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Analysis of multiparticle production data on proton-nucleus collisions using a new variable

T AZIZ, M Z A F A R , M I R F A N , A A H M A D and M S H A F I Department of Physics, Aligarh Muslim University, Aligarh 202 001 MS received 6 March 1978

Abstract. Multiparticle production data on proton-nucleus collisions have been analyzed taking the number of 'created' charged particles instead of the observed number of shower particles as the variable. The mean normalized multiplicity, Ra, has been found to be independent of energy in the energy range (7-8000) GeV and its mass number dependence has been obtained. The modified analysis introduces some more regularities in the experimental results on p-nucleus collisions like the invariance with respect to energy of the relationship RA=a+flN~ and the KNO-like scaling of the multiplicity distributions of the created charged particles. Thefunctional form of the scaling function has been calculated.

Keywords. Multiparticle production; hadron-nucleus collisions; created particles, mean normalized multiplicity; target-size dependence.

1. In~oduc~on

In recent years, it has been realized that the observed asymptotic state o f hadron- nucleon collision is insufficient to provide enough insight into the p r o d u c t i o n dyna- mics involved in these interactions and for deeper understanding o f these processes interference with the evolving state before its reaching to multiparticle final state is necessary. The nuclear targets for this purpose are ideal because they provide the unique possibility o f the interference through the space-time development o f produc- tion process (Fishbane and Trefil 1971, 1973; D a r and Vary 1972; Subramanian 1972;

Fishbanc et al 1972, 1973; Goldhaber 1973; Gottfried 1973, 1974). This idea has resulted in the revival o f interest in the hadron-nucleus interaction studies.

An important parameter widely used to study this development o f p r o d u c t i o n pro- cess is R a which has often been referred to as the ' mean normalized multiplicity' and is defined as R a • ( N ) / ( n ) where ( n ) is the average multiplicity for colli- sions with a p r o t o n target and ( N ) is the corresponding quantity for a nuclear target o f mass number A; the projectile and the energy being same in both the cases. The knowledge o f the dependence o f R a on A and E is considered useful in distinguishing between the models o f multiparticle production which may be grouped into two broad classes. Class one models (single step models) are those where the asymptotic state is assumed to reach immediately after the collision and the particles are free to inter- act with other nucleons o f the nucleus and thereby establish an internuclear cascade.

These models predict energy dependent value e r r a much higher than unity. In class two models (double step models) the asymptotic state is delayed through the formation 323

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of intermediate states that have well defined life times in their rest frames so that particles become physical well outside the nucleus. This results in suppression of multiplicities. The value of R A is, therefore, expected to be energy independent and much smaller than that based on class one models.

In recent years the dependence of RA on energy, E, and mass number, A, has been extensively studied experimentally (Babecki et al 1973, 1974; Friedlandor et al 1974;

Gurtu et al 1974; Jain et al 1974, 1975 a,b; Otterlund 1974; Calueei 1974; Babecki 1975; Tretyakova 1974; Holynski et al 1974; Gibbs et al 1974; Hebert et al 1975, 1977; Atanelishivily et al 1975; Jones et a11975; Azimov et al 1976; Guty et a11976;

Florian et a11976; Agarwal et a11976). It has been reported that R a increases with energy up to E--~ 100 GoV and thereafter it attains essentially a constant value equal to A" with a=0.13. This behaviour of R a favours the single step mechanisms up to energies ,-,~I00 GoV and the double step mechanisms at higher energies.

The aim of the present study is to draw the attention to the fact that the relation used by different authors for estimating Ra from the experimental results is not in accordance with its definition used to predict its behaviour under different models. The predictions of the models are based on the definition of Ra as the ratio of all the final state particles produced in hadron-nucleus and hadron-nucleon colli- sions but what has been done is different because, generally, the ratio of only the charged showers (relative velocity 13 >t 0.7) of hadron-nuclens collisions and all the charged particles of hadron-nucleon collisions have been considered. Thus, two dissimilar quantities have been compared. This affects the conclusions drawn regarding the energy and mass number dependence of R A and, therefore, the conse- quent deduction from it.

