Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

A systematic measurement of energy resolution and e/p ratio ofa lead/plastic-scintillator sampling calorimeter
T. Suzuki , Y. Fujii *, K. Hara , T. Ishizaki , F. Kajino, N. Kanaya, J. Kanzaki,
K. Kawagoe, S. Kim , T. Matsui, A. Miyajima, A. Nakagawa , S. Nakazawa ,
M. Nozaki, T. Ota , K. Sendai, Y. Sugimoto, Y. Sugimoto, H. Takayama ,
H. Takeda, T. Takeshita, S. Tanaka , A. Tanaka , T. Toeda , Y. YamadaInstitute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, JapanDepartment of Physics, Kobe University, Kobe, Hyogo 657-8501, JapanDepartment of Physics, Konan University, Kobe, Hyogo 658-8501, JapanDepartment of Physics, Shinshu University, Matsumoto, Nagano 390-8621, Japan
Received 5 January 1999

Abstract
The energy resolution and the e/p ratio of a lead/plastic-scintillator sampling calorimeter were measured for various
volume ratios of the lead thickness to the scintillator thickness. For this purpose, a hanging-"le-type calorimeter module
was constructed in which the thicknesses of the lead absorber and the plastic-scintillator plates were able to be alteredvery #exibly. The thicknesses of the lead and the scintillator plates can be changed by a 2 mm step form 4 to 16 mm andfrom 2 to 6 mm, respectively. We measured energy resolution for electrons and pions with the calorimeter module as
a function of the thickness of a lead plate in the energy range 1}4 GeV. The best energy resolution for pions was obtained
to be 33.6%/(E with the con"guration where the thicknesses of the lead and the scintillator plates were 4 and 2 mm,
respectively. The e/p ratio was measured in the energy range 1}4 GeV. The compensation was found to be achieved forthe lead thickness of 9.1$0.3 mm in the case of 2 mm-thick scintillator.  1999 Elsevier Science B.V. All rights
reserved.
PACS: 29.40.Mc; 29.40.Vj
Keywords: Calorimeter; Tile/"ber; Compensation; Linear collider* Corresponding author. Tel.: #81-298-64-5369; fax: 81-298-64-2580.
E-mail address: yoshiaki.fujii@kek.jp (Y. Fujii) Present address: FUJITSU LIMITED, Kawasaki, Kanagawa, Japan
 Present address: Department of Physics, Tohoku University, Sendai, Miyagi 980-8578, Japan
 Present address: Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization, Tsukuba, Ibaraki
305-0801, Japan
 Present address: Netwave Co. Ltd., Kyoto, 604-8112, Japan
 Present address: Department of Physics, Nagoya University, Nagoya, Aichi 464-8602, Japan
0168-9002/99/$ - see front matter  1999 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 0 3 9 4 - 0

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

1. Introduction
In the future linear collider experiments, a good
hadron energy measurement is indispensable tohave good sensitivities to new physics as well as toperform precise measurements of the Standard
Model [1]. To achieve a good hadron energy resolution, compensation plays a crucial role in sampling calorimeters [2]. In general, the pulse height ofcalorimeter is di!erent for electromagnetic (EM)showers and for hadron showers. The compensation is a condition that a calorimeter is made tohave equal pulse height for EM showers and forhadron component in hadron showers; namely,e/h,pulse height for EM showers
pulse height for hadron component in hadron showers"1(1)

for the compensated calorimeters. This minimizes
the degradation of hadron energy resolution due to#uctuation of the EM component in hadron
shower development, and hence minimizes nonGaussian behaviour and constant term of energy
resolution and achieve good linearity for energy49

measurement. This condition can be achieved byadjusting the calorimeter con"guration properly;
what to use for active and absorber materials, andtheir thicknesses.
Experimentally e/p ratio is commonly used toestimate a degree of compensation. The e/p ratio isde"ned as
pulse height for EM showers.
e/p,pulse height for charged pions(2)

Empirical relation between the e/h ratio and thee/p ratio is described in Ref. [3]. The result of someexperiments about e/p ratio [4}6], and calculationsof e/h ratio [2] indicate that a calorimeter consisting of lead and plastic scintillator with a volume
ratio of about 4 : 1 may achieve compensation.
However, the e/p ratio approaches 1.0 at
higher energies regardless of compensation due toincrease of p component in the hadron shower.
The results of the above experiments are e/p&1.1
for E410 GeV, and more systematic study
is necessary to con"rm the achievability ofcompensation.
As mentioned above, the e/h ratio, or the e/pratio, is a function of the volume ratio of theFig. 1. Schematic view of the hanging-"le type calorimeter module.

50

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

absorber and the active material [2]. However, it
has not been measured systematically for the
combination of lead and plastic scintillator. For
this purpose, we constructed a hanging-"le typecalorimeter module and performed beam tests tomeasure the volume ratio dependence of the energy
resolution and the e/p ratio.
In Section 2, we describe the optical characteristics of the plastic scintillator tile/"ber system used
for the calorimeter module. The experimental setup
is brie#y described in Section 3. The analysis procedure is described in Section 4. The results are
given in Section 5.

