CERN - European Organization for Nuclear Research

LCD-Note-2010-001

Comparison of the Performance of Tungsten and SteelHadronic Sampling Calorimeters

Peter Speckmayer∗, Christian Grefe∗†

∗ CERN, Switzerland, † Bonn University, Germany

February 8, 2010

Abstract

In this note the performance of tungsten and steel hadronic sampling calorimeters isstudied using GEANT4 simulations. Various configurations with different samplingratios and total calorimeter lengths for both materials have been investigated. Pionsof up to 300 GeV have been simulated in all configurations and the energy has beenreconstructed using a neural network.

Taking into account leakage and intrinsic resolution for the different calorimeterconfigurations, an optimal configuration depending on the HCAL size has beenfound. The impact of a tail-catcher providing information on leakage into the coil,which will be outside of the calorimeters and constraining their size in future highenergy collider experiments, has also been studied.

1 Introduction

Space, cost and technical constraints in typical high energy experimentsput a limit on the mate-rial and depth of the hadronic calorimeter (HCAL). A reduced depth leadsto parts of the show-ers (especially those caused by high energy hadrons) leaking out downstream of the calorimeter,thus reducing the resolution of the energy measurement.

In this study, sampling calorimeters using steel and tungsten as absorber material were in-vestigated using GEANT4 simulations[1, 2]. The passive material thickness was varied from5 mm up to 30 mm for both absorber materials. The active layers, consisting of5 mm Scintilla-tor (Polystyrene) plates, and the electronics and readout, representedby 2.5 mm of G10, wereidentical in all simulated setups.

The aim of this study is to estimate the energy resolution and linearity of single pions forsteel and tungsten calorimeters for a variety of sampling ratios. The pions are simulated withan energy of up to 300 GeV which can be assumed to resemble the leading particles energy ofhadronic jets of at least 750 GeV. Since a perfect readout and no noise is assumed, this study willnot provide accurate numbers for a real detector. However, it will provide information to makea reasonable decision on the depth of the hadronic calorimeter and the thickness of the passivelayers for tungsten and steel as well as a mixture of both materials.

As shown in [3], the quality of the energy reconstruction with particle flow algorithms ofhigh jet energies is correlated to the “conventional” pure calorimetric energy measurements.Therefore, optimizing the pure calorimetric performance of the detector is animportant step, beit for particle flow or even more for a classical energy measurement.

2

2 Simulation

For this study several toy calorimeters have been simulated with the SLIC-framework version2.4.5[4] which uses GEANT4 version 9.2.4 to simulate the interactions of particles with matter.

For each toy calorimeter configuration a sample of 100000π+ events have been simulatedwith thegeneral particle source (gps) from the GEANT4-package using the parameters shownin App. A. The π+ energies within each sample range from 1 GeV to 300 GeV following anexponential drop with twice as many events at 1 GeV as at 300 GeV.

The interaction with matter was simulated using the GEANT4 physics list QGSPBERT HP.The high precision physics list was favored over the default QGSPBERT physics list becausethe detailed simulation of neutrons, especially for the tungsten case, was found to be crucial[5].

The origin of the particles is at the coordinatesx = y = z = 0. The particles are randomly shotinto a cone with an opening angle of±1◦ around the longitudinal axis of the toy calorimeter.This was introduced in order to avoid systematic errors from always hitting the same area (e.g.cracks between the cells) of the calorimeter. The particle first crosses thetracking region, whichis empty for the toy calorimeters, until it enters the calorimeter where a particle shower is builtup.

The toy calorimeters are composed of a varying number of layers depending on the absorberthickness. The total length always corresponds to much more than 20λ (nuclear interactionlength) in order to guarantee full longitudinal shower containment. Each ofthe calorimeterlayers consists of a passive layer (W or Steel or a mixture of both), an active layer (Scintillator)and a 0.25 mm thick G10-layer. The thicknesses of the passive layer are given in Sec.2.1.Each active layer is divided into 1cm×1cm readout cells. The transverse dimension of the toycalorimeters is 5m×5m in order to avoid shower leakage on the sides.

In order to compare the effect of calorimeter depth in terms of interaction lengths withoutdefining a large number of detector geometries, the region of interest is onlydefined during eventreconstruction. Therefore only one sample of 100000π+-events per passive layer configurationwas simulated (see Sec.2.1) and the decision to use a certain hit during reconstruction is basedon its position in the toy calorimeter. Using this approach it is possible to investigatethe impactof dead regions in the calorimeter, e.g. a fewλ of coil in between the main HCAL and apossible tail-catcher, without defining a new detector geometry for every setup. In this study weassumed a coil of 2λ thickness. This is approximately the same amount of material as it is inthe coil of the CMS experiment[6] as well as in the proposed detector designs for a future linearcollider[7, 8].

