Calibration of a sampling total absorption detector designed for neutrino experiments

NUCLEAR

INSTRUMENTS

AND

METHODS

I3o (1975) 49-60;

© NORTH-HOLLAND

PUBLISHING

CO.

C A L I B R A T I O N OF A S A M P L I N G T O T A L A B S O R P T I O N D E T E C T O R D E S I G N E D FOR NEUTRINO EXPERIMENTS* B. C. BARISH, J. F. BARTLETT, A. BODEK, K . W . BROWN, D. B U C H H O L Z , F. J A C Q U E T t , F. S. M E R R I T T , F . J . SCIULLI, L. STUTTE, H. SUTER +

California Institute of Technology, Pasadena, California 91125, U.S.A. H. E. F I S K and G. K R A F C Z Y K

Fermilab, Batavia, Illinois 60510, U.S.A. Received 7 July 1975 A sampling total absorption detector was calibrated at Fermilab for energies in the range 5-250 GeV. The calorimeter consisted of a sandwich of scintillator slabs and 4" thick steel plates.

Energy resolutions (rms) of 4-33%, 4- 16%, and -4-9% were achieved for the energies 10, 50, and 150 GeV, respectively.

Recent neutrino experiments 1) performed in the Fermilab narrow band neutrino beam have used a large area sampling total absorption 2) detector. The total absorption detector serves the dual purpose of being a target as well as a hadron calorimeter. This massive detector contains 143 t of steel in the form of seventy steel slabs, each 5 ' x 5' in area and 4" thick. The energy of the final state hadrons released in neutrino interactions such as

tion run at 200 GeV were reported. In this publication we report results from the more recent calibration runs for beam energies between 5 and 250 GeV. The most extensive measurements were done in August 1974. Less extensive measurements were done during June and July 1974. A schematic of the scaled-down calorimeter is shown in fig. 1. It consists of 14 modules, each made of a 4" thick plate of steel (10"× 14" in area) followed by a ~" thick plastic scintillator. The 14 scintillation counters were placed in the 1.1" thick air gaps between the steel plates. This scaled-down calorimeter is long enough to contain longitudinally the shower initiated by the incident hadrons at present Fermilab energies. In front of the calorimeter three counters T1, T2, and T3 are used to signal a single charged particle incident on the detector. The trigger is T1 T 2 T 3 . To provide a calibrating one particle signal, the steel plates in the calorimeter are removable, in which case the particles pass through the counters without interacting. Each

v + nucleus --* p - + hadrons,

(1)

v+nucleus -o v + hadrons,

(2)

and is measured by seventy scintillation counters placed after every 4" of steel (one collision length). The final state hadrons initiate a shower which is sampled by the scintillation counters. Sampling every nuclear collision length in steel is sufficient to allow the measurement of the energy of a 50 GeV shower to an rms accuracy of _ 16%. Because of the large mass of the target calorimeter, it is impractical to move it into a hadron beam for the purpose of calibration3). Instead, a scale model calorimeter of similar design but reduced transverse and longitudinal dimensions was constructed and placed in hadron beams of well defined energies at Fermilab. This scaled down model was described in an earlier publication4), where results of an early calibra-

TRIGGER COUNTERS CALORIMETER TI T2T3 4"STEEL -~' PLASTIC SCINTILLATOR

WHIHWHWHtdW

* Work supported in part by the U.S. Energy Research and Development Administration. Prepared under Contract AT (11-1)-68 for the San Francisco Operations Office. t On leave of absence from Ecole Polytechnique, Paris, France. + Swiss National F u n d for Scientific Research Fellow.

Fig. 1. Schematic of the test calorimeter.

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Counter Number 1

Single Ionizing Pulse Height

Single Ionizing Pulse Height 50 GEV MUONS

150 GEV HADRONS 4" Steel plates removed

4OO

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200

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(a)

400 PULSE HEIGHT

)

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(b)

Fig. 2. Pulse height distribution of singly ionizing particles in the first counter. (a) 150 GeV hadrons, steel plates removed. (b) 50 GeV muons, 4" steel plates in place. scintillator is equipped with its own phototube (RCA 6655); the signals are separately pulse height analyzed for each event, (using LRS 227 quad integrators) and all data are written on magnetic tape. The calorimeter was placed in the hadron beam 6) I

I

PULSE HEIGHT SUM OF 14 COUNTER: 50GEV

MUONS

PEAK 17'.9 o" =2.4

80-

(.f) I-Z i,i > LI_I

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NUMBER OF EQUIVALENT PARTICLES Fig. 3. Pulse height distribution summed over 14 counters for 50 GeV m u o n s (4" steel plates in place).

