Coordinate measurements with a hodoscope hadron calorimeter at energies up to 300 GeV

Nuclear Instruments and Methods 206 (1983) 373-378 North-Holland Publishing Company

COORDINATE MEASUREMENTS E N E R G I E S U P T O 300 GeV IHEP

I-IISN 2-LAPP

F. B I N O N

2.+

WITH A HODOSCOPE

3 COLLABORATION

V.A. DAVYDOV

373

1, S.Vo

HADRON CALORIMETER AT

*

DONSKOV

J, P. D U T E I L

4, M . G O U A N I ~ R E

V.A. KACHANOV I D.B. KAKAURIDZE 1, G . V . K H A U S T O V 1, Y u . V . M I K H A I L O V T. M O U T H U Y 2.+, j . p . P E I G N E U X 3 Y u . D . P R O K O S H K I N I a n d J.P. S T R O O T 2,+

3 I

l Institute for High Energy Physics, Serpukhov, USSR : lnstitut Interuniversitaire des Sciences NuclOaires, Belgium 3 Laboratoire d'Anneo' de Physique des Particules, France 4 CERN, Geneva, Switzerland

Received 19 July 1982

The possibilities offered by a novel experimental technique - the hodoscope hadron calorimeter - to determine coordinates of high-energy hadrons accurately by measuring the transverse spread of their associated showers have been studied. This accuracy is shown to improve with energy as (ln4E + q l E ) l / 2 / E and at E = 300 GeV it reaches % = 3 mm. The shrinkage of the hadron shower and the growth of its central component with increasing energy have been measured. As for energy resolution, the hodoscope calorimeter does not yield to conventional calorimeters.

I. Introduction It has been shown in a previous work [1] that h a d r o n calorimeters with a hodoscope structure allow to measure not only the energy of h a d r o n s but also their impact coordinates by measuring the transverse spread of the showers [2]. With the first detector of this type a coordinate accuracy of - 1 cm has been o b t a i n e d for ~ - , K - a n d p - between 25 and 40 GeV [1,3]. The present work is devoted to the study of the resolution of the hodoscope h a d r o n calorimeter at higher energies, E = 100-300 GeV. The energy resolution of a calorimeter improves like l / r E with increasing energy (see review [4] for experimental data). According to [5], approximately the same energy d e p e n d e n c e is expected for the accuracy of h a d r o n coordinates measurements with a hodoscope calorimeter. One of the aims of the experiments described below was to verify this statement.

2. Characteristics and calibration of the calorimeter The calorimeter, installed on the H8 b e a m line of the C E R N SPS, has been irradiated with ~r- of 100, 200 and 300 GeV. The K - a n d p c o n t a m i n a t i o n of the b e a m is low: 6, 4 and 1%, respectively [6]. The impact point of the particles on the calorimeter has been * Joint Experiments of IHEP, Serpukhov, USSR and CERN, Geneva, Switzerland + Mailing address: EP Division, CERN, 1211 Geneva, Switzerland. 0 1 6 7 - 5 0 8 7 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 0 3 . 0 0 © 1983 N o r t h - H o l l a n d

d e t e r m i n e d with a precision of _+0.5 m m with auxiliary x - y scintillation hodoscopes. A detailed description of the hodoscope h a d r o n calorimeter has been given in the preceding paper [1]. In short, it is a total absorption detector of sandwich type in which hodoscope planes made of scintillator strips of width d = 5 cm (perpendicularly to the b e a m direction) alternate with 2.5 cm thick iron converter planes. The detector has an aperture 70 × 70 cm 2. It is divided in three identical blocks (25 cm of iron in each block) which allow to follow the longitudinal development of the h a d r o n shower. C o m b i n a t i o n s of signals from the last dynode of the PMs are used for triggering purposes, namely the sum of corresponding channels in the three blocks and the sum of all 84 counters in the calorimeter. This makes it possible to tune the detector with a parasitic beam, using this last s u m m a t i o n as a trigger for muons. The adjustment and the calibration of the 84 calorimeter counters have been made, as before [1], by irradiating the detector with muons. Nevertheless, the procedure becomes much more involved at higher energies. At 300 GeV, the amplitude of the global signal due to a h a d r o n is 200 times larger than tat due to a muon. This difference is even 2 or 3 times bigger for a single counter of the calorimeter at the m a x i m u m of the shower. The photomultipliers FEU-84-3 used in the detector are linear over this dynamical range. Nevertheless, in order to cover such a wide range, it is necessary to carry out the calibration in a few steps, c o m p a r i n g each time