2. Calorimeter module
The calorimeter module consists of lead absorberand plastic scintillator plates of `hanging-"leacon"guration, where the absorber plates and scintillator plates are hung over a pair of parallel beams, as shown in Fig. 1. The thicknesses of the leadplates can be changed from 4 to 16 mm with a stepof 2 mm. The thickness of the scintillator plates is"xed to 2 mm for measurements described in thispaper.
Tile/"ber techniques are employed in order toeasily alter the absorber thicknesses and opticalreadout system. The optical con"guration of thetile/"ber system is shown in Fig. 2. A scintillator
plate is 1;1 m, and 2 mm thick. Each scintillator
plate has six straight grooves with a key hole shapewith a groove distance of 20 cm. The four sides ofthe plates are painted white with TiO -based emul
sion paint (Nippon Paint &Odecoat'). The scintillator plates are covered in TiO -added white PET"lms. The "ber is made up of a 1 m long wavelength-shifter "ber (WLS "ber) spliced at the eachend to a clear "ber by a heat-fusing method [11].
The diameter of the "bers is 1 mm. Kuraray
SCSN38 and SCSN88 polystyrene-based scintillators and Y11 multiclad WLS "bers [7}10] areused.
In the beam tests, clear "bers from "ve successive scintillator layers are bundled to make asuperlayer. Each side of the clear "ber bundle
is connected to a phototube (HAMAMATSU
H1949).

Fig. 2. Optical con"guration of the tile/"ber system for thehanging-"le type calorimeter module.

The light yield of the tile/"ber systems was measured at a test bench using penetrating b-rays froma Sr source. Response mapping was carried out inboth parallel and perpendicular directions to the
WLS "bers using an automatic scanning system. In
the direction perpendicular to the "bers, the lightyield peaked at the points near the "bers as shownin Fig. 3. In the direction parallel to the "bers, thelight yield was fairly #at except the points near thetile edge as shown in Fig. 4.
The distribution of the average light yield andnon-uniformity in the direction perpendicular tothe "bers (except the points near the "bers) are
shown in Fig. 5. The mean light yield and its rms
variation were 1.7 photoelectrons/mip (minimum
ionizing particle) and 14.3%, respectively. Note thatthe variation did not include those of the PMTs
and clear "bers used for the beam tests: we used
the same system through the test bench measurements. The mean and rms variation of non-uniformity in a tile in the direction perpendicular

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

Fig. 3. Light yield vs. position scanned across the WLS "bers(along the vertical arrow (X) shown in Fig. 2).

51

Fig. 5. Distribution of the average light yield (top) and its
non-uniformity in a tile (bottom) in the direction across the"bers (except the points near the "bers).

The calorimeter con"gurations are summarizedin Table 1.

3. Experimental setup of the beam test

Fig. 4. Light yield vs. position scanned along the "bers from thecenter to the edge of the tile (along the arrow (>) shown in
Fig. 2).

to the "bers (except the points near the "bers)
were 5.0 and 2.7%, respectively, while the nonuniformity in a tile in the direction parallel to the"bers was 3%.

The beam test was carried out at p2 beam line of
KEK-PS in two periods, from February to Marchand from May to June in 1997 which we call T405
and T411, respectively. Experimental setups areshown in Fig. 6.
The measurements were performed with negatively charged particles. The beam energy was set to1, 2, 3 and 4 GeV. The momentum bite of the beam
was 1% (FWHM). The beam was unseparated andcontains pions, muons, and electrons. The beam
was de"ned by coincidence of scintillation trigger
counters S1, S2, and S3 in T405, and S1, S2, S3, andS4 in T411. The electron trigger required a coincidence between the beam signal and the signals inboth Cherenkov counters C1 and C2, "lled with
CO gas where the pressure of the gas was set
to be 1 atm. The muon trigger required a coincidence between the beam signal and the signals

52

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

Table 1
Calorimeter con"gurations tested in T405 and T411. X and j are radiation length and nuclear interaction length, respectively'Con"guration in T405 lead : scintillator (in mm)

8:2

10 : 2

12 : 2

14 : 2

16 : 2

Number of lead/scintillator layers
Lead thickness (mm)Scintillator thickness (mm)Number of superlayers
Number of PMTs
Absorber thickness of a superlayer (X )
Total absorber thickness (j )'Total absorber thickness (X )
Average density of the calorimeter (g/cm)

105
8
2
21
42
7.14
4.92
150.0
6.64

100
10
2
20
40
8.93
5.85
178.7
8.05

70
12
2
14
28
10.7
4.92
150.0
7.53

70
14
2
14
28
12.5
5.73
174.7
8.35

55
16
2
11
22
14.29
5.15
157.1
8.22

Con"guration in T411 lead : scintillator (in mm)

4:2

6:2

8:2

10 : 2

16 : 2

Number of lead/scintillator layers
Lead thickness (mm)Scintillator thickness (mm)Number of superlayers
Number of PMTs
Absorber thickness of a superlayer (X )
Total absorbe thickness (j )'Total absorber thickness (X )
Average density of the calorimeter (g/cm)

210
4
2
42
84
3.57
4.92
150.0
6.69

160
6
2
32
64
5.36
5.62
171.1
7.41

120
8
2
24
48
7.14
5.62
171.1
7.64

100
10
2
20
40
8.93
5.85
178.7
8.32

55
16
2
11
22
14.29
5.15
157.1
8.81

Fig. 6. Schematic layout of the setups of the beam test, (a) for T405 and (b) for T411.