that is normally used for the 30" bubble chamber in the neutrino area at Fermilab. The primary 300 GeV proton beam was directed onto a production target. A momentum and sign selected secondary beam was transported to the location of the calorimeter 1650 ft. downstream by a series of bending and focusing magnets. The beam was primarily composed ofhadrons (mostly protons and pions for positive sign selection and mostly pions for negative sign selection) with a small muon component. At energies less than 100 GeV there the beam contained a substantial electron contamination (30% at 50 GeV). The electron component was removed prior to the final momentum selection by a 1" thick lead absorber placed 590 ft. upstream of the calorimeter. Data were first taken with all the steel removed in order to calibrate the 14 counters with singly ionizing hadrons. The signals from the photomultipliers were amplified by a factor of 35 for this calibration. The pulse height distribution for singly ionizing 150 GeV hadrons in the first counter is shown in fig. 2a. Runs were taken with positive sign selected beams at 10 and 150 GeV, and with negative sign selected beams at 20 and 100 GeV. The peak positions (i.e. the most probable value or the mode of the distribution) were independent of the energy or sign of the hadron beam. The average peak positions in the 14 counters were the same at 10, 20, 100 and 150 GeV to + 0 . 4 % . With the steel back in place, we repeated the test with positive sign selected muons at 30 and 50 GeV. The pulse height

CALIBRATION

OF A DETECTOR

the 14 counters is shown in fig. 3, where the abscissa is the number of equivalent singly ionizing particles. The steel plates were back in place for this test. A Gaussian fit to the distribution yields a mean of 17.9 equivalent particles and a standard deviation of 2.4. The difference between 14.0 and 17.9 is also a reflection of the difference between the mean energy deposition and the most probable energy deposition in a counter by 50 GeV muons. The peak positions for singly ionizing straightthrough muons are also used to calibrate the counters of the large area calorimeter. The hadron shower pulse heights in both the large area calorimeter and in the scaled-down model are expressed in terms of the equivalent number of singly ionizing particles. When expressed that way, the calibration and resolution of

distribution of singly ionizing muons in the first counter is shown in fig. 2b. Here also the peak positions of singly ionizing muons were independent of energy and equal to the peak for singly ionizing hadrons to + 0.4%. The curves that are shown correspond to those from a simple model in which each ionizing particle produces a pulse height which is Poisson distributed and in addition can produce a delta ray, traversing the z8" of scintillator, with a probability of 0.12. We use the most probable value to define a single ionizing pulse because theoretical calculations 5) indicate that, unlike the mean value, the most probable value is independent of energy for energies greater than 5 GeV. This fact is corroborated by the above described studies. The pulse height distribution for non-interacting straight-through muons summed over r

t

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Fig. 4a. (Upper half) Pulse height distributions s u m m e d over 14 counters for 5, 10, 20, 30, a n d 50 GeM h a d r o n s (4" steel spacing). (Lower half) Pulse height distributions s u m m e d over 14 counters for 100, 150, 200, a n d 250 G e V h a d r o n s (4" steel spacing). T h e curves are the best fit Poisson distributions.

52

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NUMBER OF EQUIVALENT

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Fig. 4b.

the scale model should be the same as that of the large area calorimeter. With the steel plates back in place we recorded hadron shower events for a variety of incident energies ranging from 5 to 250 GeV. The signals were not amplified in this case, because hadron showers give much larger pulse height than those of singly ionizing particles. The pulse height distributions summed over the 14 counters for hadron energies of 5, 10, 20, 30, 50, 100, 150 and 250 GeV are shown in figs. 4a and 4b, where the abscissa is the number of equivalent singly ionizing particles in the shower. The distributions that are shown represent only hadron events which satisfied conditions designed to discriminate against background events such as non-interacting muons and low energy electrons (e.g. electrons from interactions in the beam

pipe, decays, etc.). Also, criteria that ensured the containment of the hadron shower within the scaleddown calorimeter were applied. These conditions are discussed below. Background low energy electrons were characterized by a large pulse in the first counter, a smaller pulse in the second counter and no signal in the third counter. These background electrons were not a serious problem at energies greater than 30 GeV. At these energies the hadron shower events were more numerous than background events, and the pulse heights summed over the 14 counters were much larger for hadron events than for background events. At energies less than 30 GeV, the electron background was removed by requiring the pulse height in the third counter to be larger than a minimum value. The muon background

CALIBRATION

TABLE 1 Hadron shower energy deposition in the calorimeter expressed in terms of equivalent number of singly ionizing particles. Run