In high energy collider experiments there is usually an electromagnetic calorimeter (ECAL)in front of the HCAL. The ECAL is added to achieve a better energy resolution for the pureelectromagnetic showers of electrons and photons which are coming from the interaction region.This can be achieved by a finer granularity compared to the HCAL. In this study only a stand-

3

alone HCAL is simulated and no ECAL is present. When interpreting the results from Sec.4 thishas to be taken into account. Therefore, the nuclear interaction length of apossible ECAL hasto be subtracted from the total needed nuclear interaction length in order to get to the requirednuclear interaction length in the HCAL.

2.1 Parameters of the Toy Calorimeters

The two absorber materials investigated in this study are a Tungsten alloy, consisting of 93% W,6.1% Ni, 0.9 %Fe (for simplicity refered to as tungsten or W), and the iron alloy steel235 asdefined in GEANT4 (refered to as steel). In addition to the simulations done withtungstenor steel also a mixture of 50% Tungsten and 50% steel have been investigated, where bothmaterials are added together as a sandwich of two plates with a plate thickness of half of theabsorber thickness each. Because of the very high radiation length of tungsten compared to steelthe order of the two plates has an impact on the electromagnetic shower component measuredin the scintillator. In order to quantify this effect, both possibilities have been simulated. Forthis study the term tungsten-steel refers to the setup, where the tungsten layer is closer to theparticle source (i.e. each layer consists of tungsten-steel-scintillator-G10), while steel-tungstenrefers to the opposite case (steel-tungsten-scintillator-G10). Table1 shows the different detectorgeometries which where simulated.

The detector geometries were defined using the compact.xml-file format[9], which is con-verted to an LCDD-file[10] using GeomConverter[11]. The LCDD-file is the geometry input toSLIC. A sample detector geometry can be found in App.B.

4

Table 1: List of all different HCAL geometries simulated.

absorber absorber number ofλ per total totalmaterial thickness (mm) layers layer depth (m) depth (λ )

tungsten 5 400 0.06 5.00 24.0tungsten 10 400 0.11 7.00 44.0tungsten 15 300 0.16 6.75 48.0tungsten 20 200 0.21 5.50 42.0

steel 10 400 0.07 7.00 28.0steel 15 300 0.10 6.75 30.0steel 20 200 0.13 5.50 26.0steel 25 160 0.16 5.20 25.6steel 30 135 0.19 5.06 25.6

tungsten-steel 10 400 0.09 7.00 36.0tungsten-steel 15 300 0.13 6.75 39.0tungsten-steel 20 200 0.17 5.50 34.0steel-tungsten 10 400 0.09 7.00 36.0steel-tungsten 15 300 0.13 6.75 39.0steel-tungsten 20 200 0.17 5.50 34.0

5

3 Reconstruction of the Energy of Pions

For the reconstruction of the energy a global approach has been chosen using the regressionanalysis techniques of the Toolkit for Multivariate Data Analysis (TMVA)[12] in particular theneural network implementation. A neural network is created with two hidden layers with thenumber of nodes of N+5 and N+4 where N is the number of input variables.

The particle energy of the incoming particle is the output variable and should be estimated bythe neural network. The training sample consists of half of the events randomly chosen from thesimulated samples described in Sec.2. With this approach, all effects (e.g. leakage, fluctuationof the electromagnetic content of the particle showers) are estimated in one step and the energyof the incoming particle is directly reconstructed.

3.1 Definition of the Input Variables for the Energy Reconstru ction

As input variables for the energy reconstruction with the neural network, the information ofthe calorimeter cells is combined into several variables describing the particle shower, such asenergy, energy distribution and shape. In this study the high granularity of the calorimeter isnot exploited. Analyzing the details of the shower could lead to an improvementof the resultsshown here.

The following re variables were used. They are explained below.

• Ncells, number of all cells containing at least one hit and with a deposited energy of at least250 keV.

• zcell,i, distance of the celli to the particle source inz-direction (direction of the incomingparticle).

• xcell,i, distance of the celli to thez-axis inx-direction.

• ycell,i, distance of the celli to thez-axis iny-direction.

• rcell,i =(

x2cell,i + y2

cell,

)12, radial distance of the celli to the axis of the incoming particle.

• Ecell,i, Energy deposited in the celli (only cells with at least one hit and a deposited energyof at least 250 keV are considered).

• lcoil, depth of the coil (inz-direction)

• lc, depth of the calorimeter before the coil

• l0, first compartment of the calorimeter with the depth of 1λ interaction length.

• l2, last compartment of the calorimeter before the coil with the depth of 1λ interactionlengths.

• l1, middle compartment of the calorimeter with the length oflc− l0− l2.

6

• ltc, depth of the tail-catcher after the coil (in units of interaction lengths).