F Binon et a L / Coordinate measurements with a hodoseope hadron calorimeter

374

the signals from m u o n s with those from reference light pulses delivered by the light e m i t t i n g diodes ( L E D ) of the calorimeter light calibration s y s t e m [1,7]. At first, the gain of each c o u n t e r is t u n e d so that the average c o n v e r t e d a m p l i t u d e for m u o n s ( A , ( k ) ) is a b o u t 50 units of a 12-bit A D C a n d the L E D signal (A~I[zD(k)) is a b o u t 1000 units on the same scale * This m e a s u r e m e n t fixes the scale b e t w e e n m u o n signals a n d the signals of the L E D system. After, the gain o f the P M s is r e d u c e d several times c h a n g i n g the high voltage and the n e w value (A(L~i)(k)) is measured. T h e n , the a m p l i t u d e of L E D signals is increased a n d a n e w value (A(L~o(k)) is o b t a i n e d . This p r o c e d u r e is r e p e a t e d n (3 to 4) times until the a m p l i t u d e o f the signal due to p i o n s in each c o u n t e r A,~(k) stays within the range of c o n v e r s i o n o f the A D C s . T h e calibration coefficient fit for each calorimeter c o u n t e r is then simply the p r o d u c t o f m e a s u r e d ratios:

1

a_

0

const. ilk-

5

10

15

20 y [cm]

(A,(k)) x

(A~D(k))

...

(A(;h)'(k))

(1)

All the quantities e n t e r i n g (1) have been m e a s u r e d with a statistical accuracy better than 1%. The error o n the value of the calibration coefficients has been e s t i m a t e d to be less than 4% from the s y m m e t r y deviation and from the s m o o t h n e s s of the flk ( A , , ( k ) ) distribution.

Fig. I. Differential distribution of average amplitude (shower profile) versus the distance to the impact point on the cell, measured with the hodoscope calorimeter and ~r- of 25 [1] and 300 GeV. The full curve is the weighted sum of two exponentials (2). The profile of 3 TeV showers (dashed curve) deduced from the extrapolated parameters in fig. 2 is used to illustrate the prospects of the method. Normalization is d(A,(O))/d.v = 1.

b2=(7.5_+0.3)E

0.,)6±00, cm

(4)

3. Results o f / h e measurements

3.1. Hadron shower profile T h e possibility to m e a s u r e h a d r o n c o o r d i n a t e s with the h o d o s c o p e calorimeter d e p e n d s on a basic c h a r a c t e r istic of the s h o w e r s n a m e l y their profile, i.e. the energy d i s t r i b u t i o n of the s h o w e r s in the transverse direction. T h e s h o w e r profiles m e a s u r e d in the p r e s e n t work (fig. 1) as well as those m e a s u r e d at low energies [1], are described by two e x p o n e n t i a l functions:

d(A,,()')) dy

(here a n d b e l o w E is expressed in GeV). The decrease of the peripheral part of the s h o w e r ( a 2 ) seems to slow d o w n a b o v e 100 GeV. C o n t r a r y to e l e c t r o m a g n e t i c s h o w e r s [5], h a d r o n

- - 0 ~ 0

o

~

o

b I = (3.9 + 0 . 2 ) E

0.17±0.02 cm,

_

_

o

~

[32

2 - - ~ ° ~ ° ~ O ~

a lexp(-[yl/bl)+a2exp(-lvl/b2).

o

b,

V~V .

.

(2)

The values o f the p a r a m e t e r s a p p e a r i n g in expression (2) are s h o w n in fig. 2. b 1 and b 2 decrease slowly with increasing energy, a c c o r d i n g to the following p o w e r laws **"

05

.

.

02

(3) 01 I0C-eV

* Here and below brackets ( ) around a value, or a bar above it, stand for its average value taken over a set of events. ** In the 10 GeV to 1 TeV region, the energy dependence of h I and b2 may also be described with logarithmic functions: h t - ( 3 . 0 _ + 0 . 2 ) - ( 0 . 2 7 + 0 . 0 4 ) l n E cm, b 2 - ( 7 . 3 _ + 0 . 4 ) (0.35_+0.03) In E cm, which practically coincide with (3), (4).