August August August August August August July June June

Sign Momentum selection (GeV) ---+ --

5 10 20 30 50 100 150 200 250

Mean

a/Mean

18.24- 4 52.74- 5 106.34- 4 164.54- 7 269.0:1:5 538.04- 5 808.04- 5 1056.0 4- 53 1287.04-65

0.3844-0.200 0.3314-0.031 0.2534-0.010 0.1994-0.010 0.158±0.007 0.111 4-0.007 0.0894-0.004 0.079 4-0.004 0.0734-0.004

which yielded a p e a k at 17.9 equivalent particles was only i m p o r t a n t at 5 a n d 10 G e V where the h a d r o n showers were small. A t those energies m u o n s were recognized by the presence o f a p e n e t r a t i n g particle in the d o w n s t r e a m counters o f the c a l o r i m e t e r A d d i tional d i s c r i m i n a t i o n against m u o n s was o b t a i n e d by forcing an interaction in the first module. A t high energies, the r e q u i r e m e n t o f an interaction in the first m o d u l e ( o b t a i n e d by requiring the pulse height in the first c o u n t e r to be larger t h a n a m i n i m u m value) ensured the l o n g i t u d i n a l c o n t a i n m e n t o f the shower a n d enabled us to study the shower d e v e l o p m e n t f r o m the p o i n t o f the p r i m a r y interaction. This m o r e nearly simulates the case o f a neutrino interaction in the large c a l o r i m e t e r where we k n o w the vertex position. In o r d e r to a v o i d a bias in f a v o r o f large h a d r o n showers (i.e. showers with a large electromagnetic c o m p o n e n t ) we never required the n u m b e r o f particles in any c o u n t e r to be m o r e t h a n 10% o f the average n u m b e r o f particles in that c o u n t e r for typical h a d r o n showers. A s u m m a r y o f the event selection c o n d i t i o n s is given in a p p e n d i x A. A l s o given in this a p p e n d i x are the shower d e v e l o p m e n t tables which c o n t a i n the m e a n n u m b e r o f particles in each c o u n t e r for all the incident energies t h a t were studied as well as the m e a n fraction o f the energy that is d e p o s i t e d in each counter. The shower d e v e l o p m e n t tables indicate t h a t the l o n g i t u d i n a l c o n t a i n m e n t o f the shower is c o m p l e t e for energies u p to 150 G e V (when an interaction is forced in the first counter). A t the higher energies, a 1 % or 2 % energy loss o u t the b a c k o f the c a l o r i m e t e r c a n n o t be ruled out. W e also investigated the transverse c o n t a i n m e n t o f the shower by aiming the incident b e a m at various distances f r o m the edge o f the calorimeter. This type o f d a t a p r o v i d e only a n d indirect 7) measure o f the

53

OF A D E T E C T O R

transverse c o n t a i n m e n t o f the shower. Such a study d o n e at 150 G e V indicated t h a t there is a small energy leakage o u t the side o f a b o u t 2.2 %. The side leakage at 200 a n d 250 G e V was n o t investigated b u t is expected to be similar s). The large area ( 5 ' x 5') c a l o r i m e t e r used in the n e u t r i n o experiment is large e n o u g h to transversely c o n t a i n the h a d r o n shower; therefore, the means o f the distributions at 150, 200 and 250 G e V were corrected by a multiplicative factor o f 1.022. Similar studies d o n e at the lower energies were less extensive a n d were inconclusiveT). N o side loss corrections were a p p l i e d to the lower energy data. M o n t e C a r l o calculations 8) indicate t h a t the side loss m a y be on the o r d e r o f 1 % to 3 % for E > 50 GeV, and m a y be as large as 6 % at E = 5 GeV. T h e distributions o f total pulse height ( s u m m e d over all 14 counters) o f h a d r o n showers in the c a l o r i m eter were f o u n d to be best represented by Poisson d i s t r i b u t i o n s (see a p p e n d i x C), especially at low energies. The best fit Poisson distributions are d r a w n on t o p o f the d a t a in figs. 4a a n d 4b. G a u s s i a n distributions (with the negative tails t r u n c a t e d ) wich have the same means a n d s t a n d a r d deviations as those o f the Poisson distributions p r o v i d e fair fits to the data. The 1400 u3 W U 1200 (D I-h ¢ Y I000

o~ ~ ~oo ~oo ~ _~ 400 0

w

20C 20

40

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1000

Fig. 5. a) The mean number of equivalent singly ionizing particles deposited in the calorimeter vs the incident hadron energy (4" steel spacing). The curve corresponds to the fit described in the text. b) The rms resolution of the calorimeter vs the incident hadron energy (4" steel spacing). The curve corresponds to

1.105/~/E.

