity regulationof the stacking room were improved. The honeycomb spacers, which keep theelectrodes centered on the gap, were modified to ensure a better positioning.They were measured and tested under high voltage before stacking andchecked at the nominal high voltage settings after each gap stacking. Motherboards, plugged on top of the summing boards, ensure the signal routingand the distribution of calibration signals. .4 Quality control measurements
During the production a number of quality control measurements was per-formed on all barrel modules. The lead thickness, the argon gap width andsome electrical parameters linked to the electrode design are key parametersfor the response of the calorimeter. These measurements were done to ensurethat all components were made with the required precision. Similar measure-ments were also performed on the endcap modules, details of the gap variationwill be discussed in the endcap data analysis section.
Before assembling the modules, the thickness of all lead sheets were measuredby means of an ultra sound system, producing a map with a 5 × gran-ularity [9,15]. These maps have been used to select the stacking order of thelead sheets to minimize the thickness fluctuations across each module. Foreach lead plate the measurements are averaged projectively along the showeraxis. As most of the shower energy is shared by five absorbers, the thicknessesfor | η | < . | η | > .
8) normalized to their nominal values are averaged ina sliding window of five consecutive absorbers. Finally to emulate the energyprofile within the electron cluster, each average is weighted according to a typ-ical electron energy deposition shape. In Fig. 1 the variation of the normalizedlead thickness as a function of the middle cell η index (as described below)for the modules P13, P15 and M10 is shown. The dispersions do not exceed0.3 % per module.For barrel modules the η middle cell indices run from 0 to 54 covering thepseudo rapidity range from 0 to 1.35. The φ cell indices correspond to incre-ments in azimuthal angle of π/ η index used covers the region in pseudo rapidity from1.375 up to 3.2 with indices ranging from 0 to 50. The φ middle cell indicesincrement is the same as that of the barrel modules for the outer wheel and π/
32 for the inner wheel. In the φ direction these indices range from 0 to 31in the outer wheel and from 0 to 7 in the inner wheel.Similar measurements were also performed on endcap modules. The disper-sions of the normalized lead thicknesses are within 0.3 % for all modules. At the end of modules stacking, the gap capacitance of each sector of ∆ η = 0 . .970.980.991 0 0.2 0.4 0.6 0.8 1 1.2 1.4 h P13 f =9 f =10 f =11 f =12 f =13 f =14 R e l . T h i c kn e ss ( % ) RMS = 0.15 % P15 f =9 f =10 f =11 f =12 f =13 f =14 R e l . T h i c kn e ss ( % ) RMS = 0.24 % M10 f =9 f =10 f =11 f =12 f =13 f =14 Middle Cell h index R e l . T h i c kn e ss ( % ) RMS = 0.29 % Fig. 1.
Weighted average lead absorber thickness per middle cell as a function of themiddle cell η index for various φ regions. The distribution of the measurements isalso shown and the dispersion is indicated. variations were extracted. Similarly to the lead thickness, most of the showeris shared in a few gaps. Using a typical electromagnetic lateral shower energyprofile, a sliding energy-weighted-gap was calculated. Its dispersion is summa-rized in Table 2 for the 3 barrel modules. While P13 and P15 show similarresults, the module M10 has a larger dispersion. This effect was explained bythe use of electrodes made before and after the modification of the bendingprocess. Module P13 P15 M10Total 0.62 % 0.64 % 1.66 %FT0 subset 0.58 % 0.39 % 1.41 %Table 2.
Dispersions of the weighted average gaps for each barrel module P13, P15and M10. The FT0 subset corresponds to the region instrumented with the readoutelectronics used in the analyses described in Sec. 2.1 and Sec. 4.7.
Readout Electronics
As described in Sec 1.1, the readout signal consists of the sum of signalsmeasured in various electrodes. The analog sum is made by summing boardsconnected at both ends of the electrodes; at the front for the strip compartmentand at the back for the middle and back compartments. The motherboards,plugged on top of the summing boards, send the signals through cold cablesout to the front-end boards placed outside the cryostat at room temperature.The readout electronics are located in crates at both ends of the cryostat.To extract the calorimeter signals from inside the cold vessel the feedthrough(FT) connexion devices are used [8]. Two FTs are required for each barrelmodule. Each of them covers half a module in φ . Three FTs are required foreach endcap module. The readout front-end electronics crates are placed ontop of the FT devices. In particular, for the beam test barrel modules there aretwo FT devices covering a half barrel each. The regions covered are denotedFT-1 and FT0.In the front-end boards, signals are amplified and shaped through a bipolarCR · RC filter with a time constant τ S = 15 ns, then sampled every 25 nsand digitized. The shaping consists in one derivation (CR) to form a bi-polarsignal and two integrations (RC) allowing both to reduce the impact of thepile-up and electronic noise. The choice of shaping time constant results fromthe minimization of the electronic noise and pile-up.The energy dynamical range covered by the calorimeter signals requires 16 bits whereas the available Analog-to-Digital Converter (ADC) modules are limitedto 12 bits . To produce the adequate signal range the shapers produce threesignals amplified in three different gains low, medium and high in the ratioof respectively 1, 9.3 and 93. All signals are then stored in an analog pipelineawaiting for a first level trigger decision. When the decision is made the signalseither from the three gains or from the most suited one according to a hardware10ain selection are digitized. In the beam test setup the signals are directlyreadout while in the full ATLAS configuration they are sent to a higher levelfirmware system where the energy is fully reconstructed for further use bothhigher level trigger and in physics analysis. Detector Electrical Properties
A detector cell can be seen as a resonant circuit as illustrated in Fig. 2. Theresonance frequency is linked to the capacitance and inductance of the detectorcell and summing boards. These resonance frequencies have been measuredon the assembled calorimeter for each module using a network analyzer [17].In Fig. 3 the results for the module P13 and P15 filled with liquid argonare displayed. The structure is mainly due to the variation of the inductancealong η resulting from the electrode design in which the lines serving to extractthe signal of middle cells varies with η . The differencies along φ reflect nonuniformities of the summing boards. The φ dispersion of these frequenciesamounts to about 1.2 %, which is compatible with the expected gap variation. LC read-out line r CR-RC I ion I cal H r.o. Fig. 2.
Simple schematic electrical model of the cell electronic environment. Theshape of the calibration and ionization signals is also illustrated along with the outputpulse. Here C is the cell capacitance, L the inductive path of the signal and r is theresistance. Similar measurements were made on endcap modules yielding frequencies in-creasing as a function of η from 20 to 40 MHz. Calibration System
The calorimeter is equipped with an electronic calibration system [18] thatallows prompt measures of the gain and electrical response of each readout cell.This system is based on the ability to inject into the detector an exponential
A small offset f s is present, due to the resistive component of the inductance inthe calibration board. Typically f s ≃ I cal ( t )) that mimics the ionization pulsegenerated by the particles hitting the detector: I cal ( t ) = I cal0 θ ( t ) h f s + (1 − f s )e − tτ c i (1)with a time decay constant τ c ≃
350 ns ( θ ( t ) is the unit step function). Thecalibrated pulse shape ( g cal ( t )) is reconstructed using programmable delays bysteps of about 1 ns. P13 f = 1 f = 2 f = 3 f = 4 f = 5 f = 6 f = 7 f = 8 f = 9 f = 10 f = 11 f = 12 f = 13 f = 14 F re qu e n c y ( M H z ) P15 f = 1 f = 2 f = 3 f = 4 f = 5 f = 6 f = 7 f = 8 f = 9 f = 10 f = 11 f = 12 f = 13 f = 14 Middle Cells h index F re qu e n c y ( M H z ) Fig. 3.
Resonance frequencies for modules P13 and P15 as a function of the η indexfor all middle cells for various φ regions. The signal is generated by means of a digital-to-analog converter (DAC) whichcontrols the input current. Its value is proportional to the DAC requested. Aconstant very small parasitic charge injection DAC value is present due toparasitic couplings. It was measured and its value accounted for.The signal is produced in calibration boards placed in the front-end crates. Itis then carried into the cold vessel and distributed to the electrodes throughinjection resistors R inj which are precise at the 0.1 % level. These resistors areplaced on the motherboards. 12 non uniformity of the calibration signals would affect the uniformity in fine .All potential sources of non uniformity affecting the calibration signal havethus been independently measured. The main ones are:(i) the pulsers: each line is measured on the calibration board directly. A rela-tive dispersion of 0.19 % is found.(ii) calibration resistors: each calibration resistor is measured and a relativedispersion of 0.08 % is found for barrel modules and 0.05 % in the endcaps.(iii) cables: The attenuation by skin effect which is proportional to the cablelength is corrected in average, however a small relative dispersion of atmost 0.1 % could still impact the energy uniformity.The overall precision of the calibration system is ∼ Energy Reconstruction
When electrons and photons hit the calorimeter they interact within the leadabsorbers producing an electromagnetic cascade. Its charged component ion-izes the liquid argon in the gaps, inducing a triangular current signal [19]( I ion ( t )): I ion ( t ) = I ion0 θ ( t ) θ ( T D − t ) (cid:18) − tT D (cid:19) (2)whose length equals the drift time, T D ≃
450 ns (in the endcaps the drift timedecreases from 550 down to 250 ns as a function of η ).The ionization signal amplitude is reconstructed in each gain from the five dig-itized samples S k , to which the pedestals have been subtracted (see Sec. 2.4.1),located around the peak, using the optimal filtering (OF) technique [20]: A = P k =1 a k S k A × τ = P k =1 b k S k (3)where A is the amplitude estimator and τ is the signal arrival time estimatewith respect to the readout clock. The coefficients a k and b k are chosen in orderto minimize the effect of electronic noise. They are analytically calculatedthrough a Lagrange multiplier technique [20], provided one knows for eachreadout cell the normalized shape of the ionization signal g ion ( t ), its derivativeand the noise time autocorrelation. The latter is computed from the dataacquired during the pedestal runs. 13he cell energy is then reconstructed from the cell signal amplitude A usingthe following prescription: E cellvis = 1 f I/E ξA This formula can be read as the sequence of the following operations: (i) theconversion of the signal in ADC counts A into a current in µ A correspond-ing to the calibration of the readout electronics with the function ξ ; (ii) theconversion factor from current to energy f I/E . During the running period, data in absence of beam were taken daily to assessthe level of signal without any energy deposition in each cell for all gains ofall modules. In addition, in order to address precisely the more subtle possiblevariations on a run-by-run basis the pedestals can be evaluated from triggerstaken at random during the run. The variations between no-beam runs andrandom triggers are in general negligible and thus not taken into accountbut for a few runs small instabilities, in particular in the presampler, couldproduce a detectable bias in energy not exceeding 20 MeV. The subtractionof pedestals is done on all signal samples ( S k ) before applying the optimalfiltering method. The calibration procedure establishes the correspondence between a signalreadout in ADC counts and a known injected current in the cell in µ A. Cal-ibration data were taken approximately twice daily throughout the runningperiod.The procedure consists in fitting the ADC response as a function of the DACvalues knowing that the injection currents vary linearly with the DAC values.A second order polynomial form ξ is used. The higher order fine structure of thenon linear response of the calibration is not relevant here. The aforementionedfunction also contains a DAC to current constant conversion factor. Estimating from first principles the relation between the measured currentand the energy is an intricate task, as numerous complex effects can introducebiases as detailed in [21]. However, the simplified model estimation of f I/E ∼ . / MeV in the barrel accordion in the straight sections (7 % less whentaking into account the folds [22]), yields a result accurate to the few percentlevel. This value is in agreement with a more precise calculation in which thedetailed cell electric fields and recombination effects are taken into account. Inthe case of the analysis of the barrel modules where a complete and thoroughsimulation of the calorimeter was used a more precise estimate of the f I/E factor is obtained from a comparison of the Monte Carlo simulation with thedata (see Sec. 4.5).