~

20

30

50 70 I00

200 300

500 700 ITeV

2

3

E

Fig. 2. Variation of the shower profile with increasing ~" energy. The points on the figure are measured values of the parameters appearing in expression (2) in the energy region 25 300 GeV. The straight lines correspond to the power functions (3) and (4). The lower curve is a guide for the eye only. ~1 I - -

1

a 2 .

F. Binon et al. / Coordinate measurements with a hodoscope hadron calorimeter ~f [cm]

375

yf [cm]

8 /

i/o °

6 °'

.•,ofl

/ g~l

11 0

I 2

I

I 3

I 4

d:1Ocm

d/2

i

J

i

0

2

4

I

_

h

6

Yc [ c m ]

8 Yc [ c m ]

Fig. 3. Dependence of the measured coordinates of a shower ~f on the ~v impact point in the cell v~L-at E = 200 GeV. The error bars shown are a,., y = 0 corresponds to the border of the cell and y = d / 2 to its center. Results shown on the left correspond to a cell width d = 5 cm, while those on the right correspond to d = 10 cm.

showers shrink whith rising energy. This is explained by the growth of ~r° c o n t r i b u t i o n a n d the corresponding increase of the electromagnetic c o m p o n e n t in the h a d r o n shower (see e.g. [8]). It can be seen in fig. 2 that the h a d r o n shower must keep shrinking in the TeV energy region (fig. 1). The shrinkage of the shower with increasing energy, a n d also the d i m i n u t i o n of the relative fluctuations of the energy release, lead to a better localisation of showers in the hodoscope calorimeter and to a more effective spatial separation of showers from adjacent hadrons. 3.2. Measurement o f hadron coordinates The coordinate of a h a d r o n is obtained from the center of gravity of its associated shower Y0 = d~kkflkA,~(k)/~flkA~(k) after a small bias correction [1] due to the exponential form of the shower (2). The measured coordinate Yr corresponds to the true coordinate y~ with a high accuracy (fig. 3). This procedure eliminates systematic errors for wider cells also *, where the non-linearity of,Y0 towards Yc increases. The accuracy o~ of the reconstructed h a d r o n coordinates, which as shown in ref. [1] is i n d e p e n d e n t of the nature of the particle, varies with the location of the impact point on the calorimeter cell. The closer to the cell b o u n d a r y the impact is, the better the accuracy is (fig. 4). The amplitude of this variation is larger in wider cells [9,10] as a consequence of the exponential profile of the shower. It depends also on the algorithm chosen

to determine the coordinates (for more details, see [3,9]). The spatial resolution of the hodoscope calorimeter is well described by a G a u s s i a n distribution (fig. 5). At 300 G e V the accuracy of the coordinate determination for hadrons, averaged over the calorimeter cell, reaches ~. = 2.9 m m , i.e. it is improved by a factor 3 for the energy increase b y an order of magnitude. The dependence of the coordinate accuracy on energy is shown in fig. 6. As expected [5], it follows the relationship ~v = q0( ln4E + q , E ) ' / 2 / E "

(5)

Extrapolation of these data into the TeV energy region shows that a hodoscope h a d r o n calorimeter should provide a one millimeter coordinate accuracy at U N K energies (3 TeV).

0

[mini

+

6

÷

÷

÷

÷

+

,,. ÷

+ + ÷ +

100GeV

+ o o o o o o o o o + ÷ o o o o o o • • • • •

3 0 0 GeV

+

Z.

+

+ ÷

o

o

÷ +

~:o0

o

e

o

o

•

o

•

o

•

2 0 0 GeV

•

o

2

d/2 0

* The summation of signals from adjacent cells allows to get also results for calorimeters with wider cells: d = 10, 15 and 20 cm.

~ 0

~ 10

J 20

I 30 Yc [ m m ]

Fig. 4. Dependence of the coordinate accuracy 6,' on the impact point in the calorimeter of E = 100, 200 and 300 GeV ~r .

F. Binon et el. / Coordinate measurements with a hodoscope hadron calorimeter

376

N3°° 200

100 0

as follows from the s h o w e r profile (2). In this case d o - 2 b 2, if d > 2 b p E x p r e s s i o n (6) describes well the e x p e r i m e n t a l n u m b e r s (fig. 7). T h e q u a n t i t y d o is cons t a n t within the limits of errors o f m e a s u r e m e n t in the energy interval 2 5 - 3 0 0 G e V a n d is equal to (11.8 _+ 1.5) cm, which is close to the value of 2 b 2 (see fig. 2). It follows that (fig. 8)

E=300GeV

~

-10

o o = (3.6 + 0 . 2 ) / r E

i~ ~

-5

0

5

10

Yf-Yc[mm] Fig. 5. Distribution of the difference between measured (yf) and real (y~) ~ coordinates obtained with a d = 5 cm wide cell uniformly irradiated with 300 GeV ~ . The dashed curve is a Gaussian distribution with ~ = 3 mm.