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

53

in both muon trigger scintillation counters M1
and M2 located behind the backup calorimeter(s).
The pion trigger was just the beam signal,and muons and electrons were reduced in o%ine
analysis.
The fraction of muons in the beam was estimatedto be about 1% for the energy of 4 GeV (T405). The
fraction of electrons in the beam was estimated to
be about 8, 3, 1.5, and 1% for 1, 2, 3, and 4 GeV,
respectively (T405).

4. Gain calibration, event selection, and systematic
uncertainties
4.1. Gain calibration
The muon events with a beam energy of 4 GeV
are used to calibrate the relative gain of the whole
readout systems including the phototubes and the
ADC since a 4 GeV-muon penetrate through themodule as a mip. The absolute energy calibration isdone using 4 GeV electron events. The muon trigger data contain a small fraction of pion events.
These pions cause an increase in the mean of thepulse height for muon trigger events than that ofpure muon events, especially for the forward superlayers. These pions are rejected in o%ine analysis as
described in Section 4.2.
We perform the gain calibration by the following
iteration:(1) Determine initial calibration constants frommean ADC counts for all 4 GeV muon-triggered
events.
(2) Select muon events as described in Section
4.2 with gain constants determined by the previous
step.
(3) Determine new calibration constants for theselected muon events.
The sequences of (2) and (3) are repeated until
calibration constants are converged. Actually two
iterations are su$cient. The above gain calibrationis performed each time when we altered the calorimeter con"guration. Through these procedures, thepion fraction in the muon-triggered data is found to
be about 5%. After the muon selection procedure,
the fraction of the pions in the muon-selected
events become negligible.

Fig. 7. Typical distribution of the quantity VAR for 4 GeV
electron-, l-, and p-triggered events. The con"guration islead"8 mm and scintillator"2 mm.

4.2. Event selection
The selection of the electron, muon, and pion
events is based on the longitudinal shower pro"lemeasured with the calorimeter itself, in addition to
the muon and Cherenkov counters. We de"neda quantity VAR as follows:(1/(N !1) ,1* (x !x )
1*
G G
 ,
VAR"
x

1 ,1*
x
(3)
x "
 N
G
1*G
where x is the pulse height deposited in ith superG
layer, and x
is the average of pulse heights
in a superlayer, and N is the number of super1*
layers.
Shown in Fig. 7 are typical distributions of thequantity VAR for the electron, muon, and piontriggered events. For muon events, VAR is small
because the pulse heights are similar to each otherwithin #uctuations of dE/dx and photostatistics.
For electron events, pulse heights in forward superlayers are large, and those in backward are zero or

54

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

Fig. 8. Typical pulse-height distributions for 4 GeV electrons,muons, and pions before and after event selection. The con"guration is lead"8 mm and scintillator"2 mm. The dashedhistograms are the pulse-height distribution before the event
selection. The solid histograms are those after the event
selection.

very small. The quantity VAR is thus large forelectron events. The VAR for pions distributes between those for muons and electrons. As seen in
Fig. 7, there are some muon events in the electron
and pion triggers.
The electrons are selected with a cut VAR'2.5.
After this electron selection, the pion contamination in electron triggered events is less than 0.5%.
The pions are selected with a cut VAR'1 andrequiring that the both Cherenkov counters haveno signals. After this pion selection, contaminationby the electrons in the pion events is less thanO(10\) and negligibly small to evaluate the performance for pions. The muons are selected with a cut
VAR(1 and requiring that all the superlayers
have signals well above the pedestals, and that thepulse height of any superlayer in an event is lessthan 3.5 mip-equivalent.
Typical pulse height distributions before/after
these event selection are shown in Fig. 8, for
4 GeV electrons, muons, and pions for the con"g-Fig. 9. The distribution of rms variation of relative PMT gain
between three muon data sets.

uration of 8 mm lead and 2 mm scintillator plates(T411).
4.3. Systematic uncertainties
We have evaluated the following sources of thesystematic uncertainties on the energy resolution
and the e/p ratio measurements.
(a) PMT gain instability: 1.2% from run to run.
(b) Pedestal instability: Typically 0.75 ADC counts(0.25 pC/count) from run to run, corresponding toa 1.4% change of the gain calibration constants.
(c) Lead thickness variations: 100 lm for a nominal thickness of 4 mm.
(d) Light yield variations of tile/"ber systems:
14% as described in Section 2.
(e) Lateral non-uniformity in a tile/"ber system:
5% as described in Section 2.
E!ect of the source (a) is estimated as follows.
The change of the gain is obtained using three data
sets of penetrating muon runs acquired at di!erent
times for the same con"guration. The distributionof rms variation of the relative PMT gain between
three muon data sets is shown in Fig. 9. The mean