• ξ , factor defining the depth in cm divided by the depth in units of the interaction lengthλ . This factor depends on the thickness and the material used to build up the calorimeterlayers.

The cluster energyEcluster (Eq. 1) is the sum of the energies of all cells which have at leastone hit and where an energy of at least 250 keV has been deposited. This energy threshold cor-responds roughly to the energy deposited by a minimum ionizing particle (mip) passing throughone active cell in the direction of the incoming beam.

Ecluster=Ncells

∑i

Ecell,i (1)

The energy density of the cluster (Eq.2) is the cluster energy divided by the number of cellswhere energy has been measured.

ρE,cluster=Ecluster

Ncells(2)

Since all incoming particles are emitted into thez-direction with a small angular spread (seeSec.2) and no magnetic field is present, the shower-axis can be assumed to be thez-axis. Thisallows for a simplified calculation of the mean shower position (barycenter) and the dimensionslongitudinally (along thez-axis) and radially (in thexy-plane). The barycenter is calculated asgiven in Eq.3 and Eq.4 by summing thez (r) coordinates of all cells weighted by their energyand normalizing to the cluster energy (Eq.1)

〈z〉cluster=1

Ecluster

Ncells

∑i

zcell,iEcell,i (3)

〈r〉cluster=1

Ecluster

Ncells

∑i

rcell,iEcell,i (4)

As a measure for the length and the width of the showers, the RMS of the barycenter inz andin r are taken (see Eq.5 and Eq.6).

σz,cluster=1

Ecluster

(

Ncells

∑i

(zcell,i −〈z〉)2 E2cell,i

)12

(5)

σr,cluster=1

Ecluster

(

Ncells

∑i

(rcell,i −〈r〉)2 E2cell,i

)12

(6)

Four longitudinal adjacent compartments of the calorimeter are created by grouping togetherneighbouring layers and the energy therein is computed. Layer 0, 1 and 2with the thicknessesof l0 λ , l1 λ andl2 λ respectively are calculated as shown in the Eqs.7, 8 and9.

El0,cluster={celli | zcell,i ≤ ξ l0}

∑i

Ecell,i (7)

7

El1,cluster={celli | zcell,i > ξ l0∧zcell,i≤ξ (l0+l1)}

∑i

Ecell,i (8)

El2,cluster={celli | zcell,i > ξ l0+l1∧zcell,i≤ξ (l0+l1+l2)}

∑i

Ecell,i (9)

The energy measured in the tail catcher is computed with Eq.10.

Eltc,cluster={celli | zcell,i > ξ (lc+lcoil)∧zcell,i≤ξ (lc+lcoil+ltc)}

∑i

Ecell,i (10)

3.2 Determining the Energy Resolution

The energy resolution (Eq.11) of the reconstructed energyEreco at different values ofEtrue isdefined by the following equation.

RMS(∆E/E) =1

(N −1)〈Ereco〉

√

N

∑i=0

(Ereco,i −Etrue)2 (11)

The definition of the energy resolution given in Eq.11 can be redefined using the RMS ofEreco/Etrue instead of∆E/E = (Ereco,i −Etrue,i)/〈Ereco〉. With this redefinition, and

⟨

Ereco, j

Etrue, j

⟩

=1N

N

∑i=0

Ereco,i/Etrue,i (12)

the resolution can be determined for an interval ofEtrue.

RMS(Ereco/Etrue) =1

N −1

√

N

∑i

(

Ereco,i

Etrue,i−⟨

Ereco, j

Etrue, j

⟩)2

(13)

Eq.13 is equivalent to Eq.11when using the two following approximations:

• Etrue,i ∼ 〈Etrue〉, if the interval of which the values ofEtrue,i are chosen is small comparedto 〈Etrue〉 (which is clearly the case if events with a single true energy (Etrue) are taken).

• 〈Ereco〉 ∼ 〈Etrue〉 which is valid if the linearity of the reconstruction is good and the dis-tribution of the reconstructed energiesEreco,i follows a Gaussian with the mean close to〈Etrue〉.

From these assumptions it follows, that〈Ereco,i/Etrue,i〉 ∼ 〈Ereco,i/Etrue〉 ∼ 1. Inserting this into

8

Eq.13gives:

RMS(Ereco/Etrue) ≈1

N −1

√

N

∑i=0

(

Ereco,i

Etrue−1

)2

(14)

≈ 1N −1

√

N

∑i=0

(

Ereco,i −Etrue

Etrue

)2

(15)

≈ 1(N −1)〈Ereco〉

√

N

∑i=0

(Ereco,i −Etrue)2 (16)

Hence, for the mentioned approximations it can be written:

RMS

(

Ereco

Etrue

)

= RMS

(

∆EE

)

(17)

3.3 RMS90

With samples of small statistics, the RMS might be strongly biased by a few outliers with valuesfar away from the values of the bulk of events for the analysis the RMS90 has been taken. Inthis work, the RMS90 is defined as the RMS of the narrowest interval which contains 90% of theevents.