2. Estimation of RA

Although, it is very difficult to have an exact knowledge of all the final state particles of hadron-nucloon and hadron-nucle~ts collisions and consequently of Ra, we here suggest some ways to estimate R a so that its comparison with different models may become meaningful.

2.1. Estimation o f R a by considering all the final state particles

The best but the most difficult way would be to use the total number of final state particles produced in hadron-nucteon and hadron-nuclens collisions to estimate the value of R a. In case of pp collisions the average charged multiplicity (rich), repre- sents the average number of total charged particles present in the final channel in which the two charges of initial channel are also included. Therefore, subtracting 2 from (rich) gives only t h e ' created charges ' (essentially pions) of the final channel.

Using the observation of charge symmetry (e.g. Daniel et al 1973; Boggild et al 1971 and Jones et at 1975 report that ½ ( n . + ) := (n~O)) we may take that 3/2 (n,-q-) particles are created in a pp collision and thus the average number of total particles (charged and nentral both) in the final state may be given as;

( n ) = 3/2 (<nob) - 2) + 2. (1)

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Similarly, subtracting 1 from ( N , ) which corresponds to the proton in the incident channel, whore (N,) is the average number of shower particles observed in p- nucleus collisions, one gets the number of charged particles 'created' in p-nucleus collisions. These particles are characterised by the relative velocity/3 1>0"7. How- ever, a very small fraction of the produced particles appears as grey tracks (slow pions), i.e., w i t h / / < 0 . 7 . The number of such pions i s , ~ 8 ~ of the total number of grey tracks at lower energies (Gottfried 1973 and Khan et a11977). At 24 GeV, Khan et al report the frequency of slow pions, appearing as grey tracks to be ,-~ 0"33. For pro- per analysis this fraction of slow pions must also be taken into account while esti- mating the number of created particles. However, since this fraction is small enough to give rise to any significant effect on the results, we neglect it at present. There- fore, ~N~)--I may be taken to represent almost all the created charged particles.

Thus, the average number of total created particles may be given as:

--- 3/2 ( ( N , ) - 1). (2)

Now adding 1 to (N,,o) to account for the incident proton, which must appear in the final state (as a neutron or proton), and the average number of nucleons, ( v ) , encountered with the incident particle in its traversal through the nucleus, we get the average value o f the total number of the particles in the final state given as;

( N ) --- 3/2 ((N~) -- 1) -k ~v) -t- 1. (3)

Thus the value of Ra may be given as;

RA _ ( N ) _ Total number of particles produced in p-nucleus collision ( n ) Total number of particles produced in pp collision at the

same energy

= 1.5 ( ( N s ) - - 1) q- ( v ) + I = Aa"

1.5 ((rich) - - 2) + 2 (4)

The experimental data available for the average number of shower particles, ( N , ) , observed in p-nucleus collisions are mainly those using the nuclei of the nuclear emul- sions as the targets. The nuclear emulsions essentially compose of three groups of elements-H; CNO; and AgBr. Approximately 71 ~o o f the interactions occur with heavy nuclei AgBr ( ( A ) = 9 4 ) , 2 5 ~ with light nuclei CNO ( ( A ) = 1 4 ) and only 4 ~ with hydrogen. Gurtu et al (1974) have compiled data on the average number of shower particles, (N~), observed in proton interactions with emulsion nuclei at different energies (7 GeV to 8000 GeV) and have given the best fitted values for (rich) at the corresponding energies. More data on proton interactions with emulsion nuclei are available but mostly with incident particles having energies~, 200 GeV and the reported values of (N~) are very close to those given by Gurtu et al at the same energy. We, therefore, use the experimental results compiled by Gurtu et al together with the results reported by Jain et al (1975) at 300 GeV for estimating the value of R~ using relation (4). We use the theoretically calculated value of (v) for emulsion nuclei because there is no way to know this number exactly from

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Table 1. Values of Ram at different energies.