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RESOLUTIONvs SPACING/ 200 GeV

///

/

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Z o_ I-- 2o d O i0 -- / 03 Lid -" n- 0 I

I I I I 0 4 8 12 16 20 SPACING BETWEEN COUNTERS(INCH-'S)

Fig. 6. The resolution at 200 GeV vs spacing between counters.

Poisson fit means and standard deviations are given in table 1. The errors that are given are point to point errors (the errors in the means for the 200 and 250 GeV data are larger because they include an additional 5 % normalization error due to equipment related difficulties encountered during the June run). The overall systematic error in the means is estimated at ___5 %. The uncertainty in the energy loss out the sides leads to an additional error in the corrected means varying from 2 % at the highest energy to 6 % at the lowest energy. The Monte-CarloS) calculations indicate that the resolution of a calorimeter where no energy is lost out the sides may be narrower than what we measured by amounts varying from 5 % at the highest energy to 20% at the lowest energy. These uncertainties will be greatly reduced with further investigations of the lateral containment of the shower. The low energy data ( E < 30 GeV), given in table 1, include a small correction to account for the fact that the primary interaction in neutrino reactions can occur uniformly throughout the 4" of steel while the primary interaction of the hadron beam tends to occur in the first part of the steel. This correction is described in appendix B. An interesting quantity to calculate is the fractional observed energy, i.e. the energy that is not lost in nuclear disintegrations. This quantity can be obtained approximately by a comparison of muon and hadron pulse heights. The assumption involved is that the mean energy deposition of charged particles in the scintillator is proportional to the mean energy loss due to ionization in the steel. Under the above assumption, the difference between muon and hadron pulse heights is due to the unobserved energy loss in nuclear disintegrations initiated by the hadrons. The mean pulse

etal.

height of 50 GeV muons traversing the 14 modules of the calorimeters is 17.9-t-2.0 singly ionizing signals. Using the mean dE/dx value of 16.09 MeV/cm for 50 GeV muons in steel9), we find that a 50 GeV muon loses 2.287 GeV while traversing the calorimeter. Therefore, our definition of a singly ionizing signal corresponds to 2.287/17.9 GeV or 127.8 MeV. The mean pulse height of a 50 GeV hadron shower is 2 6 9 + 5 singly ionizing signals or 34.4 GeV. This means that the fractional observed energy for hadrons in our calorimeter is 69 % at 50 GeV. Another method of obtaining a measure of the fractional observed energy is by the direct comparison of electron and hadron pulse heights. This method (see appendix B) yields the value of 80% for the fractional observed energy at 50 GeV. The dependence of the peak position on energy was very close to linear for hadron showers completely contained in the calorimeter. The following fit provides a good representation of the data (see fig. 5a) 5.428 T 2 mean - - T+0.721'

(3)

where the mean is expressed in number of equivalent singly ionizing particles, and T is the kinetic energy ]°) of the incident hadron in GeV. The choice of the above functional form [eq. (3)] for the parametrization of the mean as a function of energy was motivated by the fact that Monte-Carlo s ) calculations indicate that the fractional observed energy should be smaller at lower energies ~J). A good representation of the dependence of the rms resolution (a/mean) on energy is provided by the fit (see fig. 5b) Resolution (rms) = 1.105/~T,

(4)

where the kinetic energy 1°) T is in GeV. The data and the fit are shown in fig. 5b. By making appropriate sums of the calorimeter counters, we can investigate the effects of different counter spacing on resolution (for spacing greater than the nominal 4"). For example, adding the even counters allows a measurement of the resolution with 8" spacing (i.e. 8" of steel between scintillators). Such a study was done in the early calibration run 4) at 200 GeV. The results of that study are shown in fig. 6 where the resolution is plotted vs amount of steel between any two counters. The dependence is linear between 4" and 12" (the curves are drawn to guide the eye). The pulse height distributions summed over the 7 even counters (8" spacing) are shown in figs. 7a and

C A L I B R A T I O N OF A D E T E C T O R

7b. Table 2 shows a comparison between the resolution with 4" spacing and the resolution with 8" spacing for energies investigated in the present study. The resolution with 8" spacing is roughly twice the resolution with 4" spacing. It is not expected that this linear relation continues for spacing smaller than 4" [as shown by other published data s)]. The above result is important because neutrino interactions in the large area calorimeter initiate hadron final state showers with mean momenta in a direction not necessarily normal to the plates of the calorimeter. A hadron shower produced at an angle OH with respect to the axis of the calorimeter will have a calibration which is independent of OH. This is because although the effective steel spacing is increased by a factor of l/cos OH, the amount of light produced by each secondary particle is increased by the same factor as