3.4 Gaussian Fits

Alternatively, a Gaussian function has been fitted to the distributions ofEreco/Etrue for eachenergy range. The mean and the width of the Gaussian distribution are driven by the bulk ofevents in the center of the distribution. Thus, the impact of events in the tail of the distributionis suppressed and the resolution computed from a Gaussian fit is typically toooptimistic. Sincethe tails of the distributions should be taken into account for this study, it has been decided notto use Gaussian fits for the computation of the resolutions (and the linearity).

9

4 Results

Resolution and linearity are computed as shown in Sec.3.2with test samples that are statisticallyindependent from the samples which have been used for training. The test samples have the sameenergy distribution as the training samples (see Sec.2). The energy has been reconstructed inseveral energy bins. All test samples within the energy range of the bin are taken: |Etrue−Ecenter| < Erange whereEcenter is the center of the energy bin andErange defines its half-width.The ratios ofEreco/Etrue of the samples in this bin are used to calculate the mean deviation ofreconstructed energy from true energy〈Ereco/Etrue〉 and the energy resolution RMS(Ereco/Etrue).This evaluation is done for several energy bins from low to high energies. The energy range foreach bin has been chosen such that a reasonable statistics was obtained.

In each bin of true energy, the resolution is obtained by plotting the RMS of thedeviationsof the reconstructed from the true energy. The points of the resolution are then fitted with theresolution function given by:

∆EE

=s√E⊕ c (18)

wheres is denotedsampling term andc is denotedconstant term. Usually in calorimetry a noiseterm n/E is added to the resolution function. Since an ideal detector and readout is simulated,there is no noise and therefore this term is not taken into account.

For each bin of true energy, the mean deviation of the reconstructed fromthe true energy iscomputed (〈Ereco/Etrue〉 j). Commonly thelinearity of the energy reconstruction is defined bythe smallest valueL , with

L ≥ 2

∣

∣

∣

∣

∣

⟨

Ereco

Etrue

⟩

j−1

∣

∣

∣

∣

∣

(19)

for all energy binsj.

4.1 The “Infinite” Calorimeter

The resolution of an infinite sampling calorimeter is limited by the stochastic and the samplingfluctuations (both contribute to the stochastic terms/

√

(E)). The energy resolution of hadronicshowers is at minimum when the electromagnetic content of the shower produces the sameaverage signal as the hadronic content of the shower [13].

4.2 Single Material Passive Layers

In Fig. 1 the resolution functions for the reconstructed particle energies (see Sec. 3) are shownfor the case of an “infinite” calorimeter (i.e.≥ 24 λ ). After the reconstruction, the linearitystays within∼ 2% (see Fig.2). The best resolution (27.7%/

√E ⊕ 0.3%) is achieved with a

thickness of the passive layer of 5 mm. With larger thicknesses, the sampling term of the resolu-tion function worsenes up to (54.0%/

√E) for the 20 mm tungsten plates. The constant term is

small for all plate thicknesses, since there is no leakage and the calorimeter isideal (no detector

10

[GeV]trueE

100 200

)tr

ue/E

reco

(E90

RM

S

0

0.02

0.04

0.06

0.08

0.1

1.1%⊕ E

54.0%

0.4%⊕ E

45.1%

0.4%⊕ E

37.6%

0.3%⊕ E

27.7%

passivematerial wtungsten 2.0 cmtungsten 1.5 cmtungsten 1.0 cmtungsten 0.5 cm

Figure 1: Energy resolutions for “infinite” tungsten calorimeters (lhcal≥ 24λ ) for different thick-nesses of the passive layer as a function of the true energy of the incoming pions.

[GeV]trueE

100 200

>tr

ue/E

reco

<E

0.98

0.99

1

1.01

1.02

passivematerial wtungsten 2.0 cmtungsten 1.5 cmtungsten 1.0 cmtungsten 0.5 cm

Figure 2: Linearity for “infinite” tungsten calorimeters (lhcal≥ 24λ ) for different thicknesses ofthe passive layer as a function of the true energy of the incoming pions.

effects). The remaining small constant term is mainly due to imperfections of thereconstructionalgorithm.