Energy _-

in GeV (nch) (Ns) Rern ~Nch)cr (*)

(nch)cr

<N> (**) Rem = (n) 2.02t0.03

7-1 2 " 9 4 - 0 " 0 3 2"624-0"05 2"804-0"04 1"91 4-0"03 ~ 1"824-0"03 1"72+0.04 ~ 1"944-0"03 1"984-0"02 9"9 3"244-0"03 3"2 4-0"05 1-774-0-06 1"94+0-08

2 0 - 5 4 " 1 0 4 - 0 " 0 4 5.294-0.13 2"044-0"05 2"074-0'04 2 3 " 4 4"224-0"04 5"614-0"11 2"084-0.05 2"094-0"04 27.0 4"41 4-0-04 6 - 2 3 4 - 0 . 2 2"174-0"07 2-15 4-0"06 2 7 " 9 4"464-0"04 6"6 4-0.1 2.284-0.04 2.21 -t-0.04 6 7 - 9 5 . 8 9 4 - 0 . 0 7 9-574-0.23 2.2 4-0-06 } 2.224-0.04 2.184-0-05

9.734-0.23 2.244-0.06 2.214-0.05 j 2.204-0.04 200 7 . 6 4 4 - 0 . 1 7 13.044-0.4 2"144-0.08" 1 2.13 4-0.08"~

13.084-0"3 2.144-0.07~ 2.13+0.07~

13.31-t-0.3 2.184-0.07{ 2.144-0.04 2.174-0.07{ 2"14:5:0.04 12.9 -4-0.4 2.114-0.08) 2.114-0.08)

300 8-86-t-0.16t 16.0 4-1-57 2-194-0-21 2-174-0"18 I000 10'6 -t-0"6 19.2 4 - 1 . 9 2.124-0.24 2.114-0.23 3000 12'6 4-0"7 21.7 4 - 1 . 6 1.954-0.18 1"974-0"18 8000 14.4 -t-0.8 23'3 4 - 2 . 0 1.80-t-0.18 1.834-0.18

* (Rem > = 2.06 4-0.03 ** (Rein)= 2"08 4-0"03 a = 0"1814-0'003 a = 0"1834-0"003 t Jain et al (1975a)

experiments. N o clear-cut separation is possible between the directly hit target nucleons and the nucleons coming out o f the nucleus through the indirect push in a secondary collision and thus it is difficult to ascertain the fraction o f Ng (grey tracks, 0-3 ~/3 < 0 . 7 ) or Nh (heavy tracks,/3 < 0 . 7 ) which represents the directly hit nucleons.

We have thus used (V>,m=3"2 as evaluated by Gottfried (1973). The values of R~m estimated by using relation (4) have been given in table 1. It m a y be noticed that Rein remains practically constant in the entire energy range considered. The average value o f R~m is;

(Rein > =2"084-0'03 Putting Rein = A a, gives;

a = 0 . 1 8 3 + 0 " 0 0 3 2.2. Estimation o f R A by applying/3 cut

Another approach for estimating R A is to impose a strict 13 cut to the final states o f both the hadron-nucleon and hadron-nucleus collisions and compare the final states o f different/3 intervals. An analysis along this line has been performed by Holynski et al (1974) at 200 GeV where they have compared particles in different rapidity intervals. However, sufficient a m o u n t o f data in the entire energy rangÙ are needed to draw arty conclusion.

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2.3. Estimation o f R A by considering only the created charged particles

Estimation of R a by considering all the particles produced in p-nucleus and pp colli- sions is in exact accordance with its definition used in predicting its bohaviour on the basis of difforortt models. What one measures experimentally is not the total number of particles produced but only the number of charged particles and as we have seen in § 2.1 that the estimation of the total number of produced particles from the experi- mental information involves various assumptions. However, we feel that we can get rid of those difficulties without losing the spirit of the definition of R a if we consi- der the number o f ' c r e a t e d ' charged particles for estimating R a. To estimate the number of created charged particles, the initial channel charges are excluded from the number of charged particles observed both in pp and p-nucleus collisions. In case of pp collision, two charged particles are present in the initial channel which should also appear in the final channel whore the total charged particles observed are (rich). Subtracting 2 from (rich) should, therefore, give the average number of created charged particles in pp collisions, i.e., (nch)c r = (rich) - - 2 (Hwa 1972;