I

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55 TABLE 2

Comparison of the resolutions of calorimeters with 4 ~ and 8" steel spacing. Momentum (GeV)

Resolution 4 ~ steel

Resolution 8" steel

Ratio 8"/4"

10 20 30 50 100 150 200 250

0.331 0.253 0.199 0.158 0.Ill 0.089 0.079 0.072

0.710 0.444 0.367 0.319 0.225 0.167 0.160 0.148

2.15 1.76 1.84 2.02 2.03 1.88 2.03 2.07

the particles are traversing the scintillator at an angle. The resolution on the other hand will be that of a 1

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IO GEV NEGATIVE HADRONS 8" STEEL

I 1

20 GEV NEGAT,VE H ORONS

8" STEEL o-/~ = 444°/°

I00

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NEGATIVE HADRONS 8" STEEL o-/y. = 36.7%

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zW

80 I00 50 NUMBER OF EQUIVALENT PARTICLES

~

3

1

.

"STEEL 9

%

30

> w 20

I0

50

I00

150 0 50 , I00 NUMBER OF EQUIVALENT PARTICLES

150

200

250

Fig. 7a. (Upper half) Pulse height distributions (8 ~ spacing) for 10, 20, 30, and 50 GeV hadrons. The curves are the best fit Poisson distributions. (Lower half) Pulse height distributions (8 ~ spacing) for 100, 150, 200, and 250 GeV. The curves are the best fit Poisson distributions.

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80 o') I-z w > w

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-

H

NEGATIVE HADRONS I + 8" STEEL I'J @/~ = 22.5%

I ~]~z,' ,m

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150 GEV 2 0 0 - POSITIVE HADRONS 8" STEEL cr//.,c = 16.7

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150 60

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80(

250 GEV NEGATIVE HADRONS 8" STEEL o-//,~ = 14.8%

300

03 I'Z 200 > w

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I00 I00

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NUMBER OF EQUIVALENT PARTICLES Fig. 7b.

calorimeter of steel spacing equal to 4"/cos 0H. The results presented in table 2 indicate that for small angles the resolution is directly proportional to 1/cos 0H. Further studies of calorimeters of various steel spacing are planned. Special emphasis will be placed on studies of the transverse containment of hadron showers and on the behavior at low ( E < 2 0 GeV) beam energies. Also planned are studies of the low and high energy tails of the distributions and the development of an algorithm to improve the resolution by using the information in the longitudinal development of the shower. We wish to acknowledge the help of the Fermilab/ Neutrino Area staff.

Appendix A Shower development tables The mean number of particles in each counter for various incident momenta are given in table 3. The symbol + denotes positively charged hadrons and the symbol - denotes negatively charged hadrons. Because of equipment related difficulties encountered during the June run, there are larger uncertainties in the counter to counter calibrations of the 200 and 250 GeV data. The overall normalization of that data is correct to _+5 % because the mean for the sum of 14 counters measured with 150 GeV hadrons in the June run agreed with later measurements taken with 150GeV hadrons during the July run. The shower development can also be described in

57

C A L I B R A T I O N OF A DETECTOR TABLE 3 Mean number of particles in each counter for various incident energies. Counter

- 5 GeV

- 10 GeV

- 20 GeV

- 30 GeV

- 50 GeV

- 100 GeV

+ 150 GeV

- 200 GeV

- 250 GeV

1 2 3 4 5 6 7 8 9 10 11 12 13 14

11.4 5.1 1.4 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

21.1 14.1 6.2 4.4 2.0 1.5 0.8 0.4 0.3 0.2 0.1 0.1 0.1 0.1

36.2 32.2 15.3 9.1 5.0 3.0 1.7 0.8 0.5 0.3 0.1 0.1 0.1 0.1

51.4 50.6 22.2 14.0 9.4 5.4 3.8 2.1 1.0 0.7 0.5 0.2 0.1 0.2

66.0 83.5 41.9 27.7 18.9 11.3 7.4 4.4 3.0 1.8 1.4 0.7 0.4 0.5

108.0 157.0 87.7 59.3 43.1 27.1 19.5 12.1 8.4 5.4 3.7 2.2 1.5 1.2

138.0 198.0 140.0 91.8 73.1 48.3 35.9 32.8 17.1 13.0 7.4 4.3 2.7 2.6

193.0 247.1 183.8 107.2 102.1 57.2 43.9 30.6 20.4 16.3 8.2 5.1 3.1 2.0

207.8 283.3 227.6 132.4 129.9 74.2 60.6 40.8 29.7 23.5 12.4 7.4 4.9 3.7

TABLE 4 The mean fractional energy deposition in each counter for various incident momenta. Counter