Fig. 3 shows the energy resolution of particles with a true energy from 230 GeV to270 GeVas a function of the depth of the HCAL. The resolution for the≥24λ case is not shown, sincefeasibility and cost limit the depth of the calorimeter that can be built. It is thus zoomed to theinteresting region from about 50 cm to 220 cm for the HCAL length. It can be observed that allgraphs have an asymptotic behaviour when going to large HCAL lengths. For a large HCAL thehadronic particle showers of the observed energy are fully contained and increasing the HCALlength does not result in measuring more energy. Going to shorter HCAL depths the resolutionworsens due to energy leaking longitudinally out of the calorimeter. For thicker passive layers,the effect of leakage ends at shorter total HCAL lengths. For thinner passive layers a longer

11

length [cm]

100 150 200

=[2

30,2

70]G

eVtr

ueE)

true

/Ere

co(E

90R

MS

0

0.02

0.04

0.0666666666

77777777

88888888 9999999966666666

7777777788888888 99999999

66666666

77777777 8888888899999999

66666666

77777777

88888888 99999999

20 GeV±=250trueE

passivematerial wtungsten 2.0 cmtungsten 1.5 cmtungsten 1.0 cmtungsten 0.5 cm

Figure 3: Energy resolution for particles in the HCAL with an energy from 230 GeV to 270 GeVas a function of the HCAL length. The resolutions for passive layers madeof tungstenand with thicknesses ranging from 5 to 20 mm are shown.

HCAL is necessary to avoid leakage. It can be seen from Fig.3 that for a certain HCAL lengtha trade-off between better intrinsic resolution and less leakage is necessary to obtain the optimalresolution.

Fig. 4 shows the energy resolution for passive layers made of steel. It can beseen that anadditional HCAL depth of around 50 cm is necessary to get into the region where the curve getsflatter and thus leakage is not dominating the resolution.

4.3 Mixed material passive layers

Since a compromise has to be found between a detector which is ideal from thepoint of viewof physics performance, one which can be built mechanically and one where the material andconstruction cost stays within reasonable boundaries the combination of different materials hasto be looked at as well. Tungsten is a dense and brittle material. To achieve a reliable mechanicalstability a combination with steel seems to be inevitable[14]. The aim of this part of the studyis to explore the resolution for an HCAL with passive layers made of a mixture of tungstenand steel in comparison to the previously shown configurations using only tungsten or steel aspassive material.

The effective nuclear interaction length of a tungsten-steel layer is the same as of a steel-tungsten layer. A difference of the measured signal in the active layer following the passivelayer is caused by the different radiation lengths (X0) of tungsten and steel. In case the activelayer follows tungsten, electrons produced in the steel part or the tungsten part are less likely toreach the active layer than in the case where the active layer follows the steel part.

12

length [cm]

150 200 250

=[2

30,2

70]G

eVtr

ueE)

true

/Ere

co(E

90R

MS

0

0.02

0.04

0.06

66666666

7777777788888888 99999999

66666666

77777777

88888888 99999999

66666666

77777777

88888888

99999999

66666666

7777777788888888

99999999

66666666

77777777

88888888

99999999

20 GeV±=250trueE

passivematerial wsteel 3.0 cmsteel 2.5 cmsteel 2.0 cmsteel 1.5 cmsteel 1.0 cm

Figure 4: Energy resolution for particles in the HCAL with an energy from 230 GeV to 270 GeVas a function of the HCAL length. The resolutions for passive layers madeof steeland with thicknesses ranging from 10 to 30 mm are shown. For very deep calorimeterswhere (almost) all hadronic showers are fully contained (outside the scope of the fig-ure) the energy resolution is best for 10 mm thick passive layers and worsens for 15,20, 25 and 30 mm in that order.

length [cm]

100 150 200

=[2

30,2

70]G

eVtr

ueE)

true

/Ere

co(E

90R

MS

0

0.02

0.04

0.06

66666666

77777777

8888888899999999

66666666

77777777 88888888 99999999

66666666

7777777788888888 99999999

66666666

77777777

88888888

99999999

66666666

7777777788888888

99999999

66666666

7777777788888888

99999999

20 GeV±=250trueE

passivematerial wsteeltungsten 2.0 cmsteeltungsten 1.5 cmsteeltungsten 1.0 cmtungstensteel 2.0 cmtungstensteel 1.5 cmtungstensteel 1.0 cm

Figure 5: Energy resolution for particles in the HCAL with an energy from 230 GeV to 270 GeVas a function of the HCAL length. The resolutions for passive layers madeof tungsten-steel and steel-tungsten and with thicknesses ranging from 10 to 20 mm are shown.

13

[GeV]trueE

100 200

)tr

ue/E

reco

(E90

RM

S

0

0.02

0.04

0.06

1.4%⊕ E

29.9%

1.1%⊕ E

28.8%

0.9%⊕ E

29.0%

tc lpassivematerial w λtungsten 0.5 cm 0.0 λtungsten 0.5 cm 1.0 λtungsten 0.5 cm 5.0

Figure 6: Energy resolution for pions showering in the HCAL with 5 mm thick tungsten passivelayers as a function of the length of the tail-catcherltc. For ltc = 0λ no active layer(and no passive layer) is taken into account, for 1 and 5λ tail-catcher length the samelayer structure from the calorimeter is taken.