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

55

of rms variation of the relative PMT gain is 1.2%.
This change of the gain consists of two components; coherent drift of all PMTs, and independentchange of each PMT. Energy resolution measurement is a!ected only by the independent component, while the e/p ratio is a!ected dominantly by
the coherent drift. However, it is not easy to
decompose the measured changes into coherent
component and independent component. We thus
assumed systematic uncertainties conservatively as
follows.
E When estimating the e!ect on energy resolution, we assume that measured gain change istotally incoherent. We randomly change thecalibration constants according to the measured
shift, and examine the e!ect on the energy
resolution.
E When estimating the e!ect on the e/p ratio,
we assume that measured change is totallycoherent. In this case, the e/p ratio simply
shifts by an amount of the gain shift. This
was taken as the introduced error to the e/pratio.
We have measured the pedestals frequently,
which are used to measure the pedestal instability(b). We examine this e!ect by comparing the resultsof the analysis using various pedestal dataset
combinations.
E!ects of (c), (d), and (e) are estimated using
a GEANT 3.2/GHEISHA shower simulation [12].
All the interaction processes available in GEANT
are turned on. The cut o! energies in the simulation
are set to 10 keV for electrons and photons, and100 keV for the hadrons.
In order to estimate the e!ect of the source (c),the thicknesses of the lead plates are randomly
varied according to the measured precision.
Twenty independent con"guration sets are madeand simulated. The same calibration procedure isapplied for these simulated data sets as the case forreal data. Examples of performance di!erence
distribution due to lead thickness variation are
shown in Fig. 10.
We estimate the e!ect of the source (d) in thesame way as (c). 100 sets of calorimeter con"guration are made in which the light yield of eachFig. 10. Typical distributions of performance di!erence causedby the lead thickness variation; (a) energy resolution for 4 GeV
electrons, (b) energy resolution for 4 GeV pions, and (c) e/p
ratio for 4 GeV. The con"guration is lead"8 mm and scintillator"2 mm.

Fig. 11. Typical distributions of performance di!erence causedby the light yield variation; (a) energy resolution for 4 GeV
electrons, (b) energy resolution for 4 GeV pions, and (c) e/p
ratio for 4 GeV. The con"guration is lead"8 mm and scintillator"2 mm.

56

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

Fig. 12. Systematic uncertainty on energy resolution for electrons.

tile/"ber system is smeared according to a Gaussian distribution with a standard deviation of 15%.
Examples of such distributions are shown in
Fig. 11.
E!ect of the source (e) is examined similarly.
A scintillator tile is divided into 100 strips of 1 cm
wide, and each response is varied according to themeasured response map. Average light yield is kept
same for all the tile/"ber systems, since the lightyield variation in di!erent tile/"ber systems is taken
into account in (d).
Systematic uncertainties obtained in the aboveon the energy resolution and e/p ratio are plottedin Figs. 12}14. Typical total systematic uncertainties are 0.5, 0.3, and 2.3% on the energy
resolution p/E for 4 GeV electrons, p/E for
4 GeV pions, and the e/p ratio for 4 GeV,
respectively, for the con"guration of 8 mm leadand 2 mm scintillator plates (T411). We notethat the lead thickness variation is the dominantsource for the systematic uncertainty on the energy
resolution (Figs. 12 and 13), while the tile gain
variation is dominant on the e/p ratio (Fig. 14).
The change in the performance due to (e) is
negligible, and therefore is not plotted. Error

Fig. 13. Systematic uncertainty on energy resolution for pions.

Fig. 14. Systematic uncertainty on e/p ratio.

bars shown in the "gures are the statistical errors
in estimating the total systematic uncertainty.
Total systematic uncertainties are summarized inTable 2.

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65
Table 2
Total systematic uncertainties on energy resolution for electrons(top), for pions (middle), and the e/p ratio (bottom)
Con"guration
lead : scintillator(in mm)*(p/E) for electrons (%)
1 GeV

2 GeV

3 GeV

4 GeV

4 : 2 in T411
6 : 2 in T411
8 : 2 in T405
8 : 2 in T411
10 : 2 in T405
10 : 2 in T411
12 : 2 in T405
14 : 2 in T405
16 : 2 in T405
16 : 2 in T411

0.5
0.8
1.2
1.2
1.0
No data
0.9
1.1
1.7
1.4

0.6
0.8
0.8
0.8
1.1
1.1
0.8
1.0
0.8
0.7

0.5
0.6
0.7
0.7
0.9
0.9
0.8
0.6
0.5
0.5

0.5
0.4
0.5
0.5
0.5
0.6
0.9
0.6
1.0
1.1

Con"guration
lead : scintillator(in mm)*(p/E) for pions (%)
1 GeV

2 GeV

3 GeV

4 GeV

4 : 2 in T411
6 : 2 in T411
8 : 2 in T405
8 : 2 in T411
10 : 2 in T405
10 : 2 in T411
12 : 2 in T405
14 : 2 in T405
16 : 2 in T405
16 : 2 in T411