3.3. Dependence of the coordinate accuracy on the cell width T h e error on r e c o n s t r u c t e d h a d r o n c o o r d i n a t e s grows rapidly with the c a l o r i m e t e r cell d i m e n s i o n s . F o r the central part of the cell (y~ = d / 2 ) the g r o w t h is exp o n e n t i a l [5]:

o,,(y~ = d / 2 ) = % exp( d / d o ) ,

(6)

~y[mm]

cm.

(7)

T h e c o o r d i n a t e a c c u r a c y averaged over the cell, o~,, is given in table 1. Its d e p e n d e n c e o n the cell w i d t h is m o r e c o m p l e x than (6), specially for small d a n d large E values. This results f r o m the d e p e n d e n c e of the coordin a t e resolution on the i m p a c t p o i n t on the cell (fig. 4). T h e variation of o~. with h a d r o n energy for various cell w i d t h s is a n a l o g o u s to (5).

3.4. Energy resolution of the calorimeter T h e m a i n goal o f the p r e s e n t work was to study the possibility to m e a s u r e precisely the c o o r d i n a t e s of highenergy h a d r o n s with a h o d o s c o p e calorimeter. As an energy m e a s u r i n g i n s t r u m e n t , the h o d o s c o p e calorimeter is nevertheless similar to c o n v e n t i o n a l c a l o r i m e t e r s w h o s e energy resolution has been s t u d i e d in detail [4,11]. It has not been a t t e m p t e d in this w o r k to reach the best a t t a i n a b l e energy resolution. T h e s p e c t r u m o f the s u m o f the signals from all cells o f the calorimeter, Ato t, irradiated with 100 G e V ~r is s h o w n in fig. 9. As in the previous work [1], events in w h i c h the s h o w e r is starting to d e v e l o p in the first c a l o r i m e t e r block have been selected. T h e spectra look the s a m e for E = 200 a n d 300 GeV. T h e total thickness of iron in the c a l o r i m e t e r cells is

10

,~/ 40OeV

8 6 °~

~,

/ looG~v

/,

!

is

I

#'/

~

10

~5

300G~v

2~

10GeV 20

50

100 200

S00

1TeV 2 E

Fig. 6. Dependence of the coordinate accuracy 5~. on rr energy. The cell of the calorimeter is uniformly irradiated. Data in the range 25 to 40 GeV are taken from [1], data between 100 and 300 GeV are results obtained in the present work. The curve shows the dependence (5), normalized at E = 25 GeV with q0-1-8cmandq~=4GeV 115].

0

5

L

d[¢m]

20

Fig. 7. Coordinate accuracy at the center of the cells %(.~.'~= d / 2 ) versus cell width d for several ~r energies. The curves represent relation (6).

377

F. Binon et al. / Coordinate measurements with a hodoscope hadron calorimeler

E

300

/,/¢/~

6

E 4

1~7

E_1/2 1

1000

300

100

I 50

/ /

200

I 30

E = 100 GeV

lOO

I 20 GeV

Fig. 8. Variation of the parameter a0 in formula (6) with ~r energy. The straight line is relation (7).

o

_ _ 1

20

40

60

8O

100

120 A t ot

l = 80 cm. This ensures practically full absorption ( > 95%) of E - 3 0 G e V h a d r o n showers, the thickness needed for 95% a b s o r p t i o n being equal to [5] /0.95 (cm of iron) = 40 + 9 In E.

Fig, 9. Spectrum of the sum of the signals from all cells in the calorimeter irradiated with 100 GeV ~- . Ato t = ~ k f l k A ( k ) . Dashed curve is a Gauss±an distribution with OE/E = 6.7%.