In Fig. 5 mixtures of tungsten and steel are shown. The passive layer consists ofa tung-sten and a steel layer, where both are equally thick (half of the total passive layer thickness).Both options—tungsten upstream and steel upstream—are compared. The tungsten-steel caseperforms always slightly better, than the steel-tungsten case. As expected, the combination oftungsten and steel for the passive layer achieves resolutions for given passive layer thicknessesin between those of pure tungsten or steel layers.

5 Impact of a Tail-Catcher on the Calorimetric Resolution

The effect of a tail-catcher on the quality of the energy reconstruction has been studied forcalorimeters with tungsten passive layers of 5 mm and 10 mm and steel passive layers of 25 mm.In Fig. 6 the effect of the tail-catcher is shown for 5 mm tungsten passive layers. It can beseen, that the improvement from no tail-catcher (0λ ) to a 1λ tail-catcher is significant while theimprovement from going from 1λ to 5λ is small.

The same conclusions can be drawn from Fig.7 where 10 mm passive tungsten layers havebeen used.

In Fig. 8 the effect of the tail-catcher is shown for a steel calorimeter. Again, a larger stepfrom 0 to 1λ and a smaller one from 1 to 5λ can be seen. At 200 GeV the tail-catcher leads toan improvement of the energy resolution from 3.0% to 2.6%.

Independent from the passive layer material the use of a tail-catcher is advisable in order toimprove energy reconstruction. The length of the tail-catcher is less important,because in allcases most parts of the shower are measured in front of the coil. The mostimportant benefit of

14

[GeV]trueE

100 200

)tr

ue/E

reco

(E90

RM

S

0

0.02

0.04

0.06

0.08

1.1%⊕ E

43.0%

1.2%⊕ E

39.0% 0.9%⊕

E39.1%

tc lpassivematerial w

λtungsten 1.0 cm 0.0 λtungsten 1.0 cm 1.0 λtungsten 1.0 cm 5.0

Figure 7: Energy resolution for pions showering in the HCAL with 10 mm thick tungsten passivelayers as a function of the length of the tail-catcherltc. For ltc = 0λ no active layer(and no passive layer) is taken into account, for 1 and 5λ tail-catcher length the samelayer structure from the calorimeter is taken.

[GeV]trueE

100 200

)tr

ue/E

reco

(E90

RM

S

0

0.02

0.04

0.06

0.08

1.8%⊕ E

34.5%

1.3%⊕ E

31.4%

1.2%⊕ E

31.6%

tc lpassivematerial w λsteel 2.5 cm 0.0 λsteel 2.5 cm 1.0 λsteel 2.5 cm 5.0

Figure 8: Energy resolution for pions showering in the HCAL with 25 mm thick steel passivelayers as a function of the length of the tail-catcherltc. For ltc = 0λ no active layer(and no passive layer) is taken into account, for 1 and 5λ tail-catcher length the samelayer structure from the calorimeter is taken.

the tail-catcher is that it tells wether there was any leakage.

6 Effect of Requiring a Minimum Deposited Energy per Cell

For the results shown in Sections4.1, 4.2, 4.3 and5 only cells are taken into account wherean energy above 250 keV has been deposited. This threshold has to be applied in real detectorsto avoid noise hits. However, in our ideal set-up the cases with and without threshold can be

15

[GeV]trueE

100 200

)tr

ue/E

reco

(E90

RM

S

0

0.02

0.04

0.06

0.08

0.5%⊕ E

37.3%

0.3%⊕ E

28.4%

0.4%⊕ E

37.6%

0.3%⊕ E

27.7%

passivethreshold material w0.0keV tungsten 1.0 cm0.0keV tungsten 0.5 cm

250.0keV tungsten 1.0 cm250.0keV tungsten 0.5 cm

Figure 9: Energy resolution for pions showering in the HCAL with 10 mm and 5mm thick tung-sten passive layers as a function of the energies of the incoming pions. Results areshown with and without a threshold of 250 keV for each individual hit.

[GeV]trueE

100 200

)tr

ue/E

reco

(E90

RM

S

0

0.02

0.04

0.06

0.08

2.9%⊕ E

34.4%

1.6%⊕ E

28.9%

4.4%⊕ E

32.1%

2.9%⊕ E

35.8%

1.7%⊕ E

27.6%

4.7%⊕ E

28.5%

passivethreshold material w0.0keV steel 2.0 cm0.0keV steel 1.5 cm0.0keV steel 1.0 cm

250.0keV steel 2.0 cm250.0keV steel 1.5 cm250.0keV steel 1.0 cm

Figure 10: Energy resolution for pions showering in the HCAL with 15 mm, 10 mmand 5 mmthick steel passive layers as a function of the energies of the incoming pions. Resultsare shown with and without a threshold of 250 keV for each individual hit.

compared. Thus, the effect on the energy reconstruction can be studied. In this section, theobtained resolutions for the energy reconstruction with a threshold of 250keV are compared toenergy reconstructions without threshold.