0.4
0.4
0.5
0.5
0.5
No data
0.7
0.7
1.0
0.5

0.3
0.4
0.5
0.4
0.5
0.5
0.5
0.6
0.6
0.6

0.3
0.5
0.4
0.4
0.4
0.5
0.4
0.4
0.4
0.4

0.3
0.3
0.4
0.3
0.3
0.5
0.4
0.4
0.4
0.5

Con"guration
lead : scintillator(in mm)(*(e/p))/(e/p) (%)
1 GeV

2 GeV

3 GeV

4 GeV

4 : 2 in T411
6 : 2 in T411
8 : 2 in T405
8 : 2 in T411
10 : 2 in T405
10 : 2 in T411
12 : 2 in T405
14 : 2 in T405
16 : 2 in T405
16 : 2 in T411

2.1
2.1
2.5
2.3
2.7
No data
3.5
4.3
5.2
5.1

1.7
2.2
2.2
2.2
2.2
2.3
2.9
3.5
4.5
4.5

1.7
2.2
2.4
2.2
2.2
2.5
2.5
3.3
4.2
4.2

1.7
2.3
2.5
2.3
2.2
2.5
2.5
3.1
3.9
3.9

5. The results
5.1. Energy resolution for electrons
Energy resolution for electrons is obtained by"tting pulse-height distributions with a single

57

Gaussian function over the region $2.5p aroundthe mean. The measured energy resolution p/E forelectrons is listed in Table 3.
Energy resolution is well described by the following equation:p p"   p E
(E

(4)

where  denotes the sum in quadrature and E isenergy in GeV. In general, the sources of pare calibration uncertainty, shower leakage and nonuniformity of the calorimeter. A "tting with Eq. (4)to the measured energy resolution p/E is performed, and the results of the "tting are listed inTable 4. As shown in Table 4, the constant terms
are consistent to zero in most cases, but errors arelarge. Thus they are disregarded in following analyses. This is reasonable in such a low energy range
we measured.
The stochastic term for a sampling calorimeter isgiven byp/(E  
"(p
#(p
#p
);d/(E(5)    
where d is the thickness of a lead plate in mm,pdepends on the interaction of the secondary  
particles, p
is the sampling #uctuation, and pcomes from the statistical #uctuation of the 
number of photo-electrons.
Energy dependence and lead-thickness dependence of the energy resolution p/(E for each calorimeter con"guration are shown in Figs. 15 and 16,
respectively. We can see in Fig. 15 that pis  
dominant in the energy resolution for electrons as
described above. Since p/(E is dominated byp, we can "t the data in Fig. 16 with Eq. (5).
  
The "tted result is"0.0> % and  
\ 
(p
#p
"(8.31$0.06)%  with s/n.d.f."43.7/37"1.18.
The photostatistic term was estimated to be(3.8$0.1)% from the light yield measurement oftile/"ber systems described in Section 2. Thus,p
was estimated to be (7.4$0.1)%. For EM 
shower, p
is negligible.
  p

58

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

Table 3The energy resolution p/E for electrons
Con"guration
lead : scintillator (in mm)

4 : 2 in T411
6 : 2 in T411
8 : 2 in T405
8 : 2 in T411
10 : 2 in T405
10 : 2 in T411
12 : 2 in T405
14 : 2 in T405
16 : 2 in T405
16 : 2 in T411

p/E (%)
1 GeV

2 GeV

3 GeV

4 GeV

15.1$0.5
19.3$0.9
22.9$1.3
22.9$1.3
25.3$1.0
No data
27.1$1.0
31.0$1.2
34.1$1.7
33.2$1.6

11.0$0.6
14.5$0.8
16.6$0.9
16.2$0.9
18.6$1.1
18.8$1.1
20.9$0.8
23.0$1.1
25.1$0.8
24.5$0.8

8.7$0.5
11.1$0.7
13.6$0.8
13.2$0.7
15.3$0.9
15.5$0.9
17.1$0.8
18.8$0.7
20.3$0.5
20.0$0.6

7.6$0.5
9.8$0.4
11.6$0.5
11.2$0.5
13.3$0.5
13.1$0.6
14.8$0.9
16.5$0.7
16.9$1.0
18.1$1.1

Table 4The p/E "t result with Eq. (4) for electrons
Calorimeter con"gurationp(%)
  p(%)
 Lead : scintillator"4 : 2 mm in T411

15.2$0.6

Lead : scintillator"6 : 2 mm in T411

19.5$0.9

Lead : scintillator"8 : 2 mm in T405

23.0$1.2

Lead : scintillator"8 : 2 mm in T411

22.7$0.9

Lead : scintillator"10 : 2 mm in T405

25.0$1.4

Lead : scintillator"10 : 2 mm in T411

26.5$1.9

Lead : scintillator"12 : 2 mm in T405

26.5$1.50.0> \ 
1.3> \ 
1.9> \ 
0.0> \ 
4.6> \ 
0.0> \ 
7.6$2.4

Lead : scintillator"14 : 2 mm in T405

30.5$1.5

6.6$3.0

Lead : scintillator"16 : 2 mm in T405

35.0$1.3

Lead : scintillator"14 : 2 mm in T405

32.9$2.00.0> \ 
6.8> \ 

5.2. Energy resolution for pions
Energy resolution for pions is obtained with thesame procedure as for electrons. The measured
energy resolution p/E for pions is listed in Table 5.
A "tting with Eq. (4) to the measured energy
resolution p/E is performed, for 2, 3, and 4 GeV,
and the results of the "tting are listed in Table 6. As
shown in Table 6, the constant terms are again
consistent to zero in most cases, but could not be
estimated precisely and were disregarded, same aselectrons.