(8)

A t 300 GeV, the thickness of the present calorimeter is already insufficient to ensure a large enough absorption (according to (8), it should have / > 90 cm of iron). This entails a b r o a d e n i n g of the resolution curve by - 30% [4,11]. Also, the shower leakage (7% at 100 GeV, 10% at 300 GeV) gives rise to a tail on the left side of the spectrum (fig. 9) (it is absent when the shower is fully a b s o r b e d [8]). The relative energy resolution o E / E of the hodoscope calorimeter at various rr- energies appears in fig. 10 together with results from other works. In c o m p a r i n g various calorimeters one must not forget that the energy resolution changes with the thickness t of the converter: o E ~ t I/3 corresponding to the calculations [4] a n d measurements [1,8]. Taking this factor into account, the data in fig. 10 show a behaviour close to oE/E = 0.65/~-,

(9)

as expected for iron-scintillator sandwich counters. The resolution of the hodoscope calorimeter depends

also on the calibration inaccuracies (to measure Ato t, signals from a few tens of counters are summed), whose c o n t r i b u t i o n increases with the growth of the energy. T h e comparison of measured o E / E values with formula (9) shows that the b r o a d e n i n g of the resolution curve on account of the calibration errors is less t h a n 3%. It is to be noticed that the hodoscope calorimeter used in the present work at energies up to 300 G e V does n o t yield to usual h a d r o n calorimeters in so far as the accuracy of energy m e a s u r e m e n t is concerned. A d d i n g one more block should allow, according to (8), to cover the energy region up to 1 TeV without a loss of energy resolution.

4. Conclusion It has been shown that for energies of h u n d r e d s of G e V a hodoscope calorimeter allows to localize h a d r o n showers with a high spatial accuracy. This accuracy

Table 1 Coordinate accuracy 5,., averaged over the cell, versus the cell width d for various 7r- energies E 6v(mm) E(GeV)

d = 5 cm

10 cm

15 cm

20 cm

25 40 100 200 300

10.4±0.4 8.6±0.3 5.1±0.2 3.6±0.2 2.9±0.2

17.0±0.9 14.5±0.7 9.0±0.5 7.3±0.4 6.2±0.4

22.7±1.1 20.0±1.0 14.4±0.7 11.0±0.6 9.4±0.5

35.9±1.3 32.0±1.2 19.0±0.8 15.0±0.7 12.5±0.6

378

F. Binon et al. / Coordinate measurements with a hodoscope hadron calorimeter

t r a p o l a t e safely into the T e V e n e r g y region w h e r e a n a c c u r a c y of o n e m i l l i m e t e r s h o u l d be r e a c h e d . The prospects of the hodoscope hadron calorimeter m e t h o d are p a r t i c u l a r l y p r o m i s i n g in the case of detectors with a cellular s t r u c t u r e a l l o w i n g to m e a s u r e at high e n e r g y a large n u m b e r of h a d r o n s , n e u t r a l as well as c h a r g e d , at t h e s a m e t i m e [5]. L a r g e d e t e c t o r s m a y be b u i l t on this p r i n c i p l e (e.g. t h e 50 t o n cellular h a d r o n c a l o r i m e t e r of e x p e r i m e n t N A 1 2 n o w in the c o u r s e of i n s t a l l a t i o n in the H 8 b e a m - l i n e o f t h e C E R N SPS). T h e a u t h o r s w o u l d like to t h a n k the D i r e c t o r a t e s of C E R N a n d I H E P for their s u p p o r t to the p r o g r a m G A M S , in t h e f r a m e w o r k of w h i c h the s t u d i e s of t h e h o d o s c o p e h a d r o n c a l o r i m e t e r were a c c o m p l i s h e d .

020 +

O~ E

0.5

,

o.~o

+ I'

~~Let///

4, References

+ ~ ¢4,z~/4'~U

O.O5 ~ , ~

O

LL

J

E-1/2

J

~

~

103 1TeV300200 100

J

50

~

30

L

20

K

15 GeV

Fig. 10. Accuracy of ~ energy measurements with various calorimeters. • are data obtained in the present work and in previous measurements [11 with the hodoscope hadron calorimeter, O are data taken from ref. [8] (t = 2.5 cm of iron), zx are data from ref. [12] (t = 1.25 cm of iron). Other points: see ref. [51 (v, [] and + correspond to t = 4 , 5 and 10 cm of iron, respectively). The straight line is function (9), the dashed curve is the resolution expected for the described calorimeter taking into account the shower leakage.

i m p r o v e s with e n e r g y like ( l n 4 E + q t E ) l / 2 / E a n d is e q u a l to 3 m m at 300 G e V for 5 c m wide d e t e c t o r e l e m e n t s , T h i s d e p e n d e n c e h a s b e e n c h e c k e d in a b r o a d e n e r g y interval, 25 to 300 G e V , w h i c h allows to ex-

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