Josip Soln 1976; George and Snidor 1976 and Amagloboli et al 1976, 1977). In the case of p-nucleus collisions the target nucleons go with energies corresponding to grey tracks and therefore, if we subtract just 1, the charge corresponding to the incident proton, from the observed (N~) we got the number of created charged particles in p-nucleus collisions, i.e., ( N ~ ) - - I =(Ncu)c r. Thus we can write;

(/Vch)c r Number of charged particles created in p-nucleus collision Ra -- (nch)c r -- Number of such particles created in pp collision at the same

energy

(Jr,>_1

- <noh>-i =

The values of Rem SO obtained at different energies of the incident protons are given in table 1 and plotted in figure la. Again it may be noticed that Rein remains practi- cally constant in the entire energy range. The average value of Rein and the corres- ponding value of a are;

(Rein) = 2"06 4- 0"03; a =0'181 4- 0"003.

It is worth mentioning that those values of ~Rem ) and a are in excellent agreement with those obtained in § 2.1 and thus consideration of only created charged particles for estimation of R A seems to be as good as the consideration of all the particles in the final state.

In the nuclear emulsions the interactions occur with nuclei of very varying mass numbers viz., H ( A = 1), CNO ( ( A ) = 14) and AgBr ( ( A ) = 94). It is, therefore, bettor if the interactions with those groups of nuclei be analysed separately. How- over, it is not possible to make an unambiguous separation of the interactions with any one group of nuclei. Kohli (1975) has, however, estimated the values of ( N , ) for interactions with nuclei of CNO and AgBr groups at different energies. Those values are given in table 2 and have boon used to estimate the values of RCN o

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RA

3

( o 1 E m u l s i o n

2 t

# #

1

(b) C N O a -,-"t t t I

I

~l ( ¢ ) A g S r

e

tt

II~l I 10 t

, ,I I

#

I I I I I I 1 ~ ~ 1 1 1 1 1 1 1 I

i 0 2 I 0 3

Energy (Ge~)

Figure 1. Variation of R,4 with energy.

t

I I I I J I i 0 4

Table 2. Values of RCN O and RAgBr at different energies.

(Nch)cr (CNO) (Ns)AgBr RAgBr = (Nch)er (AgBr)

Energy (Ns)CNO RCNO = (nch)c r (nch)cr

in GeV

7"1 2'51 4-0.10 1"614-0"07 3"0 4-0"1 2"134-0"08 9"9 3"0 4 - 0 " 2 1'61+0"11 3"5 4-0"3 2"024-0'17 20"5 4'71 4-0"34 1"774-0"13 5"994-0"31 2"284-0"13 2 3 " 4 4'784-0"3 1"7 4-0"11 6"264-0"25 2"374-0"10 27"0 5"6 4-0"4 1"91 +0"14 7"1 4-0.25 2"534-0"09 67"9 7"4 4 - 0 " 3 1"654-0"07 11'0 4-0'3 2"574-0"08 200 10"5 4 - 0 " 5 1"684-0"091 1"704-0.06 15"2 +0"6 2"524-0.11 "~

10"7 4 - 0 " 5 1"724-0"09 14"7 4-0'5 2"434-0'10J 2"484-0.07 1000 13"1 4 - 1 " 8 1"404-0"21 23"1 4-3"6 2"574-0'43

3000 17"2 4 - 2 " 0 1"534-0"2 26-8 4 - 2 " 0 2-434-0"23 (RCNO) = 1"664-0"04 (RAgBr) = 2"39 4-0"06

a = 0"194-0'01 a = 0"1924-0"005

and RAgBr. It may again be noted from table 2 and figure lb and lc that both RCN 0 and RAgBr are practically energy-independent. The average values o f RCN O and RAgBrand the corresponding values of = are found to be;

( R c N o ) = 1"66 -4- 0-04 a = 0"19 ± 0.01, (RAgBr) = 2"39 ± 0"06 a = 0"192 -4- 0"005.