Signal Reconstruction
The normalized response g ion ( t ) of the system to the ionization current differsfrom the response g cal ( t ) to a calibration current because the two pulses arerespectively triangular and exponential, and while the former is generatedinside the detector, the latter is injected in the cell from one end of the detectorand reaches the inside through an inductive path . Typical shapes of the twosignals at the end of the readout chain are shown in Fig. 4. ionization pulsecalibration pulse t (ns) g (t) ( a . u . ) -0.200.20.40.60.81 0 100 200 300 400 500 600 700 800 Fig. 4.
Normalized calibration g ion ( t ) and ionization g cal ( t ) pulses. The difference between the calibration and the ionization pulses can be ana-lytically described by modeling the liquid argon readout cell as a lumped rLC model (see Fig. 2), where the two currents share the same readout chain whilebeing generated in different places. After taking into account the analyticaldescriptions (2) and (1), the relation between the current shapes is [24,25,26]: The effect is not negligible, as it affects the amplitude ratio of the ionization andcalibration waveforms by approximately 0.15 %/nH, and the inductance value variesthroughout the detector from 35 to 55 nH [23]. ion ( t ) = g cal ( t ) × L − " sT D − − sT D s T D s (1 + sτ c ) f s + sτ c × L − (cid:20)
11 + s LC + srC (cid:21) (4)where the normalized ionization signal g ion ( t ) can be inferred from the ob-served calibration signal g cal ( t ) by means of time-domain convolutions withfunctions that depend on the parameters T D , τ c , f s , LC, rC (where τ c , f s arethe calibration time constant and a calibration offset) only using the inverseLaplace transform L − with the Laplace variable s . The resonance frequen-cies displayed in Fig. 3 correspond to the standard oscillator circuit thus f = 1 / π √ LC . The evaluation of g ion ( t ) is completely independent of anydetails of the read-out chain.For the barrel modules the drift time T D can be estimated with various meth-ods [25,27,28], while the parameters τ c , f s and LC, rC can be extracted eitherby analyzing the observed signals or from direct measurements. In the end-caps T D varies continuously with η , it was thus considered as a parameter.Two strategies were developed for the test beam, as described in the nextsubsections. The following method [24,26] has been used to reconstruct the energy for theprototype modules [6,7] and for all tested production modules.At the test beam, the electrons reach the calorimeter at random time withrespect to the sampling clock (asynchronous events). It is thus possible tosample the ionization signal every nanosecond, similarly to what is done for thecalibration signal. However, the signal shape obtained from direct observationis imprecise, due to the low statistics and the large fluctuations in the showerdevelopment. Moreover, its normalization is arbitrary.The parameters τ c and f are measured directly on the calibration board beforeits installation on the detector.The parameters LC and rC are obtained from a fit of the predicted ionizationsignal, as obtained from equation (4), to the observed one. In the fit, two moreparameters are allowed to vary in order, to account for a time shift betweenthe two signals and for the amplitude scale factor. Once LC and rC are found, The time between the trigger given by a scintillator coincidence and the 40 MHzclock edge is measured for each event.
This method is an alternative to the one described previously: it has the ad-vantage of being based on calibration data only, thus not relying on a directknowledge of ionization pulses from asynchronous events. It relies on the ob-servation of long enough calibration signals: up to 32 digitized samples can beacquired, corresponding to a maximum length of 800 ns. The details are fullydescribed in [25], therefore only an overview is given here.The exponential decay time can be extracted from a fit of the tail of thecalibration signal. The offset f can be estimated as follows: if the injected I cal ( t ) was a step-function, then the tail of the shaped signal would be minimal.The detector response to an injected step could be calculated, by means of atime-domain convolution between g cal ( t ) and a function of time which dependson the parameters τ c and f . Once τ c is found, the best value for f is chosenas that minimizing the tail of the response function.The parameters LC and rC are extracted from a frequency analysis of thetransfer function, which exhibits a minimum for angular frequency ω = √ LC .This is achieved either by a direct use of a fast Fourier transform, or withtechniques similar to that described for the extraction of f — here the charac-teristics of the detector response to a sinusoidal injected signal are exploited:the best value for ω is that minimizing the oscillations in the tail.Such a technique has been applied to a restricted region of a production mod-ule where the 32-samples-calibration data were made available (half a modulefor the Middle and Back compartments, and only a ∆ η × ∆ φ = 0 . × . Since the predicted signal and calibration shapes are different, the responseamplitude to a normalized input signal will be different. This difference must17e taken into account in order to correctly convert ADC counts into energies.It is done using the prediction of the physics to calibration amplitude ratio,namely M phys /M cal . This ratio varies with pseudo rapidity. These variationsare displayed in Fig. 5 and 6 for the barrel and endcap modules respectively.The barrel strips M phys /M cal is reasonably consistent with 1, whereas for mid-dle cells the prediction to calibration amplitude ratio increases systematicallywith η up to the middle cell η index 48. These variations are consistent withthe resonance frequencies measured and presented in Sec. 2.2. A similar effectis observed in endcap modules. f = 9 f = 10 f = 11 f = 12 f = 13 f = 14 P13 M P h y s / M C a l f = 3 f = 4 P13
Middle Cells h index M P h y s / M C a l Fig. 5.
Bias in the signal reconstruction method as derived for the barrel P13 moduleat all middle η indices and azimuthal angles, for middle cells (upper plot) and strips(lower plot). Contrary to what will be the case in the ATLAS experiment and due to thetime spread of electron bunches, in the test beam the time phase is essentiallyrandom. For all barrel and endcap modules it was checked that in the energyreconstruction scheme no bias is observed as a function of the time phase.18 .041.061.081.11.121.141.161.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 h M P h y s / M C a l ECC0ECC1ECC5
Fig. 6.
Bias in the signal reconstruction as derived for all tested EMEC modules(ECC0, ECC1 and ECC5) for middle cells averaged in the azimuthal direction as afunction of the pseudo rapidity.
Cross Talk Issues
Various cross talk effects inherent to the design of calorimeter cells or due tothe readout electronics are present in the calorimeter. A complete descriptionof the origin of these effects can be found in [12,13]. These unavoidable effectshave been measured mainly using calibration signals [29,30,31]. A summaryof the measurements of the typical cross talks are given in Table 3 for boththe barrel and the endcap electrodes. The cross talks are here defined as peak-to-peak, i.e. , the maximum amplitude of the cross talk is normalized to thesignal amplitude. All the effects described here are those measured in nearestneighbors, second order effects are negligible, except for the secondary crosstalk between a strip and its next to nearest neighbor with a peak-to-peakvalue of 0.9 % for barrel and 0.5 % for endcap electrodes.Among these cross talk effects mainly two will affect the energy reconstruction:the strips capacitive cross talk and the middle-back inductive cross talk.The strips cross talk effect is due to the thin separation between the finelysegmented cells of the first compartment of the calorimeter, the fine segmen-tation is necessary for the π /γ separation, for a precise estimation of thepseudo rapidity of the impact point and for the estimation of the photonpointing direction. This effect non trivially affects the calibration and thesignal reconstruction. Its treatment is described in Section 2.6.2.The cross talk between the middle and the back compartment results from a19 odule Part Electrode A Electrode BCompartment Front Middle Back Front Middle BackFront 6.9 % Middle 0.07 % Back 0.04 % Module Part Outer Wheel Inner WheelCompartment Front Middle Back Front Middle BackFront 5-8 % - - -Middle 0.2 % - 1.0 % Back 0.2 % - 0.8 % Table 3.
Summary of the typical cross talks measured in the different samplingsof the barrel electrodes A and B and the outer and inner wheel of the endcap. Theindices denote the nature of the cross talk where 1, 2, 3 and 4 correspond to resistive,capacitive, inductive and mixed respectively. mixture of various effects, but is mostly inductive. Since the back compartmentplays an important role in the assessment of the longitudinal shower energyleakage it is important that this effect is measured and corrected for.All these effects were expected and are well understood. They were measuredon all modules. All cross talk effects are well reproducible among modules.