In the Figures9, 10, 11 and12 the impact of using a threshold of 250 keV is shown. In allcases the differences are marginal, only in Figures11 and12 some deviations can be observed,but the conclusion which configurations are performing best remain the same.

The changes are small because the variables used to train the neural network (see Sec.3.1)were chosen to represent the overall shower shape putting only small weight on individual cells.

16

length [cm]

100 150 200

=[2

30,2

70]G

eVtr

ueE)

true

/Ere

co(E

90R

MS

0

0.01

0.02

0.03

0.04 66666666

77777777

888888889999999966666666

7777777788888888

99999999

66666666

77777777

88888888 99999999

66666666

7777777788888888

9999999966666666

77777777 8888888899999999

66666666

77777777

8888888899999999

20 GeV±=250trueE

passivethreshold material w0.0keV tungsten 1.5 cm0.0keV tungsten 1.0 cm0.0keV tungsten 0.5 cm

250.0keV tungsten 1.5 cm250.0keV tungsten 1.0 cm250.0keV tungsten 0.5 cm

Figure 11: Energy resolution for pions showering in the HCAL with 20 mm, 15 mmand 10 mmthick tungsten passive layers as a function of the calorimeter length for pions withenergies ranging from 230 GeV to 270 GeV. Results are shown with and without athreshold of 250 keV for each individual hit.

length [cm]

100 150 200

=[5

6,64

]GeV

true

E)tr

ue/E

reco

(E90

RM

S

0

0.02

0.04

0.06

6666666677777777

88888888 9999999966666666

77777777 88888888 9999999966666666

7777777788888888 99999999

6666666677777777 88888888 99999999

6666666677777777 88888888 99999999

66666666

7777777788888888 99999999

4 GeV±=60trueE

passivethreshold material w0.0keV tungsten 1.5 cm0.0keV tungsten 1.0 cm0.0keV tungsten 0.5 cm

250.0keV tungsten 1.5 cm250.0keV tungsten 1.0 cm250.0keV tungsten 0.5 cm

Figure 12: Energy resolution for pions showering in the HCAL with 15 mm, 10 mmand 5 mmthick tungsten passive layers as a function of the calorimeter length for pions with en-ergies ranging from 56 GeV to 64 GeV. Results are shown with and without athresh-old of 250 keV for each individual hit.

Since the hits with small energy deposits have only marginal impact on the overall shower shape(i.e. shower center, length and width) the reconstructed energy is almost identical.

17

7 Summary and Conclusions

The calorimetric performance on hadrons has been evaluated for a HCALsampling calorimeterwhith active and passive layers perpendicular to the direction of the impinging pions. The thick-ness and material of the passive layers has been varied while the active layers have been leftunchanged. General shower variables have been computed from the energy depositions in thehighly segmented active layers. The detailed cell information has been discarded in this study.A perfect detector readout without noise has been assumed. The energy reconstruction basedon the general shower variables has been done with a neural network,which has been trained toestimate the true Monte Carlo energy of the primary particle.

The energy reconstruction has been done for particles in the range from 1 to 300 GeV. Duringreconstruction a 2λ thick region from the calorimeter stack has been defined as coil where noinformation on deposited energy has been used. Downstream of the coil another region has beendefined as a tail-catcher with varying thicknesses of 0 (no tail-catcher), 1λ and 5λ . This wasdone in order to study the effect of a tail-catcher to recover the loss in energy resolution due toleakage into the coil.

For an “infinite” sampling calorimeter, where the full shower is contained, thebest energy res-olution can be achieved when the calorimeter is compensating. Since the size ofthe calorimeteris limited by technical and cost constraints the loss in energy resolution due to non-compensationhas to be traded off against a loss due to energy leaking longitudinally out of the calorimeter.The energy resolution worsens steeply for calorimeter lengths where leakage becomes impor-tant. It has been shown, that by adjusting the passive layer thickness, the energy resolutionof the calorimeter can be optimized. In order to prevent from being dominatedby leakage, acalorimeter with passive layers made of steel has to be up to 50 cm larger thana calorimeterusing tungsten plates. For tungsten passive layers in the energy region of interest, the optimumcalorimeter length is around 140 cm with a passive layer thickness of 10 mm. Inthe case ofsteel passive layers, the optimum length of the calorimeter is around 180 cm with a passive layerthickness of 25 mm. When using passive layers which are combinations of a steel and a tung-sten plate (with equal plate thicknesses) it is preferable to have the steel downstream rather thanupstream. This slightly improves the energy resolution since more of the electromagnetic signalreaches the active layer. For this configuration, the optimum length is around 160 cm with a totalpassive layer thickness of 15 mm (7.5 mm tungsten and 7.5 mm steel).