The anaysis, therefore, leads to an energy independent value o f R a given by R,4 AO.19 :L 0.01.

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4 m

3

2 C CNO

- ¢ - - e -

1 ,

l O

Figure 2.

Sn P

J o n e s eta11975

F l o r i o n e t o 1 1 9 7 6

gBr.J Kohli 1975 [Em "] Gurfu etol 1974

A g B r W

-)- tsn

C r

I I I I ,I

2 0 5 0 1 0 0 2 0 0 3 0 0

A Variation of RA with mass number.

The result obtained above is based on the analysis of the emulsion data and the composite nature of emulsion creates ambiguities in such an analysis. Therefore, to check the reliability of our analysis we also give an analysis of the data available for interactions with pure targets in a limited energy range reported by Jones et al (1975) and Florian et al (1976). A plot of R a vs A on a logarithmic scale gives a straight line (figure 2) with slope = =0.19 which is a best fit to the data points. It may be soon from figure 2 that the points for emulsion, CNO and AgBr also follow the same straight line.

3. R a as a function of Nn

We shall now see that taking the number of created charged particles as the parameter in the analysis instead of (N~) and (rich), introduces certain other regularities in the data on hadronic interactions and this in turn may lead to a bettor understand- ing of the interaction process. The variation of R a with Nn has been studied by several workers (Babecki 1974; Ottorlund 1974; Jain et a11975 and Florian et a11976) and a relationship of the type R a = ~ + f l Nh has been found to exist. The value of has been found to remain practically constant over the entire energy range whereas 13 increases with energy and attains essentially a constant value ~ , 0-1 at energies , ~ 70 GeV (Babecki 1974). However, with our modified calculations for R A we find that both a and fl become energy independent. A best fit to the plot of R a vs Nh gives ,~=1"08 and fl=0"13 for the data available in the entire energy range (figure 3).

Thus, the method used here leads to a kind of scaling between R,j and Nn.

4. Scaling in multiplicity distribution

The analysis of the data in terms of the number of created charged particles shows a KNO-like scaling in case of p-nucleus collisions as well down to quite low energies.

P,---7

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A p l o t between Z ' =.,'Vch (cO / <Nch)cr and $ ( Z ' ) ---- <Nch)c r PArch (cr), where PNch (cr) is the probability t h a t the n u m b e r o f particles created in p-nucleus collisions is Arch (cr), has been given in figure 4. T h e data points given in the figure correspond to the interactions o f p r o t o n s with emulsion nuclei at energies f r o m 22 to 300 GeV.

The sealing function given by;

( Z ' ) = A Z ' ¢xp ( - - a Z ' )

5 4

RA a 3

1

O

: 1 0 0 0 GeV I 3 0 0 GeV + 2 0 0 GeV 2 8 G e V

< 1 6 0 e V

I I I I I I I I I I I I I ~ ~ I I

2 6 10 14 18 22 26 30 34 ,

Nh

Figure 3. Variation of R.,I with Nh. Data have been taken from Jain et al 1974.

The points are at the same Na i.e. at 3.7, 8.5, 13"5, 18.5, 23.5, 28 and 33"5. For the sake of clarity the points are slightly separated.

g | ' 0 3 0 0 G e v ~ '1

. 2 0 0 G e V r H e b e r t e t o l I g 7 5 )

8 J

I- . It .// .6, o.v ,o,,.o.,

= I - I II 111/[U, • 27 ~ , v a o ~ b o r o - o o . i . , o,o,

6 | 2 2 G e V

1

0 0 . 4 0 . 8 1.2 1 . 6 2 . 0 2 . 4 2 . 8 3 . 2

Z °

Figure 4. Scaled multiplicity distribution of charged particles created in collisions of protons with emulsion nuclei. Data have been taken from the references given in the figure. Solid line corresponds to the fitted scaling function (2.,) = 3.3 Z' exp (--1.83 Z') where Z" = Nch(cr)/(Nch)cr. For 22 Gev, the reference is H Wiazeler (1965).