Because an electron cluster contains a large number of strips (see Sec. 4.2and Sec. 5.1.1) almost all the electron signal is contained in the cluster cells.Therefore any signal exported from one strip to its neighboring strips is recov-ered in the reconstructed cluster energy. The energy of an electron or photoncluster is therefore at first order not sensitive to the cross talk effect. However,the readout electronics are calibrated using pulse patterns where one strip cellis pulsed out of four. To recover the signal loss in the neighboring cells, thesignal readout in the two first neighbor unpulsed cells is added to the pulsedcell and the average of the two next to nearest neighbor unpulsed cells are alsoadded to the pulsed cell. In doing so using calibration runs where the signalis sampled in 32 time intervals of one nanosecond the shape of a signal inabsence of cross talk is emulated. This new shape is used to derive the OF co-efficients and comparing it to the signal shape without applying the summingprocedure a correction factor of the ramp gains is derived. The amplitude of20he correction is around 7 %. The method has proven to be linear as the cor-rection factors appear to be independent of the DAC signal applied. Whenthe complete correction is applied, the M P hys /M Cal factor recovers a value ofapproximately 1 (its expected value if the signal reconstruction is sound) asillustrated in Fig. 5.It was also checked that the method is not sensitive to gain differences betweenneighboring cells. To avoid the possible calibration differences between stripcells, the signal read in the non-pulsed cells is first calibrated and then added.However, no noticeable difference is seen between the two approaches.Strip cells cross talk corrections show collective variations of approximately1 % of the strips energy. The devised correction thus improves the uniformity ofthe energy measurement for the total electron energy of a few percent relativebut has almost no impact on the local energy resolution.
For all modules tested in the beamline the same two FT devices equippingthe test beam cryostat were used. One unexpected and more tedious crosstalk effect appeared in the bottom barrel modules FT which was lacking goldplated contacts. It exhibited an increase with time of the ground resistancecommon to all channels inside the connectors (64 channels), therefore a longrange resistive cross-talk appeared. This problem non trivially affected mostof the channels corresponding to that FT.A correction procedure was derived which brought the uniformity of the re-sponse in channels readout with this feedthrough close to that of the otherchannels. However the data taken with the corrupted FT are not considered inthe final analyses. These data correspond to electrons impinging at azimuthalangles φ smaller than 9 in middle cell index units. To prevent this problem toappear in ATLAS, all connectors were gold plated and the connections wereverified with the final detector. Beamline Setups
The barrel and endcap production modules have been exposed to beams atCERN with 245 GeV electrons in the H8 line and 120 GeV electrons in the H6line respectively. The pion contamination of the electron beam was discussed21n [21], it is far less relevant in this context as a small bias would equally affectall the data. Similar pion contamination rejection cuts as those used in [21]were nevertheless used. Each experimental setup has been already describedin details in [6] and [7]. Each beam line is instrumented with multi wire pro-portional chambers to extrapolate the particle impact on the calorimeter. Thetrigger is built from the coincidence of three scintillators on the beam linedefining a maximal beam spot area of 4 cm . While for the barrel the projec-tivity of the beam is ensured in both directions by a proper movement of thecryostat, for the endcap the cryostat is moved along η but for the φ rotationthe calorimeter is moved inside the argon. In the endcap the amount of deadmaterial upstream of the calorimeter is almost constant at all electron impactpoints and amounts to 1.5 X . Thus it does not introduce any effect in theresponse uniformity of the calorimeter. In the barrel, however, the amount ofdead material upstream continuously increases with η . Scanning Procedure
Runs are taken with different positions of the moving table in such way thatthe complete module is exposed to the beam. The positions are chosen inorder to center projectively each middle cell of the modules into the beam.For this reason the cell coverage is not completely uniform. In particular, lesselectrons are impinging on the edge of the cells than in the center. Results aretherefore commonly presented in units of middle cells ( η , φ ) indices. Exceptionsare made for certain regions of the barrel calorimeter that have been scannedwith a half middle cell granularity. Temperature Stability
Argon temperatures were readout and recorded on the barrel setup: the tem-perature stability is better than 10 mK, but the absolute temperature differsfrom one module to another. A -2.0 % correction of the mean energy per degreeis taken into account in the analysis [27].
Data Sets
For all barrel modules runs of 10 000 events were recorded at each cell position.Additional runs were taken in order to perform systematic studies such as cell-to-cell transitions, the electrode A to electrode B transition, and to study theimpact of changing front-end and calibration boards in the front-end crates.22n the outer wheel of the EC modules only the region 1 . < | η | < . . < φ < .
725 (corresponding to 6 ≤ η cell ≤
40 and 4 ≤ φ cell ≤
29) wascovered. In the inner wheel the domain 2 . < | η | < . . < φ < . ≤ η cell ≤
49 and 2 ≤ φ cell ≤
6) was covered representing25 cells.In the ECC0 and ECC1 modules high voltages were incorrectly cabled in theinner wheel. The inner wheel uniformity was therefore only studied on ECC5.In all modules a few single isolated channels were defectuous or not respondingat all. Most of them were due to the readout electronics setup and were thusfound in all running period for EC and barrel modules. For those problem-atic channels for which the problem is intrinsic to the modules, the moduleshave been repaired for their future use in ATLAS. For instance in the ECouter wheel, four (one) electrode front connectors in ECC0 (ECC5) were notproperly plugged on their summing board. The corresponding cells ( ∼
20) areexcluded from the analysis. To avoid such problems in ATLAS, connectionsof all production modules have been checked by specific measurements.
Type Barrel endcapSet-up M10 P13 P15 ECC0 ECC1 ECC5Bad Strips 0 3 1 5 8 6Bad Middle 2 0 0 3 1 1Bad Calibration 2 2 0 0No data 2 1 15 - - -Table 4.
Number of channels which present no physical signal, those where no datawere taken and those where the calibration line was defectuous for all barrel modulesin the FT0 region only and all end-cap modules.
A problem which may appear in the future running of ATLAS is the impos-sibility to run some sectors at the nominal values of high voltage (HV). Inthe EC modules the electrodes of three HV sectors were powered on one sideonly because of HV problems that appeared at cold. In this case the energy ofthe corresponding cells is simply multiplied by a factor of ∼
2. The resultingenergy resolution is degraded by ∼
20 % in these sectors and by ∼
40 % atthe φ -transition with a good sector. The impact on the response uniformityis negligible. The correction could be refined at the φ -transition with a goodsector. These cells are kept in the encap modules analysis.For the barrel and endcap modules the scanned cells that are neighboring amiddle defectuous channel or which are behind a bad strip are excluded from23 arrel EC Outer Wheel (IW)Module M10 P13 P15 ECC0 ECC1 ECC5Scanned 324 324 324 874 910 844 (25)Kept 278 305 299 799 840 816 (25)86 % 94 % 92 % 91 % 92 % 97 % (100 %)Table 5. Number of scanned cells that are kept for the uniformity analysis. Theexcluded cells are related to problems that are specific to the beam test. The numbersindicated in parentheses correspond to cells of the inner wheel. In the barrel sectionthe altogether 756 cells were scanned on each barrel modules comprising of the FT0and FT-1 but only those pertaining to the FT0 are kept. the analysis. The same procedure is applied for problems in the calibration.When a back or a presampler cell is defectuous no specific treatment is applied.The regions covered in endcap and barrel modules are detailed in Table 5. Forthe cells removed from the analysis, in the future a special treatment involvingan energy correction could be applied.
Monte Carlo Simulation
As was done in [21] a full Monte Carlo description of the shower developmentof electrons penetrating the electromagnetic calorimeter barrel module hasbeen carried out with the GEANT simulation version 4.8 [32]. The intricategeometry of the accordion and the material of the calorimeter is thoroughlydescribed. All the particles are followed in detail up to an interaction range of20 µ m. The photon-hadron interactions are also simulated.The material within the volume of the cryostat is thoroughly simulated (lead,liquid argon, foam, cables, motherboards and G10) using our best knowledgeof its geometrical distribution as described in [8].The absorber thickness and gaps were set to their nominal values as reportedin [6] and not to the measured ones. The material contraction in cold liquidargon was not taken into account either. The main consequence of these smallinaccuracies essentially results in a absolute scale effect of a few per mil anddoes not affect the uniformity. 24he material outside and in front of the calorimeter is described in detailaccounting for the energy lost near and far from the calorimeter. The casewhere bremsstrahlung photons are not reconstructed in the calorimeter, be-cause they have been produced far upstream of the impact point, is thus takeninto account.The material distribution of the test beam set-up is illustrated in Fig. 7. Thedistributions are presented as a function of the η and φ direction separatelyand cumulatively for the material before and in the presampler, the materialbetween the presampler and the first accordion compartment and the materialin the accordion calorimeter. These distributions correspond to Monte Carlosamples simulated along the η and φ directions with a granularity of one middlecell. Each point contains at least five hundred events. To further illustrate thematerial along the φ direction scans at various fixed η values are performed. Itappears that the total amount of material is rather uniform in the φ direction.Unlike in the ATLAS experiment, in the test beam setup only a small amountof material is located upstream of the calorimeter. It is therefore a uniqueopportunity to test the simulation of the calorimeter alone.In particular, the material upstream has been tuned by varying the amountof liquid argon in front of the presampler that is not well known from theconstruction. This allowed to optimize the agreement of the Monte Carlo withthe data in the presampler alone. As was the case in [21] the best agreementis found for a thickness of 2 cm.The large capacitive cross talk between strips is not simulated. The cross talkeffect between the middle and back compartments of the calorimeter is takeninto account in the simulation. Clustering
The electron energy is reconstructed by summing the calibrated cell energiesdeposited in the three calorimeter compartments and in the presampler. Acluster is built around the cell with the largest energy deposit in the middlecompartment. The cluster size, expressed in number of cells in ∆ η cell × ∆ φ cell is3 × × φ , the cluster contains 1 or 2 cells,depending on whether the shower develops near or far from the cell center. Inthe presampler the corresponding 3 cells in η within the two corresponding φ positions are chosen to be part of the cluster.25 S i m . M a t . ( X ) CryostatLAr in front of PSFoamPre-Sampler S i m . M a t . ( X ) LAr Between PS and StripsG10 barCablesMotherboards
Middle Cell h index S i m . M a t . ( X ) Middle Cell f index Acc. Lead and ElectrodesLArgTotal Material Cost
Fig. 7.