It is possible to slightly improve the energy resolution by adding a tail-catcher downstream ofthe coil. While a tail-catcher of 1λ yields some improvement, adding much more active layers(i.e. an equivalent of 5λ ) improves the energy resolution further only by a small amount.

18

Appendices

A Slic-Macro Used to Simulate π+-Events

/physics/select QGSP_BERT_HP

/generator/select gps

/gps/pos/type Point

/gps/pos/centre 0. 0. 0.

/gps/ang/type iso

/gps/ang/mintheta 179

/gps/ang/maxtheta 181

/gps/ang/minphi 0 deg

/gps/ang/maxphi 360 deg

/gps/ene/type Exp

/gps/ene/min 1 GeV

/gps/ene/max 300 GeV

/gps/ene/ezero 150500

/gps/particle pi+

/lcdd/url DETECTORFILE.lcdd

/lcio/filename OUTPUTFILENAME

/lcio/path OUTPUTPATH

/lcio/PDGFlag true

/random/seed

/run/beamOn 100000

19

B Compact Description of the 5 mm Tungsten Calorimeter

<lccdd xmlns:compact="http://www.lcsim.org/schemas/compact/1.0"

xmlns:xs="http://www.w3.org/2001/XMLSchema-instance"

xs:noNamespaceSchemaLocation=

"http://www.lcsim.org/schemas/compact/1.0/compact.xsd">

<info name="clichcalstacktungsten_0.5"</info>

<define>

<constant name="cm" value="10"/>

<constant name="world_side" value="5000*cm" />

<constant name="world_x" value="world_side" />

<constant name="world_y" value="world_side" />

<constant name="world_z" value="world_side" />

<constant name="tracking_region_radius" value="126.5*cm"/>

<constant name="tracking_region_zmax" value="100.*cm"/>

</define>

<materials>

<material name="TungstenDens24">

<D value="17.8" unit="g/cm3"/>

<fraction n="0.93" ref="W"/>

<fraction n="0.061" ref="Ni"/>

<fraction n="0.009" ref="Fe"/>

</material>

</materials>

<detectors>

<detector id="1" name="HCAL" type="TestBeamCalorimeter" readout="HCALHits"

insideTrackingVolume="false">

<dimensions x="500.0 * cm" y="500.0 * cm" />

<position z="5000" />

<layer repeat="400">

<slice material= "TungstenDens24" thickness= "0.5*cm" />

<slice material= "Polystyrene" thickness= "0.50*cm" sensitive= "yes" />

<slice material= "G10" thickness= "0.25*cm" />

</layer>

</detector>

</detectors>

<readouts>

<readout name="HCALHits">

<segmentation type="GridXYZ" gridSizeX="1.0*cm" gridSizeY="1.0*cm" />

<id>system:8,layer:16,barrel:3,x:32:-16,y:-16</id>

</readout>

</readouts>

</lccdd>

20

References

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[2] J. Allison et al. Geant4 developments and applications.IEEE T. Nucl. Sci., vol. 53(1) pp.270–278, 2006.

[3] M. A. Thomson. Particle Flow Calorimetry and the PandoraPFA Algorithm.Nucl. Instrum.Meth., vol. A611 pp. 25–40, 2009.

[4] Simulator for the Linear Collider (SLIC). Website:http://lcsim.org/software/slic/.

[5] P. Speckmayer. Impact of the Choice of Physics List on GEANT4 Simulations of HadronicShowers in Tungsten. LCD-Note-2010-002, 2010.

[6] G. Acquistapace et al. CMS, the magnet project: Technical design report. CERN-LHCC-97-10.

[7] ILD Concept Group. The International Large Detector Letter of Intent. 2009. DESY-09-087.

[8] H. Aihara, (Ed. ) et al. SiD Letter of Intent. 2009.

[9] Compact Detector Description. Website:http://lcsim.org/software/geomconverter/

apidocs/org/lcsim/geometry/compact/package-summary.html.

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[11] GeomConverter. Website:http://lcsim.org/software/geomconverter/.

[12] A. Hoecker, et al. TMVA - Toolkit for Multivariate Data Analysis.POSACAT, vol. 040,2007.

[13] R. Wigmans.Calorimetry. Oxford University Press, 2000.

[14] Ronan McGovern. Tungsten HCAL Mechanics. EDMS:https://edms.cern.ch/

document/1058015/1. Presentation given at the 2009 CALICE Collaboration Meeting,16-18 Sept 2009, Lyon, France .

21