- 5 GeV

- 10 GeV

- 20 GeV

- 30 GeV

- 50 GeV

- 100 GeV

+ 150 GeV

- 200 GeV

- 250 GeV

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.680 0.224 0.079 0.017 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.413 0.276 0.123 0.083 0.038 0.027 0.016 0.008 0.005 0.004 0.002 0.001 0.001 0.001

0.346 0.306 0.146 0.087 0.048 0.027 0.016 0.008 0.005 0.003 0.001 0.001 0.001 0.001

0.319 0.310 0.139 0.088 0.057 0.034 0.023 0.013 0.006 0.004 0.003 0.001 0.001 0.001

0.246 0.306 0.156 0.105 0.070 0.053 0.028 0.016 0.011 0.007 0.005 0.003 0.002 0.002

0.200 0.288 0.163 0.112 0.081 0.051 0.037 0.023 0.016 0.010 0.007 0.004 0.003 0.003

0.174 0.249 0.175 0.116 0.092 0.060 0.045 0.030 0.021 0.016 0.009 0.005 0.004 0.004

0.189 0.242 0.180 0.105 0.100 0.056 0.043 0.030 0.020 0.016 0.008 0.005 0.003 0.002

0.168 0.229 0.184 0.107 0.105 0.060 0.049 0.033 0.024 0.019 0.010 0.006 0.004 0.003

t e r m s o f t h e a v e r a g e f r a c t i o n a l e n e r g y d e p o s i t i o n in e a c h c o u n t e r , i.e. , w h e r e N~ is t h e n u m b e r o f p a r t i c l e s in c o u n t e r n u m b e r i, a n d Ntota I = E Ni (see t a b l e 4). i The shower development tables describe the shower from the point of the primary interaction. As described in t h e text, a n i n t e r a c t i o n w a s f o r c e d in t h e first c o u n t e r b y r e q u i r i n g t h e p u l s e h e i g h t in t h e first c o u n t e r t o b e l a r g e r t h a n a m i n i m u m v a l u e (see t a b l e 5). Other conditions were applied to discriminate against b a c k g r o u n d p a r t i c l e s . All t h e c o n d i t i o n s a r e s u m m a r i z e d in t a b l e 5.

A s c a n b e a s c e r t a i n e d f r o m t a b l e 4, t h e a v e r a g e f r a c t i o n a l e n e r g y d e p o s i t i o n in t h e b a c k h a l f o f t h e c a l o r i m e t e r is s m a l l . H o w e v e r , a t h i g h e n e r g i e s t h e r e are always events where a large fraction of the energy is d e p o s i t e d in t h e b a c k half. T h i s p o i n t is i l l u s t r a t e d in fig. 8 w h e r e t h e d i s t r i b u t i o n s o f p u l s e h e i g h t s in t h e first h a l f o f t h e c a l o r i m e t e r a r e c o m p a r e d t o t h e d i s t r i b u t i o n s o f p u l s e h e i g h t s in t h e e n t i r e c a l o r i m e t e r . T h e l o w e n e r g y tails are c l e a r l y e v i d e n t . I n g e n e r a l , l o w e n e r g y tails a r e c h a r a c t e r i s t i c o f l a c k o f c o n t a i n m e n t (fig. 8) w h i l e h i g h e n e r g y tails a r e c h a r a c t e r i s t i c o f i n f r e q u e n t s a m p l i n g (figs. 7a a n d 7b).

58

B.C.

B A R I S H et al.

TABLE 5

Appendix B

Events selection criteria. Conditions are in terms of singly ionizing signals. C I - C 1 4 denote the counter numbers (placed every 4" of steel). Momentum (GeV)

5 10 20 30 50 100 150 200 250

Additional studies and various corrections

As described in the main text, there were conditions and corrections applied to the data in order to eliminate possible biases between charged particle induced showers in the test calorimeter and neutrino induced showers in the large area calorimeter. These are summarized below. 1) Background from muons and low energy electrons was removed. 2) An interaction was forced in the first module in order to ensure containment of the shower at high energies. Where applicable, corrections for noncontainment were applied. 3) The dependence of the resolution on the steel

Conditions

C I > 2.0, C I > 4.0, C I > 5.0, C I > 5.0, C1 > 10.0 CI>10.0 CI>10.0 C1 > 10.0

C2>0.9, C2>0.9, C2>2.0, C2>2.0,

C13 <0.2, C14<0.2 C 3 > 0 . 3 , C13<0.3, C14<0.3 C3>0.9 C3>1.0 C3>1.0

l

I ,5oi.-

|

~,oo

I

I

EnhreCalorimeter _ I -J (56"Sleel)- ~Jf'~k ,oo GEV I,~ I '1

I

|

I

NEGATIVE HADRONS 4 II STEEL°

~ rlI'~, , /• '~ ~

L

cr/p.:ll.lY,

i I' i t / ~ 'I~t

I

0

First Half Only (28" Sleel, ~ " ~ t

200

6OO_

~ 400

NEGATIVE HADRONS 4" STEEL.

o-/~. : 7.9 y.