Distributions of the simulated material for the main material types in unitsof radiation lengths ( X ) as a function of η and φ . The upper two plots represent thecumulative amounts of material before and in the presampler. The two intermediateplots represent the cumulative distributions of the material between the presamplerand the strips compartment of the accordion calorimeter. In order to illustrate thevarious structures in φ , in the η plots the average values correspond to various fixed φ values, the corresponding averages are thus different in η and φ . The bottom twoplots represent the amount of material in the accordion calorimeter as well as thetotal amount of material in the entire setup. Energy Reconstruction Scheme
Several electron energy reconstruction schemes were tried. In particular thetwo most effective ones were those used in [21] and an additional reconstruc-tion scheme which took into account the shower depth dependence of thesampling fractions and the leakage energy [33]. The energy reconstructionscheme used in [21] was chosen for its simplicity as it could be applied acrossthe entire η range with a simple analytical parametrization. This energy re-construction scheme is mostly based on our best knowledge of the detector as26mplemented in the Monte Carlo simulation. The total reconstructed electro-magnetic (EM) shower energy E rec is evaluated from the measurements of thevisible cell energies in the presampler ( E measP S = P P S E cellvis ), all compartmentsof the accordion added together ( E measAcc = P Acc E cellvis ), the energy measured inthe strips ( E measStrips = P Strips E cellvis ) and the energy measured in the back com-partment ( E measBack = P Back E cellvis ). These measurements are carried out withinthe EM cluster.The basic principles of the energy scheme for the reconstruction of test beamelectrons are reviewed in [21]. The total deposited energy is reconstructed infour steps: (1) the energy upstream of the presampler is evaluated using themeasured presampler energy; (2) the energy deposited between the presamplerand the strips is evaluated using the measured presampler and strips energies;(3) the energy deposited in the accordion is evaluated using the measuredenergy in the accordion cells; (4) the leakage energy is evaluated from theaverage expected leakage at a given position in the detector and the amountof energy in the last accordion compartment. The scheme can be written asfollows: E recraw = a η + b η × E measP S + c η × q E measP S E measStrips + E measAcc d eta + ξ ( E measBack ) (5)yielding the raw reconstructed energy, corresponding to the complete rawshower energy.As shown in Section 4.1, the amount of material is rather uniform in theazimuthal direction, therefore all parameters are derived only as a function ofthe η direction where the variations of material are large.As explained in detail in [21], this energy scheme has numerous advantageswith respect to the one used before [6]. The most prominent are:(i) It optimizes both resolution and linearity.(ii) The parametrization of the energy deposited between the presampler andthe strips compartment of the accordion allows to sample a different partof the shower and to absorb most of the shower depth dependence of theoverall sampling fraction.(iii) The offset in the parametrization of the energy deposited before the pre-sampler allows to account optimally for the energy loss by ionization by thebeam electrons.The main differences with the energy scheme used in [21] are the following:(i) The parameters are derived as a function of η and not as a function of theenergy as the scan is done at fixed energy.(ii) The leakage energy is derived from the energy in the back compartment27f the accordion. The electron energies in the present analysis are higherthan those used in [21] where beam test runs were taken at a fixed η valueof 0.687 corresponding to a region of the detector where the longitudinalleakage is the close to smallest. The expected leakage is much larger here. Ithas to be thoroughly corrected in order to reach a good energy resolution. The parameters of the shower energy reconstruction are derived for all posi-tions in η in steps with the granularity of one middle cell. The parameters arederived by fitting the energies measured within the cluster with respect to theenergies within the complete physical volume of the setup. This allows to takeautomatically into account a rather large lateral leakage typically amountingto ∼ η indices in Fig. 8.These parameters are obtained as follows.- a η and b η : are fitted using the distribution of total energy deposited priorand in the presampler versus the energy measured in the presampler withinthe cluster. As expected, the offset a η scales with the amount of materialand the sampling b η parameter is almost constant.- c η : is fitted using the distribution of total energy deposited between thepresampler and the strips compartment of the accordion versus the squareroot of the product of energy measured in the presampler and the strips(corresponding to the geometrical average of these two energies).- d η : is fitted using the distribution of the total energy deposited in the ac-cordion versus the measured energy in all compartments of the accordionwithin the electromagnetic EM cluster.The discontinuity in the parameters c η and d η is due to the difference in leadthickness between the electrodes A and B. Apart from the discontinuity at thetransition, the accordion total sampling fraction is mostly constant.The variation of the c η parameter reflects the non trivial interplay of twoeffects: the design of the strips was made with a constant longitudinal extentin units of radiation lengths corresponding to about 4 X and the design of thepresampler which has a constant thickness and thus has an increasing depthin units of radiation lengths. Depending on the η coordinate of electrons impinging at 245 GeV on themodules the amount of leakage can reach non negligible values. However, theseamounts are rather small in regions far from the edges of the modules. A simple28
12 0 10 20 30 40 50 a P a r a m . ( G e V ) b P a r a m .
024 0 10 20 30 40 50 c P a r a m . Middle h index d P a r a m . Fig. 8.
Calibration parameters used to reconstruct the cluster energy. In the firstand second upper figures the constant and linear coefficients respectively of theparametrization of the energy deposited before and within the presampler are shown.In the second lowest figure the parameters of the energy reconstruction betweenthe strips and the presampler are illustrated. The last figure represents the accor-dion sampling fraction. The functional parametrization of all the parameters is alsoshown. correction corresponding to adding the average value of the expected leakageenergy as a function of the location of point of impact would be sufficient inregions where the average leakage does not exceed a few GeV. However, inorder to optimize the energy resolution in the regions near the module edges,the correlation between the energy deposited in the back compartment of theaccordion and the energy lost longitudinally can be exploited. The correlationbetween the longitudinal leakage energy and the energy deposited in the Back29ompartment of the accordion is shown in Fig. 9 where the leakage energyis represented as the difference between the leakage and its average value fora given pseudo rapidity. The average leakage is shown in the upper plot ofFig. 10. -4-202468 1 2 3 4 5 6 E Back (GeV) D E L e a k ( G e V ) h = 1 h = 10 h = 20 h = 50 Fig. 9.
Difference between actual and average leakage energy as a function of theenergy deposition in the back compartment for various electron impact points.
The average values of the longitudinal leakage are parametrized as a functionof the pseudo rapidity of the impact position of the electron, as measured bythe strips. The expected distributions of the energy leakage as a function of theenergy measured in the back compartment are fitted for all pseudo rapiditieswith a granularity of one middle accordion cell as follows:∆ E Leak ( η ) = E Leak ( η ) − < E Leak > ( η ) = α η + β η E Back ( η )The β η factor represents the approximately constant ratio of energy leakedlongitudinally and the energy deposited in the back compartment. The α η termcan be interpreted as the weighted average energy in the back compartment i.e. α η = − β η < E Back > .The results of these fits are also parametrized as functions of the pseudorapidity. The leakage is assessed analytically as follows: ξ ( E measBack ) = < E Leak > ( η ) + α η + β η E Back ( η )It is then simply added to the shower energy to form the raw reconstructedenergy.In this procedure the leakage energy depends largely on the energy depositedin the back compartment of the calorimeter. Since the leakage correction isevaluated from the Monte Carlo, it is crucial that the cross talk betweenmiddle and back as described in Section 2.6 be well understood. Because all30
510 0 10 20 30 40 50 L e a k ag e ( G e V ) -5-2.50 0 10 20 30 40 50 O ff s e t a ( G e V )
024 0 10 20 30 40 50
Middle h index S l o p e b Fig. 10.
Calibration parameters used to reconstruct the leakage energy. The upperplot illustrates the average leakage energy as a function of pseudo rapidity. Thesecond and third plots show the variations in η of the constant ( α ) and linear ( β )coefficients used to reconstruct the leakage energy on an event-by-event basis usingthe measured energy in the back compartment. measured values of this effect are compatible, it is corrected for in the MonteCarlo. The leakage correction can then be directly applied to the data.The linear correlation between energy deposition in the back compartmentand the leakage energy is manifest. However, at low values of energy deposi-tion in the back compartment the leakage energy is systematically above thatexpected from a pure linear correlation. This effect arises from events where anearly hard hadronic photon-nucleus interaction occurs within the showeringprocess. The produced hadronic particles escape the volume of the electro-magnetic calorimeter implying a large longitudinal leakage without depositingany significant amount of energy in the back compartment. Such events arerelatively rare but when they occur they carry a lot of energy outside thecalorimeter. In this analysis those events presenting a very large leakage dueto photon-nucleus interaction are removed by the pion hadronic veto. Theevents with a small though non negligible fraction of leakage from a photon-nucleus interaction could not be properly treated in our test beam protocol.31evertheless a correction could be designed for ATLAS where the hadroncalorimeter could catch the hadronic tails of electrons undergoing hadronicinteractions. Energy Reconstruction Scheme Performance
The application of the described energy reconstruction scheme to the MonteCarlo simulation for electrons impinging a single cell of the middle compart-ment results in a non-uniformity of 0.10 %. The uncertainty due to lim-ited statistics of the Monte Carlo samples implies a non uniformity of about0.05 %. The expected systematic non uniformity arising from the Monte Carloparametrization thus amounts to 0.09 %.
Comparison of Data to Monte Carlo
As mentioned in Sec. 2.4.3, the conversion factor f I/E from current to energyis estimated from a comparison of data and the Monte Carlo simulation. Thepresampler and the accordion are normalized independently for each electrodesA and B. For the 2001 running period the normalizations are evaluated from acomparison between M10 data and the Monte Carlo simulation. For the 2002running period the normalization is estimated using the P13 data only. Theconstants derived from the comparison with the module P13 are also appliedto the P15 module. When comparing the ratio of the constants derived fromthe data between electrodes A and B to those directly inferred from firstprinciples, as described in Sec. 2.4.3, in the simulation the difference amountsto less than 1 %.To illustrate the performance of the simulation Fig. 11 displays a comparisonof the visible energy in the data of the module P15 with the Monte Carlo foreach individual compartments of the calorimeter as a function of the η middlecell index. A general very good agreement is observed. In particular, it can benoted that:(i) The overall energy calibration of the module P15 is in good agreement withthat of the module P13 and moreover the inter-calibration of the electrodesA and B is also well reproduced.(ii) The good agreement in the absolute scale of the strips results from a soundtreatment of the large capacitive cross talk.(iii) The overall acceptable agreement in the back compartment illustrates thatcross talk between the middle and back compartments has been correctlytaken into account. 32 P S E n e . ( G e V ) DataMC (2 s Stat.) h F r o n t E n e . ( G e V ) DataMC (2 s Stat.) M i d . E n e . ( G e V ) DataMC (2 s Stat.)