The best energy resolution for pions of
33.6%/(E is obtained with the con"guration
where the thicknesses of lead and scintillator plate
were 4 and 2 mm, respectively.
The results for each energy and each con"guration are shown in Figs. 17 and 18. As seen in Fig. 17,pis also dominant for pions in the energy  
range we measured as described above. Thus p/(Ewas "tted with Eq. (5) as a function of lead thickness
as shown in Fig. 18. Here the data for 2, 3, and 4 GeV
and those for 1 GeV are "tted separately, since
1 GeV shower behaves di!erently as seen in Fig. 17.

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

Fig. 15. Energy resolution p/(E vs. energy for electrons.

Fig. 16. Energy resolution p/(E vs. Pb thickness for electrons.
Solid curve is a "t to Eq. (5).

The results are

and

p

(p
#p  "(8.9$0.3)% for 1 GeV.
 


"(24.4$0.7)%
  
and
#p
(p
"(11.2$0.2)%
  
for 2, 3, and 4 GeV
p

59"(25.6$0.9)%
  s/n.d.f. of these "ttings are 24.0/28"0.86 (for 2, 3,
4 GeV) and 3.32/7"0.474 (for 1 GeV). p
is  
estimated to be about 25% for lead/scintillator
sampling calorimeters. As p
is estimated to be (3.8$0.1)%, p
are estimated to be 

Table 5The energy resolution p/E for pions
Con"guration
lead : scintillator (in mm)

4 : 2 in T411
6 : 2 in T411
8 : 2 in T405
8 : 2 in T411
10 : 2 in T405
10 : 2 in T411
12 : 2 in T405
14 : 2 in T405
16 : 2 in T405
16 : 2 in T411

p/E (%)
1 GeV

2 GeV

3 GeV

4 GeV

31.4$0.6
33.7$0.6
35.7$0.6
35.7$0.7
38.3$0.8
No data
40.6$1.0
40.6$1.0
44.6$1.3
44.7$1.1

24.4$0.5
25.7$0.5
28.1$0.6
28.0$0.6
30.3$0.6
30.8$0.7
32.6$0.7
32.9$0.8
36.0$0.9
34.9$1.0

19.1$0.4
21.1$0.6
22.6$0.4
23.3$0.5
24.9$0.5
25.3$0.7
26.8$0.6
27.3$0.6
29.8$0.6
29.9$0.6

16.5$0.4
17.3$0.5
20.0$0.5
19.7$0.4
21.5$0.4
21.7$0.6
23.2$0.6
24.5$0.5
26.6$0.6
26.1$0.7

60

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

Table 6
The p/E "t result with Eq. (4) for pions
Calorimeter con"gurationp(%)
  p(%)
 Lead : scintillator"4 : 2 mm in T411

33.6$0.5

Lead : scintillator"6 : 2 mm in T411

36.0$0.6

Lead : scintillator"8 : 2 mm in T405

39.4$1.3

Lead : scintillator"8 : 2 mm in T411

39.7$1.0

Lead : scintillator"10 : 2 mm in T405

42.7$0.5

Lead : scintillator"10 : 2 mm in T411

43.6$1.4

Lead : scintillator"12 : 2 mm in T405

45.8$1.7

Lead : scintillator"14 : 2 mm in T405

43.6$2.50.0> \ 
0.0> \ 
1.9> \ 
0.0> \ 
2.6> \ 
0.0> \ 
3.9> \ 
11.9$3.3

Lead : scintillator"16 : 2 mm in T405

48.3$2.8

11.0$4.4

Lead : scintillator"14 : 2 mm in T405

46.8$3.2

12.0$4.4

Fig. 17. Energy resolution p/(E vs. energy for pions.

(10.5$0.2)% for 2}4 GeV and (8.0$0.3)% for
1 GeV.
As shown in Fig. 18, p
for 1 GeV pions  is smaller than those for 2}4 GeV, indicatingthat 1 GeV pions do not develop shower
su$ciently.

Fig. 18. Energy resolution p/(E vs. Pb thickness for pions.
Solid and dashed curves shown in the "gure are "tting results to
Eq. (5) for 2}4 and 1 GeV, respectively.