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with A=3"3 and a-~1.83 is found to give the best fit to the data. The overall xa/D.F.

for all the data points is 0.54 excluding one point for Z ' > 3 at 27 GeV. Martin et al (1975) have also plotted ~b(Z) vs Z where Z = N~ / (No) and have found that the sealing function,

~b (Z) = ( A Z + B Z s + C Z 5 + D Z 7) exp (--EZ),

represents the data points with x2/D.F. =0"79. We wish to point out that the analysis of the data in terms of created particles not only simplifies the form of the sealing function considerably but also that data covering wider energy range have been sealed with smaller value of x~/D.F. Further we feel that the data at much lower energies may be scaled by the same function if one could add the contribution of the slow pions produced to the number of created particles. It is worthwhile mentioning here that recently Amaglobeli et al (1977) have shown that analytic formula for the universal KNO-sealing function becomes very simple when the distribution with respect to multiplicity o f ' t r u l y produced ' total particles is considered in hadron- nucleon collisions.

5. Conclusions

On the basis of the above analysis we arrive at the following conclusions;

(i) The number of created charged particles is a more suitable variable than ( N , ) or (nch) for analysing the p-nucleus and pp data on multiparticle production.

(ii) The ' mean normalized multiplicity ' R a varies with mass number as A °'l°*°'°x and it does not depend on the energy of the incident particle.

(iii) The energy independent and only weakly A dependent value of R a suggests that the multiparticle production occurs through double step mechanism.

(iv) The relationship R A = a + t S N ~ with a = l ' 0 8 and ~=0.13 is invariant with respect to energy of the incident particle.

(v) A KNO-like sealing exists for multiplicity distribution of created charged particles in p-nucleus collisions in the entire energy range.

References

Agarwal M M et al Prec. II1 High-Energy Phys. Symp. Bhubaneswar Nov. 1-5 p IX 2 Albini E, Capiluppi P, Giaeomelli G and Rossi A M 1976 Nuovo Cimento A32 101 Arnaglobeli N S e t al 1976 JINR, Dubna EI-9820; 1977 Sov. J. Nucl. Phys. 25

Atanelishivily M I, Bardzenishivili O L 1975 Prec. I4th Int. Cos. Ray Conf. Munchen, Germany, August 15-29 2286

Azimov S A e t al 1976 Nucl. Phys. B107 45

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Barbaro-Galtieri A et al 1961 Nuovo Cimento 21 469 Boggild H et al 1971 NucL Phys. 1327 285

Calucci G 1974 Prec. Vth Int. Symp. on Many Particle Hydrodynamics, Eiesenach and Leipzig

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Daniel R R, Ganguli S N, Gurtu A and Malhotra P K 1973 Tata Institute of Fundamental Research Rep. No. TIFR-BC-73-4

Dar A and Vary J 1972 Phys. Rev. D6 2412 Fishbane P M and Trefil J S 1971 Phys. Rev. D3 238 Fishbane P M and Trefil J S 1973 Phys. Rev. D8 1467

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Friedlander E M, Marcu M and Nitu R 1974 Lett. Nuovo Cimento 9 341 George A Koelsh and Dale R Snider 1976 Phys. Rev. D14 1889

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Jain P L, Kazuno M, Thomas G and Girard B 1974 Phys. Rev. Lett. 33 660 Jain P L, Kazuno M, Thomas G and Girard B 1975a Lett. Nuovo Cimento 12 653 Jain P L, Girard B, Kazuno M and Thomas G 1975b Phys. Rev. Lett. 34 972 Josip Soln 1976 Phys. Rev. D13 591

Jones L W, Longo M J, Bruke D and Vishwanath P R 1975 14th Int. Cos. Ray Conf. Munchen, Germany Aug. 15-29 2263

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References

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