Middle h index B a c k E n e . ( G e V ) DataMC (2 s Stat.)
Fig. 11.
P15 data versus Monte Carlo comparison in the η direction for each com-partment individually: the presampler (PS); strips (front), Middle (Mid.) and Back.The comparison is made at the constant φ middle cell index of 11. Cluster Level Corrections
To improve the accuracy of the energy reconstruction there are three furthereffects that should be taken into account. The first one is the cluster energydependence on the EM particle impact position within one middle cell. Alongthe η and φ directions although the transverse leakage is corrected for thereis a residual energy modulation effect due to the limited extent of the cluster.Along the φ direction there is an additional energy modulation due to thestructure of the interleaved accordion absorbers. These two effects are takeninto account in the correction factor f CI ( η, φ ). The second effect is the energyloss in the electrodes transition region. It is corrected using the factor f T R ( η ).The third effect is the systematic variation in the electronic calibration due to33ifferences in calibration cable lengths. It is corrected by means of the factor f Cables ( η ). The final EM particle energy reconstruction scheme can be writtenas follows: E rec = ( E recraw × f CI ( η, φ ) × f T R ( η ) × f Cables ( η )) In order to correct for the energy modulations using data, a precise and unbi-ased measurement of the impinging electron impact position is necessary. The η position is accurately given by the energy deposition in the strips. A simpleweighted average yields an accurate estimation of the pseudo rapidity of theelectron impact on the calorimeter. In the azimuthal direction the finest gran-ularity is given by middle cells and is eight times coarser than that of stripsalong the η direction. Given the exponentially slender electron shower profilethe azimuthal coordinate given by the weighted average of the energy deposi-tions in the middle compartment is biased towards the center of the cell. Thisbias is referred to as S-shape alluding to the shape of the distribution of thereconstructed position with respect to the original one. It is also present alongthe η direction but can be neglected in these studies. Advantage is thereforetaken of the precise position measurement of the wire chambers located inthe test beam to evaluate this S-shape in order to re-establish an unbiasedestimate of the azimuthal coordinate of the cluster. An energy distribution asa function of η and φ is evaluated for each middle cell of the P13 module.These distributions correspond to sliding averages of five cells in η in order toaccumulate enough statistics to precisely fit the shape of the modulations. Allcells are fitted and the evolution of the fit coefficients are parametrized. Themodulation correction is therefore fully analytical. All spectra in η and φ aredisplayed in Fig. 12 and grouped into four regions in η .The energy modulations in η are parametrized by a parabola as follows: E η − corr. ( η ) = E recraw / h C ( η − η C ) + C ( η − η C ) i (6)where E rec is the raw electron reconstructed energy, η C is the coordinate of themaximum of the parabola. C is the curvature of the parabola. It is directlylinked to the amount of lateral leakage. C is a linear term that introduces anasymmetry in the energy distribution as a function of η . This asymmetry isexpected given the cells geometry. The latter term is always very small. Allcoefficients are then parametrized using simple functional forms throughoutthe module.When the aforementioned S-shape correction is applied, the energy modula-34ions become consistent with an expected two-fold modulation with lengthsin middle cell units of 1 / / E φ − corr. ( φ abs ) = E recraw / [(1 + C ( φ abs − φ C ) + C ( φ abs − φ C ) ) × a π (cos 8 π ( φ abs − φ C ) + a π (cos 16 π ( φ abs − φ C ))] E n e . ( G e V ) h = 0 h = 4 h = 8 h = 12 Electrode A Sector 1 E n e . ( G e V ) h = 16 h = 20 h = 24 h = 28 Electrode A Sector 2 E n e . ( G e V ) h = 36 h = 40 h = 44 Electrode B Sector 1 h (Middle cell Unit) E n e . ( G e V ) h = 48 h = 52 Electrode B Sector 2 -0.25 0 0.25 f (Middle Cell Unit) Fig. 12.
Energy modulations as a function of the η (left plots) and φ (right plots)directions for different regions covering middle cell indices in the η direction andintegrating four cells units both in the azimuthal and pseudo rapidity directions. φ C is the azimuthal coordinate of parabola’s maximum. The coefficients C and C are the parameters of the parabola. The linear term is again negligible.35 π and a π are the amplitudes of the 1 / / Due to the cylindrical geometry of the barrel calorimeter the sampling fre-quency decreases with pseudo rapidity. In order to balance the energy res-olution each module consists of two parts with two separate electrodes anddifferent lead thicknesses. The lead thickness at high pseudo rapidity is smallerin order to increase the sampling fraction and the sampling frequency, giventhat the geometry is unchanged. Unfortunately the transition between theelectrode A at low pseudo rapidity and electrode B at higher pseudo rapidi-ties involves a small uninstrumented region of roughly 2-3 mm.In order to study in detail this transition, special high statistics runs weretaken with the P13 module with electrons uniformly covering the transitionregion. The average energy evaluated from a Gaussian fit to the fully correctedenergy distribution in η -bins of a quarter of one strip cell unit as a function ofthe pseudo rapidity is shown in Fig. 13. Due to the discontinuity in the leadthickness the sampling fractions are also discontinuous, therefore in order tohave a continuous energy distribution across the transition, electron samplingfractions need to be applied at the cell level.At the transition, the electron energy measurement can be underestimated byup to ∼
20 %. The width of the energy gap is approximately three strip cellslarge. A double Fermi-Dirac function added to a Gaussian is used to fit theenergy loss as shown in Fig. 13. In this figure the deterioration factor ( σ T /σ S ,where σ T and σ S are the resolutions at the transition and in the neighboringmiddle cells) in energy resolution is also shown. After the correction is applied,the energy resolution is degraded by a factor ∼ ∼ h Strip Index E n er gy ( G e V ) After CorrectionBefore CorrectionCorrection Function h Strip Index D e g r a d a t i o n f a c t o r After CorrectionBefore Correction
Fig. 13.
In the upper figure the variations of the measured energy across the tran-sition gap between electrodes A and B before and after the correction is applied areillustrated. The functional form used to correct for the energy loss in the transitionis also shown. The lower plot illustrates the degradation of the energy resolutionwith respect to the neighboring cells throughout the transition. count for this effect and the gap distortion was unfolded in the pre-bendingdesign. That was not the case for the absorbers which present a curved tran-sition after bending. In the Monte Carlo this effect was taken into accountand the gap width was tuned to 2.5 mm on the data. This value correspondsprecisely to the one measured on the modules.
The calibration cables carrying the signal from the calibration boards to themotherboards have different lengths. The resulting variation in the input sig-nal attenuation is corrected for with the factor f Cables ( η ) which is evaluatedfrom detailed measurements of the cable lengths. Because the attenuation oc-curs before the calibration signal injection it introduces a small bias in thecalibration procedure. The correction is made a posteriori at the cluster levelin each layer. It amounts to ∼ .7 Modules Uniformity
When all corrections are applied the energy distribution for each run corre-sponding to one middle cell unit for all barrel modules is fitted with a Gaussianform starting from -1.5 σ off the mean value to determine both the average en-ergy and resolution. All problematic cells described in Sec. 4.2 are excluded.The mean energies resulting from the fits to the energy distribution corre-sponding to the FT0 of all barrel modules as a function of η and for all φ values are shown in Fig. 14. η RangeModule Overall [1-54] Electrode A [1-31] Electrode B [32-54]M10 0.48 ± ± ± ± ± ± ± ± ± Non-uniformity expressed in terms of RMS values of the dispersion ofthe average energies in the FT0 domain, overall and for each electrode A and Bindependently. The statistical uncertainties are also displayed.
A measure of the non-uniformity at the granularity level of one middle cell isgiven by the dispersion (RMS/ < E > ) of the measured averages. The valuesobtained are summarized in Table 6.Non uniformities of the calorimeter response are typically of the order of onehalf percent.The widths of the aforementioned Gaussian energy fits as a function of η andfor all values of φ pertaining to the FT0 are shown in Fig. 15. As can be seenin Fig. 15 in module M10 around the middle cell η index of 14 and in themodules P13 and P15 around the index 48, a degradation of the resolutionis observed. These effects are due to bad presampler cells. An overall betterenergy resolution is obtained in the module P15, although the modulationcorrections were derived from the module P13. The origin of this differencecannot be easily traced back. Matter effects could be responsible for differencesin local energy resolution between the module P13 and P15 either at the levelof the constant term or due to differences in the stochastic term. Differencesin manufacturing quality could produce such an effect.The general increasing trend of the resolution with respect to pseudo rapidityis in part due to the increase of the stochastic term and in part due to theincrease of material upstream. 38 M e a n E n er gy ( G e V ) P13 f =9 f =10 f =11 f =12 f =13 f =14
25 50 75 100
E = 245.1 GeVRMS/E = 0.43 % M e a n E n er gy ( G e V ) P15 f =9 f =10 f =11 f =12 f =13 f =14
25 50 75 100
E = 245.0 GeVRMS/E = 0.40 % Middle h index M e a n E n er gy ( G e V ) M10 f =9 f =10 f =11 f =12 f =13 f =14
25 50 75 100
E = 244.8 GeVRMS/E = 0.48 % Fig. 14.
Summary of the energy measurements for each barrel module for all cells ofthe FT0 as function of pseudo rapidity. The overall distribution is shown and thecorresponding average and dispersion values are indicated. The bands correspondsto twice the dispersion of the measurements.