5.3. Linearity, the e/p pulse-height ratio, and, lateralleak correction
In order to calculate linearity and the e/p pulseheight ratio, shower leakage must be corrected for

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

61

Table 7
The non-linearity
Calorimeter con"guration

For electrons (%)

For pions (%)

Lead : scintillator"4 : 2 mm in T411
Lead : scintillator"6 : 2 mm in T411
Lead : scintillator"8 : 2 mm in T405
Lead : scintillator"8 : 2 mm in T411
Lead : scintillator"10 : 2 mm in T405
Lead : scintillator"10 : 2 mm in T411
Lead : scintillator"12 : 2 mm in T405
Lead : scintillator"14 : 2 mm in T405
Lead : scintillator"16 : 2 mm in T405
Lead : scintillator"16 : 2 mm in T405

1.2$0.4
1.1$0.4
2.2$0.7
2.7$1.0
2.7$1.0
1.1$0.5
2.7$1.0
2.8$1.0
3.4$1.2
1.6$0.6

1.0$0.3
1.2$0.4
1.1$0.5
1.0$0.3
0.9$0.4
1.1$0.5
2.1$0.8
2.4$1.0
3.7$1.3
3.3$1.3

Table 8The lateral shower leakage estimated from the lateral shower pro"le function measured by SPACAL experiment [13]Con"guration
lead : scintillator (in mm)

4 : 2 in T411
6 : 2 in T411
8 : 2 in T405
8 : 2 in T411
10 : 2 in T405
10 : 2 in T411
12 : 2 in T405
14 : 2 in T405
16 : 2 in T405
16 : 2 in T411

Lateral leakage (%)
1 GeV

2 GeV

3 GeV

4 GeV

5.8$1.7
4.5$1.4
5.9$1.8
4.1$1.2
3.5$1.1*
4.1$1.2
3.1$0.9
3.4$1.0
2.8$0.8

5.3$1.6
4.1$1.2
5.4$1.6
3.8$1.1
3.2$1.0
3.0$0.9
3.8$1.1
2.9$0.9
3.1$0.9
2.5$0.8

5.0$1.5
3.9$1.2
5.1$1.5
3.6$1.1
3.1$0.9
2.9$0.9
3.6$1.1
2.7$0.8
2.9$0.9
2.4$0.7

4.7$1.4
3.7$1.1
4.8$1.5
3.4$1.0
2.9$0.9
2.8$0.9
3.4$1.0
2.6$0.8
2.8$0.8
2.3$0.7

the pion shower. This correction is done by usingparameterized shower pro"le obtained by
SPACAL experiment [13] as

 

 

dE B
r
B
r
"  exp ! #  exp ! .
ds
r
j
r
j



ence of the lateral leak fraction measured by
SPACAL experiment (Fig. 18 of Ref. [13]). Ourestimation from the extrapolation is given below.
leak at 1 GeV"leak at 5 GeV;1.25,(6)

However, SPACAL data exist only for con"guration of lead/scintillator " and for energies higherthan or equal to 5 GeV. We thus extrapolate theshower pro"le parameters according to the averagecalorimeter density and energy dependence of theleakage fraction.
Energy dependence of the lateral leak is estimated by simply extrapolating the energy depend-leak at 2 GeV"leak at 5 GeV;1.15,
leak at 3 GeV"leak at 5 GeV;1.09, andleak at 4 GeV"leak at 5 GeV;1.03.
Here relative error for shower leak at 5 GeV is
estimated to be $30% in Ref. [13].
Density dependence is calculated by scaling thelateral size parameters j and j inversely proportional to the average density of the calorimeter. For

62

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

Fig. 19. Mean pulse height/energy vs. energy for electrons.

Fig. 21. Non-linearity vs. lead thickness for electrons (top) andfor pions (above).

Fig. 20. Mean pulse height/energy vs. energy for pions.

example, in the case of 8 : 2 con"guration of T411
beam test, the average density of the calorimeter
module was 6.69 g/cm (Table 7). SPACAL groupobtained lateral size parameter j "17.7 cm and

Fig. 22. The e/p ratio (uncorrected) vs. Pb thickness. The error isdominated by systematic uncertainties introduced when the leadthickness is changed. Therefore, the errors are correlated for thedata in the same con"guration, thus irreducible by combining
data of same con"guration.

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

Fig. 23. The e/p ratio (corrected) vs. Pb thickness. The error isdominated by systematic uncertainties introduced when the leadthickness is changed. The inner error bar in the plot shows thestatistical and systematic uncertainty without lateral leakage
correction. The outer error in the plot shows the total uncertainty including lateral leakage correction. The line in the plot is theresult of linear function "tting to data. We obtained the compensation point to be d"9.1$0.3 mm from this "tting.

j "7.68 cm for their module which had an average density of 9.02 g/cm. Assuming these size
parameters are inversely proportional to the calorimeter density, we obtain j "23.9 cm and