I

I I

auu7 [ ~

,5o GEV

-~

POSITIVE HADRONS 4" STEEL°

,

~ 1 ~ 1 71"/[\ i

] J20( 7

-

1/~ "~ ~ First HaltOnly ~ ~

I

I

/ I l/

(28"Stee,)~ / /

600

--

500

I000

NUMBER OF EQUIVALENT PARTICLES

I

200 GEV

I

.-I - ~ ^ "

~1~.~.

400

,],_

I

Entire Calorimeter (56"Steel) ?I ~ii.

I

\".

I

I

Entire Calorimeter (56" Steel . ~i~ I I

I

NEGATIVE

600

.At

I

Entire Calorimeter 250 GEM (56" Steel ) - ~ r ~~"

400

I '~-

HADRONS

~,I I

4" STEEL cr/~:7.3Y.

b/I]I"~ ~] I ~

I

First Half Only

l

I

.~

Firs,HalfOnly I~I f i 2OO

20(3

500

I000

1500

500

I000

1500

NUMBER OF EQUIVALENT PARTICLES Fig. 8. Non-containment effects illustrated by the pulse height distributions in the first half of the calorimeter.

CALIBRATION

spacing was investigated in order to understand the dependence of the resolution on the angle with respect to the calorimeter axis of neutrino induced hadron showers. 4) The first interaction of hadrons in the test calorimeter tends to occur in the front part of the first module, while neutrino interactions in the large area calorimeter occur uniformly through the 4" of steel. The low energy data were corrected for this bias. The first three points were discussed in detail in the main text. The fourth point is discussed in this appendix. The difference between neutrino interactions which occur uniformly through the 4" of the steel module and hadron interactions which tend to occur near the fi'ont part of the module is that in the test calorimeter we tend to sample the shower at a later stage of development. We tested for this bias by replacing the 4" steel modules with 2" steel modules and compared the pulse height distribution of the sum of the 7 even counters (late sampling) with that of the sum of the 7 odd counters (early sampling). The average of the two distributions simulates the case of neutrino interactions where the sampling stage is unknown as the interactions occur uniformly throughout the steel. At 50 GeV, the means of the average and even distributions were the same. At I0, 20, and 30 GeV, the means of the average distributions were 2.2% higher than those of the even distributions. Therefore, a correction fitctor of 1.022 was applied to the means of the 10, 20, and 30 GeV distributions of the 4" data. The corresponding correction factor for the 5 GeV data was 1.10. The magnitudes of these corrections are comparable to the errors at these energies. The effect of late sampling is even more noticeable for 8" sampling. The means of the distributions of pulse heights summed over the 7 even counters for the 4" running (shown in figs. 7a and 7b) are 18.6, 45.3, 71.3, 129, 365, 388,473, and 574 singly ionizing signals for the energies 10, 20, 30, 50, 100, 150, 200, and 250GeV, respectively. When compared to the values given by 0.5 times the means of the pulse heights summed over all 14 counters, the means of the even distributions are 29%, 15%, 13 %, 4 % , 1%, 10%, and 11% lower, respectively. As mentioned earlier, the transverse dimensions of the test calorimeter were 10" × 14". The overall length of the calorimeter was 71". When the 4" steel slabs were replaced by 2" steel slabs the overall length of the calorimeter remained the same, as the scintillator positions were fixed. Because of the drastic reduction in density and the drastic reduction in the amount of steel in the longitudinal direction, the calorimeter in the 2" spacing configuration could not contain high