As expected, at the electrode transition where the absorber thickness changes,a discontinuity in the energy resolution is observed.
Relative Energy Scale
The P13 and P15 modules were exposed to the test beam with the samecalibration and readout electronics and with the same upstream material.The absolute energy scales for these modules should therefore be very close orit could imply that a problem at the construction level occurred. The averagereconstructed energy values for the P13 and P15 modules are 245.1 ± ± .40.60.811.2 0 10 20 30 40 50 P e a k R e s o l u t i o n ( % ) % f =9 f =10 f =11 f =12 f =13 f =14 P13
20 40 60 800.40.60.811.2 0 10 20 30 40 50 P e a k R e s o l u t i o n ( % ) % f =9 f =10 f =11 f =12 f =13 f =14 P15
20 40 60 800.40.60.811.2 0 10 20 30 40 50
Middle h index P e a k R e s o l u t i o n ( % ) % f =9 f =10 f =11 f =12 f =13 f =14 M10
20 40 60 80
Fig. 15.
The local resolution of the cell energy measurements for all modules and allcells as a function of pseudo rapidity. less than 0.1 %. This global non-uniformity contribution to the overall energyresolution is small compared to the non-uniformities observed within eachmodule.
Uncorrelated Non Uniformities
In order to disentangle the correlated non uniformities from the uncorrelatedones, for each cell of the scan the ratio of the average energies is computed.The distributions plotted in Fig. 16 are averages in φ and in η of the meanenergy in each cell and their ratio. The uniformity of the ratio corresponds tothe combination of the non correlated uniformities of the two modules. Thedispersion of the distribution of the ratios amounts to 0.30 %. The variationsin azimuthal angle are small as shown in Fig. 16.40 .9911.011.02 0 10 20 30 40 50 Middle h index N o r m a li ze d E n er g i e s P15 Norm.P13 Norm.P15/P13 Ratio
Middle f index Fig. 16.
Profiles of the normalized energy distributions as a function of pseudo ra-pidity and azimuthal angle for the modules P13 and P15 and their ratio. Theseprofiles are obtained by averaging over the FT0 cells in φ . Correlated Non Uniformities
Correlated non uniformities are typically due to the reconstruction method,inaccuracies in the Monte Carlo simulation or inaccuracies in the energy cor-rections. Since the P13 and P15 modules used the same front-end and calibra-tion electronics their related non-uniformities are accounted for as correlated.
Module Section Total Correlated Non CorrelatedOverall 0.43 % 0.34 % 0.26 %P13 Electrode A 0.35 % 0.29 % 0.20 %Electrode B 0.48 % 0.34 % 0.34 %Overall 0.40 % 0.34 % 0.21 %P15 Electrode A 0.36 % 0.29 % 0.21 %Electrode B 0.43 % 0.34 % 0.26 %Table 7.
Details of the correlated and non correlated non-uniformities for the P13and P15 modules. The values corresponding to the electrode A and B are also givenseparately.
Using the dispersion of the ratio of the measured energies for the modules P13and P15, the correlated and the uncorrelated contributions to the uniformitycan be separated. The values of correlated and non correlated non uniformitiesare displayed in Table 7. 41 .11
Contribution to the Non Uniformity
All contributions to the non uniformities of the calorimeter response cannotbe easily disentangled. Merging the beam test results with the quality controlmeasurements, the electronics performance evaluation and the monte carlosimulation, a non exhaustive list of sources of non uniformity, displaying themost prominent contributions, is proposed hereafter.
The calibration system was built within very strict requirements regarding theprecision of the electronics components. The entire system was thoroughly re-viewed and tested. The precision of the three possible sources of non uniformity(pulsers, injection resistors and cables) was estimated. All calibration boardswere measured on a test bench and were found to fulfill the requirements.Non uniformities arising from the calibration system are detailed in 2.3 anddisplayed in Table 8. The overall non uniformities amounts to ∼ Assuming that the calibration system is uniform, the properly calibrated read-out electronics should not contribute to non-uniformities. However, small dif-ferences in the readout response could infer second order effects that couldimply variations in the calorimeter response. In order to assess these varia-tions, data was taken with the P15 module where two middle cells Front EndBoards (FEB) were permuted. The new FEB configuration was calibrated andnew data were taken. The variation in the energy measurement with the boardswap amounted to approximatively 0.1 %.
For various runs taken on the P15 module the data were reconstructed usingthe two methods described in Sec. 2.5. In order to assess the possible nonuniformities arising from the signal reconstruction method the dispersion ofthe differences in the average energy between the two methods is taken. Theobserved RMS amounts to 0.25 %. This estimate is likely to be an overestimateof the intrinsic bias of the method. 42 .11.4 Monte Carlo Simulation
The full Monte Carlo simulation of the experimental setup cannot perfectlyreproduce the actual data. Non uniformities in the calorimeter response canthus arise from the simulation. The precision of the Monte Carlo descriptionwill directly impact the energy measurement. The difference between dataand Monte Carlo presented in Sec. 4.5 amounts to 0.08 %. This figure, derivedfrom the dispersion of the distribution of the difference in measured energiesbetween data and Monte Carlo, represents the expected non uniformity arisingfrom the simulation inaccuracies.
The energy reconstruction scheme involves a large number of parameteriza-tions and fits. Inaccuracies of these parameterizations will impact the energymeasurements and can induce a non uniform response. A measure of the in-accuracies of the parametrization is the residual systematic non uniformity inthe Monte Carlo simulation. As was shown in Sec. 4.4, this effect amounts to0.09 %.
The non uniformities related to the construction of the modules are the dom-inant source of non-correlated non uniformities. The main sources of the non-uniformity in the construction of modules are the lead thickness and the gapdispersion.(i) The impact of the variations in lead thickness on the EM energy mea-surements was assessed and a scaling factor of 0.6 was found between thedispersion of the lead thickness and the dispersion of the EM energies.(ii) Similarly the impact of the variations of the gap were studied and a scalingfactor of 0.4 was found between the dispersion of the gaps and that of theEM energy measurements.From the measurements presented in Sec. 1.4.1 the expected non uniformityobtained are displayed in Table 8.
The energy modulation corrections can impact the calorimeter response toelectrons at different levels either by affecting the uniformity or the localconstant term. 43he modulation corrections were evaluated on the module P13 only and werethen applied to all other modules. For this reason it is difficult to disentanglethe correlated from the non correlated part of the correction. For the sakeof simplicity this effect will be considered as exclusively non correlated. Toevaluate its impact both on the uniformity and on the local constant term,the complete analysis is done restricting the measurement to a small regionaccounting for 20 % of the cell around its center. The differences found are of0.14 % and 0.10 % for the modules P13 and P15 respectively.
In order to check the stability of the energy reconstruction, reference cells wereperiodically scanned with the 245 GeV electron beam. Two cells were chosenfor the modules P13 and P15 both at a middle cell φ index of 10 and at η indices of 12 and 36. For the module M10 only one reference cell was takenat an η index of 34. The variation of the energy reconstruction with time isillustrated in Fig. 17. Day V a r i a t i o n w . r . t A v er ag e E n er gy M10 ( h =34, f =10)P13 ( h =12, f =10) P13 ( h =36, f =10)P15 ( h =12, f =10) P15 ( h =36, f =10) Fig. 17.
Energy measurements for two reference cells in modules P13 and P15 andin module M10, as a function of time. The ± / variation band is also indicated. From the observed variations, the impact on the energy measurements areestimated to be 0.09 %, 0.15 % and 0.16 % for the modules P13, P15 and M10respectively.
All known contributions to the non uniformity are summarized in Table 8. Thegood agreement achieved between the data and the expectation illustrates that44he most sizable contributions to the non uniformities have been identified.
Correlated Contributions Impact on UniformityCalibration 0.23 %Readout Electronics 0.10 %Signal Reconstruction 0.25 %Monte Carlo 0.08 %Energy Scheme 0.09 %Overall ( data ) 0.38 % ( )Uncorrelated Contribution P13 P15Lead Thickness 0.09 % 0.14 %Gap dispersion 0.18 % 0.12 %Energy Modulation 0.14 % 0.10 %Time Stability 0.09 % 0.15 %Overall ( data ) 0.26 % ( ) 0.25 % ( )Table 8.
Detail of the expected contributions to the uniformity and to the constantterm.
The module P15 displays a slightly better uniformity than the other modules.None of the control measurements support this observation. However, as shownin Sec. 1.4.1 the granularity of the control measurements was not particularlyhigh. Manufacturing differences within such granularity may not be observablebut could impact the uniformity.
Local and Overall Constant Term
The distributions of all energy measurements for each barrel module are shownin Fig. 18. These distributions showing the overall energy measurement reso-lution throughout each module are fitted with a simple Gaussian form startingfrom -1.5 σ off the mean values.The corresponding overall resolutions are 0.93 %, 0.85 % and 0.96 % for themodules P13, P15 and M10 respectively. The main components of these reso-lutions are: (i) the non-uniformity of the modules, (ii) the local constant terms,(iii) the stochastic terms and (iv) the electronic noise.45he stochastic term (iii) has been precisely measured in [21] at one fixed pointand more broadly estimated over the full range in pseudo rapidity in [6]. Takinginto account the η -dependence of the stochastic term as derived from [6],the noise as evaluated from random trigger events, the local resolutions andthe beam energy spread amounting to 0.08 % a local constant term can bederived for each cell. The distribution of local constant terms yields an averageof 0.30 %, 0.25 % and 0.36 % for the P13, P15 and M10 modules respectively.The dispersion of the local constant term is typically of 0.11 % absolute.The overall constant term for all modules can be derived from the averagelocal constant terms by simply adding the measured non-uniformities. Theglobal constant terms obtained are thus 0.52 %, 0.48 % and 0.60 % for themodules P13, P15 and M10, respectively. These results are derived underthe assumption that the stochastic term is the same in all modules. A slightvariation in the stochastic term could also explain the differencies observedbetween the P13 and P15 resolutions. Cls. Ene. (GeV) L i n e s h a p e s Cls. Ene. (GeV)
P13 m = 245.2 GeV s = 2.21 GeV4.4 Mevts
230 240 250
Cls. Ene. (GeV)
P15 m = 245.1 GeV s = 2.01 GeV2.1 Mevts
230 240 250
Cls. Ene. (GeV)
M10 m = 244.9 GeV s = 2.36 GeV3.6 Mevts Fig. 18.