63

j "10.4 cm for our 8 : 2 module. Using theseparameters, shower pro"le function (6) is numerically integrated over 1 m and over in"nitely, andleak fraction is obtained. The results of these lateral
shower leakage are listed in Table 8.
The mean of the pulse-height distribution is obtained by "tting with a Gaussian. Figs. 19 and 20
show the mean pulse height divided by the beamenergy. We can see in these "gures that pulse heightis described by a linear function of the energy.
Non-linearity is de"ned by the rms variation of themean pulse height/energy for each con"guration,and is shown in Fig. 21. The linearity is degraded
for thick lead absorbers due to coarse sampling.
Otherwise linearity is reasonable.
The e/p ratio before and after lateral leakage
correction are plotted in Figs. 22 and 23 as a function of the absorber thickness, and also listed inTables 9 and 10 . The 1 GeV data is omitted from
Figs. 22 and 23 since 1 GeV pion shower behaves
di!erently as seen in Fig. 18. As seen from Fig. 23,
the e/p ratio decreases as the lead thickness increases, and crosses the line of e/p"1. Sincee/p"1 equivalently means e/h"1, this point gives
the compensation condition. This behaviour is approximated by a linear function and "tting is carried out. The result of the "tting is also shown in
Fig. 23. As a result of this "tting, the compensation
point is found to be 9.1$0.3 mm for 2 mm-thickplastic scintillator. This "tted e/p ratio is signi"cantly smaller than the previous measurements

Table 9The e/p ratio (before lateral leakage correction)
Con"guration
lead : scintillator (in mm)

4 : 2 in T411
6 : 2 in T411
8 : 2 in T405
8 : 2 in T411
10 : 2 in T405
10 : 2 in T411
12 : 2 in T405
14 : 2 in T405
16 : 2 in T405
16 : 2 in T411

e/p
1 GeV

2 GeV

3 GeV

4 GeV

1.12$0.02
1.06$0.02
1.06$0.03
1.03$0.02
0.94$0.03
No data
0.97$0.04
0.95$0.04
0.91$0.05
1.02$0.05

1.11$0.02
1.10$0.02
1.08$0.02
1.08$0.02
0.96$0.02
1.04$0.03
0.98$0.03
0.94$0.03
0.90$0.04
0.99$0.05

1.14$0.02
1.11$0.03
1.04$0.03
1.08$0.02
0.97$0.02
1.05$0.03
0.98$0.03
0.96$0.03
0.90$0.04
0.99$0.04

1.15$0.02
1.11$0.03
0.99$0.03
1.08$0.02
0.98$0.02
1.04$0.03
0.98$0.02
0.95$0.03
0.89$0.04
0.96$0.04

64

T. Suzuki et al. / Nuclear Instruments and Methods in Physics Research A 432 (1999) 48}65

Table 10The e/p ratio (after lateral leakage correction)
Con"guration
lead : scintillator (in mm)

4 : 2 in T411
6 : 2 in T411
8 : 2 in T405
8 : 2 in T411
10 : 2 in T405
10 : 2 in T411
12 : 2 in T405
14 : 2 in T405
16 : 2 in T405
16 : 2 in T411

e/p
1 GeV

2 GeV

3 GeV

4 GeV

1.06$0.03
1.01$0.03
1.00$0.03
0.99$0.03
0.91$0.03
No data
0.93$0.04
0.92$0.04
0.88$0.05
0.99$0.05

1.05$0.03
1.06$0.03
1.02$0.03
1.04$0.03
0.93$0.02
1.01$0.03
0.95$0.03
0.92$0.03
0.87$0.04
0.96$0.05

1.09$0.03
1.07$0.03
0.99$0.03
1.05$0.03
0.94$0.02
1.02$0.03
0.94$0.03
0.93$0.03
0.88$0.04
0.97$0.04

1.10$0.02
1.08$0.03
0.94$0.03
1.04$0.03
0.95$0.02
1.02$0.03
0.95$0.03
0.92$0.03
0.87$0.04
0.94$0.04[4}6] which gave e/p"1.1 for E410 GeV with
con"guration of 8 : 2.

2 mm-thick plastic scintillator. This ratio is a little
larger than those popularly assumed. However,tests with higher-energy beams are necessary tocon"rm the consistency with the existing data.

6. Conclusions
We measure the energy resolution and the e/pratio of lead/plastic-scintillator sampling calorimeter for various lead/scintillator volume ratios inthe energy range 1}4 GeV.
The energy resolution for electrons is measured
to be p/E"(0.0> %(8.30$0.06%);(d)/(E,\ 
where the thickness d of lead plate is in mm and theenergy E is in GeV. Energy resolution for pions ismeasured to be p/E"(24.4$0.7%(11.2$0.2%);(d/(E for 2}4 GeV and p/E"
(25.6$0.9%(8.9$0.3%);(d/(E for 1 GeV.
The best hadron energy resolution of 33.6%/(Eis obtained for 4 mm thick lead absorber case. Thisis as good as typical lead/scintillating-"ber calorimeter, and is one of the best energy resolutions
achieved so far. This enables us to construct a linear
collider calorimeter with the best hadron energy
resolution at a reasonable cost. The intrinsic hadron energy resolution of 25%(E would suggest us
to design an ambitious calorimeter with a muchbetter resolution.
The compensation is found to be achieved at thelead thickness of 9.1$0.3 mm in combination with

Acknowledgements
We would like to thank the members of theaccelerator group and the beam channel group of
the KEK proton synchrotron for their support
during the beam test. This work was supported inpart by KEK-University R&D program and by the
JSPS Japanese}German Cooperative Program.

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