59

OF A D E T E C T O R

energy showers in the longitudinal direction (see the shower development tables in appendix A). Even at low energies ( E < 50 GeV), the reduced density resulted in a 23 % energy loss out the sides of the calorimeter. This side loss could not affect the results of the above test much because we were only looking for a difference between the even and odd counters. Unlike hadron showers, electron showers are well collimated and of shorter range. Therefore, electron showers were fully contained within the calorimeter in the 2" configuration. The lack of containment of the hadron showers resulted in a clear separation between the electron and hadron peaks. Electron signals were studied by removing the lead absorber that was normally placed upstream of the calorimeter. At 4" spacing (obtained by summing the even counters in the 2" configuration) the distribution for 50 GeV electrons was Gaussian with a mean at 335 singly ionizing signals and rms width of 7.1%. A different kind of bias may result if the particle composition of pion induced hadron final states ( n - + p ~ h a d r o n s ) is different from that of current (W boson) induced hadron final states ( W - + p ~ h a d r o n s ) . The difference occurs because final state n°'s immediately decay and initiate electromagnetic showers in which the energy loss due to nuclear disintegrations is small, thus electromagnetic showers produce signals which are typically 25 % larger than hadron shower signals. The resulting bias is probably small because it changes the calibration by only 25 % of the fractional difference between the n o composition of pion induced hadronic final states and that of current induced hadronic final states. Eventually even this small bias may be removed when more information is available about the particle composition of current induced hadron final states. It may also be possible to eliminate the bias by using the information on the longitudinal development of the shower to estimate the initial n o composition in the hadron final state for each event.

Appendix C Fitting Poisson distributions As mentioned in the main text, the pulse height distributions of hadrons in the calorimeter were best represented by Poisson distributions. The Poisson distribution is an integral distribution; we transform it into a continuous distribution in the following manner. The integral Poisson distribution for N events is: P(n) = N e -n (n)", n!

60

B . C . BARISH et al.

w h e r e ~ is t h e m e a n o f t h e d i s t r i b u t i o n . W e m a k e t h e following transformation: n--*x/a, ~ ~ ~/a, n!~

r(x/a+

1). y(x) =

(~/a)
b e -<~/")

H e r e y is t h e n u m b e r o f e v e n t s p e r b i n a n d x is i n u n i t s o f e q u i v a l e n t p a r t i c l e signals. W e h a v e u s e d t h e following approximation for the F function:

F(z)=zZe-Z~/(2rcZ)(l+ z

1 +~) 12z

W e o b t a i n e d t h e b e s t v a l u e s f o r a, b a n d ff b y m i n i m i z i n g t h e c h i - s q u a r e d o f t h e fit u s i n g a n o n - l i n e a r f i t t i n g r o u t i n e . T h e b e s t fit m e a n o f t h e d i s t r i b u t i o n is if, t h e r e s o l u t i o n (or/if)= ~/(a/~), a n d t h e a r e a u n d e r t h e fit is b/a.

References 1) B. C. Barish, J. F. Bartlett, K. W. Brown, D. Buchholz, F. Jacquet, F. S. Merritt, F. J. Sciulli, H. Suter, H. E. Fisk and G. Krafczyk, Phys. Rev. Letters 34 (1975) 538; ibid. 32 (1974) 1387; ibid. 31 (1973) 180, 410, 565. 2) V. S. Murzin, in Progress in elementaryparticles and cosmic ray physics, vol. 9 (eds. J. G. Wilson and S. A. Wouthuysen; North-Holland Publ. Co., Amsterdam, 1967) p. 245.

3) j. Engler, W. Flauger, B. Gibbard, F. M6nnig, K. Runge and H. Schopper, Nucl. Instr. and Meth. 106 (1973) 189; H. Whiteside, C. J. Crannell, H. Crannell, J. F. Ormes, M. J. Ryan and W. V. Jones, Nucl. Instr. and Meth. 109 (1973) 375. 4) B. C. Barish, J. F. Bartlett, D. Buchholz, T. Humphrey, F. S. Merritt, Y. Nagashima, F. J. Sciulli, D. Shields, H. Suter, G. Krafczyk and A. Maschke, Nucl. Instr. and Meth. 116 (1974) 413. 5) R. M. Sternheimer and R. F. Peierls, Phys. Rev. B3 (1971) 3681. 6) j. Lach and S. Pruss, Fermilab Technical Memo, TM-285, 2254.00 (Jan. 1971). 7) If there is some energy loss out the sides of the test calorimeter, and the beam is aimed at points away from the center of the calorimeter, the energy loss on one side may be partially compensated by an energy gain on the other side, thus resulting in only a small change in the signal. 8) F. J. Sciulli, Rapporteur talk on Photon-Collecting Hadron Calorimeters, Proc. Calorimeter Workshop, Fermilab, May 1975 (also available as CALT 68-502 preprint); the MonteCarlo calculations are based on the work of W. V. Jones Phys. Rev. 187 (1969) 1868. 9) We have used the following fit to the mean dE/dx energy loss of muons in steel: dE/dx (MeV/cm) = 12.45 p0.06544, where the momentum P is in GeV ( P > 1 GeV). 10) The negative sign selected beam is primarily composed of pions. For pions in our energy range the momentum P = E, and is a good approximation to the kinetic energy T, since T = E--0.14. 11) Note that a possible 3-6% energy loss out the sides of the calorimeter at low energies may also cause a departure from linearity.