The energy lineshapes for the barrel modules P13, P15 and M10 containingrespectively 4.4, 2.1 and 3.6 million events. The simple gaussian fits to energy peakare displayed and the fit parameters are indicated.
The constant terms (average local or global) are considerably better for themodule P15 with respect to the other modules. This observation supports thehypothesis that the module P15 was better manufactured, but could also bedue a better stochastic term. All results are summarized in Table 16. The φ -dependence of the stochastic term is assumed to be negligible here. arrel modulesModule P13 P15 M10 < E > RMS/ < E > σ/µ Local Constant Term 0.30 % 0.25 % 0.36 %Global Constant Term 0.52 % 0.47 % 0.60 %
Table 9.
Mean energy, non-uniformity, average energy resolution and global constantterm for the three tested barrel modules over the entire analysis region.
Energy Reconstruction
The electron energy is reconstructed as in the barrel by summing the cali-brated energies deposited in the three calorimeter compartments around thecell with the largest energy deposit in the middle compartment. The choices ofcluster sizes result from the best compromise between noise and energy leak-age. Table 10 summarizes the cluster size in the three compartments. It canbe noted that the cluster size changes dramatically in the front compartmentdue to the variations in the cell granularity. As was the case in the barrelelectron clusters the choice of one or two strip cells in φ relies upon whetherthe shower develops near the cell center or not. Outer wheel Inner wheel η -range [1.5, 1.8] [1.8, 2.0] [2.0, 2.4] [2.4, 2.5] [2.5, 3.2]Front 23 × × × × × × × × Cluster size ( ∆ η cell × ∆ φ cell ) per layer around cell with maximum energydeposit. .1.2 Reconstruction Scheme As mentioned in Sec. 3, the barrel and endcap modules were tested in differentbeam lines at two different maximum energies namely 245 GeV and 119 GeVrespectively. At this lower beam electron energy the relative impact of thelongitudinal leakage is extremely small but the effect of inactive material islarger. Another major difference intrinsic to the detector is the absence ofa presampler. However, the material upstream of the calorimeter is approxi-mately constant. For these reasons the energy reconstruction scheme can beconsiderably simplified at first order in the endcaps with respect to that usedin the barrel. A single normalization factor for all modules can thus be used toderive the total energy from the visible energy measured in the liquid argon.It is derived after all corrections are applied.Nevertheless two main complications arise: the first one from the continuousdecrease of the liquid argon gap with pseudo rapidity (since the HV is seton a sector basis, the signal response will vary with η ); the second from theeffective variations of the cluster size with the pseudo rapidity. The fractionof the total 119 GeV electron energy contained in the cluster exceeds 92 % athigh η and even more at low η . A single ad hoc correction can be derived fromthe data to correct for both effects simultaneously. This correction is describedin Sec. 5.2.1 Cell Level Corrections
The fact that the liquid argon gap thickness decreases continuously along η whereas the high voltage changes by steps translates into a linear increase insignal response with η , within each high voltage sector. The transverse leakagewill affect the energy in an opposite manner and a priori not completelylinearly, however its effect is expected to be smaller. The overall variation isillustrated in Fig. 19, where the seven (two) HV sectors of the outer (inner)wheel are separated with vertical dashed lines. A good agreement is achievedwith a full Monte Carlo GEANT simulation [32]. The crack between thetwo wheels around η = 2 . η -position (taken at its center) and its HV sector ( l ), by : The 2 % discrepancy observed in B4 sector is not understood but could be dueto a bad tuning of the HV value of ∼
50 V / 1500 V. h cell E n e r g y ( G e V ) B1 B2 B3 B4 B5 B6 B7 B81.6 1.8 2.0 2.1 2.3 2.5 2.8 h true Fig. 19.
Energy averaged over φ for one module as a function of η before high voltagecorrection. The vertical dashed lines separate the high voltage sectors and the full lineat η = 2 . separates the outer and the inner wheel. The full (empty) dots correspondto cells inside (outside) the analysis region. The stars correspond to the full MonteCarlo simulation results. E cellHV − corr. ( η, l ) = E cell · β l α l · ( η − η lcenter ) (7)where η lcenter is the η -value at the center of HV sector l . The coefficients α l and β l are the correction parameters of sector l , β l being a normalizationfactor, close to 1, accounting also for inaccurate high voltage settings. Theyare determined by a linear fit. The inner wheel case is more complicated andthe resulting parameters are slightly biased. The results obtained for α l and β l in the eight scanned HV sectors are shown in Fig. 20 for the three testedmodules.A good agreement between modules is observed and α depends very weaklyon η . Therefore a single value of α = 0 .
49, in good agreement with the fullMonte Carlo simulation, is used for all modules.
Along the φ direction, the gap thickness is in principle kept constant by thehoneycomb spacers. However, the energies measured in the test beam show anunexpected non-uniformity along φ , almost at the percent level [34,35]. Thiseffect can be correlated with the variations of middle cell capacitance along φ measured independently, as shown in Fig. 21 for ECC0. The φ -dependence of The first HV sector, covering the η -range [1.375-1.5], has not been completelyscanned (at most 2 cells in η ) and is not included in the analysis. .20.30.40.50.60.7 10 20 30 40 501.5 3.2 0.911.11.2 10 20 30 40 50 h cell a B1 B2 B3 B4 B5 B6 B7 B8ECC0ECC1ECC5Simulations h true h cell b B1 B2 B3 B4 B5 B6 B7 B8 h true Fig. 20.
High voltage correction parameters α (left) and β (right) obtained in theeight scanned HV sectors for the three tested modules. Results have been averagedover φ . The vertical full line at η = 2 . separates the outer and the inner wheel.The stars correspond to the full Monte Carlo simulation results. the energy can thus be explained by local fluctuations of the gap thickness,generated during the module stacking. The effect is almost independent of η . Even if it corresponds to small absolute deviations (the gap thickness isroughly 3 mm at low η and 1 mm at high η , 1 % represents only a few tens ofmicrons), it must be corrected in order to achieve the best response uniformity. F cell N o n - un i f o r m i t y i n F ( % ) ECC0
EnergyCapacitance-3-2-10123 0 5 10 15 20 25 30
Fig. 21.
Variation along the φ direction of the measured ECC0 outer wheel mid-dle cell capacitance (red triangles) and of the energy measured in beam test (blackpoints). All points have been averaged over η . The energy is then corrected by weighing each cell in the following way : E cellcapa − corr. ( φ ) = E cell / C φ < C φ > ! α (8)where C φ is the cell capacitance, < C φ > is its average over all φ and α thehigh voltage correction parameter (see section 5.2.1). The effect is assumedto be independent of the depth. The middle cell measurements are used for50ll compartments. The α exponent was empirically chosen but was found toyield a near to optimal uniformity. It illustrates the interplay between the highvoltage and the capacitance corrections. Such a correction is not performedin the ECC5 inner wheel, whose uniformity along φ is very good. For ECC1,no accurate capacitance measurement was made. An ad hoc correction is thusextracted from the φ -dependence of the energy averaged over η . As it correctsfor local stacking effects, the correction has to be specific for each cell and eachmodule. In ATLAS the correction based on the capacitance measurementscould be further refined by inter calibrating φ -slices of the calorimeter with Z → e + e − events. Cluster Level Corrections
Another problem, which appeared on ECC1, was that two electrode sides,which were on spare lines, were not holding the high voltage, inducing anenergy loss depending on the event impact point position in φ with respectto the faulty electrode. The dependence of the cluster energy with φ wasparametrized and corrected with a parabola. The energy resolution of theaffected cells is degraded by ∼
50 % and the uniformity in the correspondingHV zone (∆ η × ∆ φ ∼ . × .
4) is degraded by ∼
20 %. η and φ energy modulation corrections To correct for energy variations along the η direction a parametrization simi-lar to that used in the barrel is considered. However, as the transverse size ofthe electromagnetic shower is constant and the cell dimension decreases withpseudo rapidity, the leakage is expected to increase with η , and thus the abso-lute value of the quadratic term of the parabola is expected to increase withpseudo rapidity. This effect is sizable only in EC modules and a good agree-ment is achieved among the three tested modules. The quadratic parameteris linearly parametrized as a function of η [34].The φ modulation for EC modules is fitted and corrected for with the followingfunction [36] : E φ − corr. ( φ abs ) = E/ X i =1 a i cos [2 πi ( φ abs − ∆ φ )] + b sin [2 πφ abs ] ! (9)where φ abs is in absorber units, a and a are the coefficients of the even51omponent (it has been checked that only two terms are necessary), b thecoefficient of the odd component one and ∆ φ a phase shift. The parameters ofthe fits are displayed in Fig. 22 for all three endcap modules. A good agreementbetween the fitted parameters for the different modules is observed. Giventhe non trivial geometry of the endcap modules this result highlights themanufacturing quality of the modules. As was the case for the barrel modules,a single correction derived from a fit of the coefficients can be used. -0.02-0.015-0.01-0.00500.0050.010.0150.02 1.6 1.8 2 2.2 2.4 h P a r a m e t er a ECC0ECC1ECC5 -0.02-0.015-0.01-0.00500.0050.010.0150.02 1.6 1.8 2 2.2 2.4 h P a r a m e t er a -0.02-0.015-0.01-0.00500.0050.010.0150.02 1.6 1.8 2 2.2 2.4 h P a r a m e t er b -0.2-0.15-0.1-0.0500.050.10.150.2 1.6 1.8 2 2.2 2.4 h P a r a m e t er Df Fig. 22.
Coefficients of φ -modulation corrections, averaged over φ , as a functionof η for the three tested modules. Their linear or parabolic parametrisations aresuperimposed. Modules uniformity
The mean energies as reconstructed from a gaussian fit to the energy distri-bution after all corrections are shown in Fig. 23 for all the cells and for thethree tested modules. Their dispersion across the outer wheel analysis regionis approximately 0.6 % for all modules [34]. It is better for ECC1 because an ad hoc capacitance correction was used. A similar result is obtained for theECC5 inner wheel: the response non-uniformity over the 25 cells is approxi-52ately 0.6 %.With the high voltage correction the uniformity is of the order of 1 % (0.78 %for ECC0, 0.86 % for ECC1 and 0.65 % for ECC5). The capacitance correctionyields an uniformity close to final one. Cluster level corrections do not signif-icantly impact the module response uniformity, but they improve the energyresolutions. The problematic channels (for instance for high voltage failuresin ECC1 and ECC5), that have been kept, do not degrade the results. If theywere excluded, the non-uniformity would improve by less than 0.01 %. Theseresults are summarized in Table 11. M e a n E n er gy ( G e V ) f =2 f =3 f =4 f =5 f =6 f =7 f =8 f =9 f =10 f =11 f =12 f =13 f =14 f =15 f =16 f =17 f =18 f =19 f =20 f =21 f =22 f =23 f =24 f =25 f =26 f =27 f =28 f =29
100 200
E = 118.8 GeVRMS/E = 0.59 % ECC0 M e a n E ( G e V ) ECC1
100 200
E = 119.1 GeVRMS/E = 0.52 % Middle h index M e a n E ( G e V ) ECC5
100 200
E = 119.3 GeVRMS/E = 0.57 % Fig. 23.
Mean reconstructed energy as a function of the hit cell position in η fora 119 GeV electron beam. Results are shown for the outer wheel of all three testedmodules. .5 Resolution and Overall Constant Term
The energy resolution as derived from the fit to the energy distribution for allcells and after all corrections are applied is shown in Fig. 24. When quadrat-ically subtracting the electronic noise term of ∼
200 MeV and a beam spreadof 0.07 % the energy resolutions are compatible with those reported in [7].Assuming an average local constant term of 0.35 % an average value of thestochastic term of 11.4 ± / √ E is found. P e a k R e s o l u t i o n ( % ) %
100 200
ECC0 P e a k R e s o l u t i o n ( % ) %
100 200
ECC1
Middle h index P e a k R e s o l u t i o n ( % ) %
100 200
ECC5
Fig. 24.
Reconstructed energy resolutions as a function of the hit cell position in η for a 119 GeV electron beam. Results are shown for the three tested modules (outerwheel). The legend used for the different φ values here is the same as in Fig. 23 The overall constant term of the energy resolution is estimated from the cu-mulative energy distribution of all cells of the analysis domain. These energylineshapes are illustrated in Fig. 25 for all tested modules. Each of these en-54 uter wheel Inner wheelModule ECC0 ECC1 ECC5 ECC5 < E >
RMS/ < E > σ/µ Constant Term 0.70 % 0.72 % 0.61 % 0.78 %
Table 11.
Mean energy and non-uniformity of the three tested modules over the wholeanalysis region. For the outer (inner) wheel, statistical errors on the mean energyare ∼ ∼ Cls. Ene. (GeV) L i n e s h a p e s ECC0 m = 118.8 GeV s = 1.51 GeV5.5 Mevts
110 115 120
Cls. Ene. (GeV)
ECC1 m = 119.1 GeV s = 1.52 GeV5.5 Mevts
110 115 120
Cls. Ene. (GeV)
ECC5 m = 119.3 GeV s = 1.45 GeV6.4 Mevts Fig. 25.
The energy lineshapes for the endcap modules ECC0, ECC1 and ECC5containing respectively 5.5, 5.5 and 6.4 million events . The simple gaussian fits toenergy peak are displayed and the fit parameters are indicated. ergy spectra is fitted with a simple Gaussian form starting from -1.5 σ off themean value. When unfolding a sampling term of ∼ ± / an elec-tronic noise term of ∼
200 MeV and the beam spread contribution amountingto ∼ ∼ CONCLUSION
The response uniformity of the ATLAS liquid argon electromagnetic calorime-ter to high energy electrons has been studied in the pseudo rapidity range55rom 0 to 3.2. These results encompass both the barrel and endcap calorime-ters which were independently tested in different beam lines using 245 and119 GeV electrons respectively. The uniformity in the pseudo rapidity rangefrom 0 to 2.4 is illustrated in Fig. 26. h N o r m . A v . E n er g i e s +2 % +1 % -1 % -2 % All Barrel Modules 0.43 % All EMEC 0.62 % Overall Barrel and EMEC 0.54 % (882 Cells) (2455 Cells) O V E R L A P Fig. 26.
Two dimensional histogram of the average energies measured in all cellsof all tested modules normalized to the mean energy of the modules. In the barrelthe energies were ∼
245 GeV and ∼
120 GeV in the EMEC. The distributions arenormalized to the number of middle cells scanned in φ for each value of η . For the barrel modules a modified version of the energy reconstruction schemedevelopped in [21] mostly based on a full Monte Carlo simulation is used.Most potential sources of non-uniformity were reviewed and their impact wasindependently estimated. When comparing the estimated non-uniformity tothe measured one a very good agreement is observed thus indicating thatthe sources of non-uniformity are well understood. For the endcap modulesthe material upstream of the calorimeter is approximately constant, a simplerenergy reconstruction scheme is thus applied. A full Monte Carlo simulationaccounting for the complex geometry of EMEC modules is performed and isin good agreement with the data.Non uniformities of the response do not exceed 7 / . Overall constant termsin the energy resolution are derived and range between 5 / and 7 / . Suchperformance is within the calorimeter design expectations.56 CKNOWLEDGMENTS
We would like to thank the accelerator division for the good working conditionsin the H8 and H6 beam lines. We are indebted to our technicians for theircontribution to the construction and running of all modules. Those of us fromnon-member states wish to thank CERN for its hospitality.
References [1] B. Aubert et al. (RD3 Collaboration), Nucl. Instrum. Meth. A , 438 (1991).[2] B. Aubert et al. (RD3 Collaboration), Nucl. Instrum. Meth. A , 467 (1992).[3] B. Aubert et al. (RD3 Collaboration), Nucl. Instrum. Meth. A , 118 (1993).[4] D. M. Gingrich et al. (RD3 Collaboration), Nucl. Instrum. Meth. A , 290(1995).[5] D. M. Gingrich et al. (RD3 Collaboration), Nucl. Instrum. Meth. A , 398(1997).[6] B. Aubert et al. (The ATLAS Electromagnetic Liquid argon CalorimeterGroup), Nucl. Instrum. Meth. A , 202 (2003).[7] B. Aubert et al. (The ATLAS Electromagnetic Liquid argon CalorimeterGroup), Nucl. Instrum. Meth. A , 178 (2003).[8] ATLAS Collaboration, Liquid Argon Calorimeter Technical Design Report,CERN-LHCC/96-41.[9] B. Aubert et al. , ATLAS Electromagnetic Liquid Argon Calorimeter group
Nucl. Instrum. Methods A (2006) 388.[10] B. Aubert et al. , ATLAS Electromagnetic Liquid Argon Calorimeter group Nucl. Instrum. Methods A (2005) 558.[11] M. L. Andrieux et al. , Nucl. Instrum. Methods A (2002) 316.[12] J. Colas et al. , ATLAS Note ATLAS-LARG-2000-004.[13] P. Pralavorio and D. Sauvage, ATLAS Note ATL-LARG-2001-006.[14] F. Berny et al. , ATLAS Note ATL-LARG-2003-005.[15] G. Garcia et al. , Nucl. Instrum. Meth. A , 513 (1998).[16] P. Barrillon et al. , ATLAS Note ATLAS-LARG-2003-004.[17] S. Baffioni et al. , ATLAS Note ATL-LARG-PUB-2007-005.[18] J. Colas et al. ATLAS Note ATL-LARG-2000-006, 2000.
19] W. Willis and V. Radeka. Nucl. Instrum. Meth. A (1974).[20] W.E. Cleland and E.G. Stern. Nucl. Instrum. Meth. A (1984).[21] M. Aharrouche et al. , Nucl. Instrum. Meth. A , 601 (2006).[22] M. Lefebvre, G. Parrour and P. Petroff, RD3 internal note 41, 1993.[23] M. Citterio, M. Delmastro and M. Fanti, ATLAS Note ATL-LARG-2001-018,2001.[24] L. Neukermans, P.Perrodo and R. Zitoun, ATLAS Note ATL-LARG-2001-008,2001.[25] D. Banfi, M. Delmastro and M. Fanti.
Journal of Instrumentation , 1:P08001,2006.[26] D. Prieur. ATLAS Note ATL-LARG-2005-001, 2005.[27] C. De La Taille, L. Serin, ATLAS Note ATL-LARG-1995-029, 1995.[28] W. Walkowiak, ATLAS Note ATL-LARG-99-009, 1999.[29] F. Hubaut, B. Laforge, D. Lacour, F. Orsini, ATLAS Note ATL-LARG-2000-007, 2000.[30] F. Hubaut, ATLAS Note ATL-LARG-2000-009.[31] B. Dekhissi, J. Derkaoui, A. El-Kharrim, F. Hubaut, F. Maaroufi andP. Pralavorio, ATLAS Note ATL-LARG-2003-012.[32] S. Agostinelli et al. (GEANT4 Collaboration), Nucl. Instrum. Meth. A ,250 (2003).[33] G. Graziani, ATLAS Note ATL-LARG-2004-001.[34] F. Hubaut and C. Serfon, ATLAS Note ATL-LARG-2004-015.[35] S. Rodier, PhD Thesis CERN-THESIS-2004-001 (2003).[36] G. Garcia, PhD Thesis DESY-THESIS-2000-010 (2000).,250 (2003).[33] G. Graziani, ATLAS Note ATL-LARG-2004-001.[34] F. Hubaut and C. Serfon, ATLAS Note ATL-LARG-2004-015.[35] S. Rodier, PhD Thesis CERN-THESIS-2004-001 (2003).[36] G. Garcia, PhD Thesis DESY-THESIS-2000-010 (2000).