Multiplicities of Forward - Backward Relativistic Charged Particles

CHINESE JOURNAL OF PHYSICS

VOL. 53, NO. 5

October 2015

Multiplicities of Forward - Backward Relativistic Charged Particles Produced in 32 S-Emulsion Interactions at 200 AGeV/c Mir Hashim Rasool,1, ∗ M. Ayaz Ahmad,2 Om Veer Singh,1 and Shafiq Ahmad1 1

Department of Physics, Aligarh Muslim University, Aligarh 202002, India 2 Physics Department, Faculty of Science, University of Tabuk, P. O. Box 741 Zip 71491, Tabuk, Saudi Arabia (Received April 14, 2015)

Experimental data on relativistic shower particles emitted in the forward (θlab < 90) and backward (θlab ≥ 90) hemispheres in the interactions of a 200 AGeV/c 32 S beam with emulsion nuclei was obtained. The experimental multiplicity distributions (NsF , NsB ) of relativistic shower particles emitted in the forward (θlab < 90) and backward (θlab ≥ 90) hemispheres produced in the interactions of a 32 S projectile with CNO, AgBr, and Em are presented and analyzed. The experimental results have been compared with the data generated with the computer code FRITIOF based on the Lund Monte Carlo Model. The FRITIOF model is useful in classifying the particle emission into the forward hemisphere (FHS) and backward hemisphere (BHS). The correlations between the relativistic charged particles emitted in the forward and backward hemispheres have been investigated. The average multiplicities of particles emitted in the forward and backward hemispheres have been studied as a function of the projectile mass number. Also the asymmetry factor (m = NsB −NsF ) m-distribution for different grey particle intervals i.e., Ng intervals is studied, and the ratio NsF /NsB as a function of Ng has been studied to show a Gaussian behaviour. Finally the scaling of the multiplicity distributions of the relativistic shower particles produced in both the forward and backward hemispheres is observed to obey the KNO scaling law. DOI: 10.6122/CJP.20150629

PACS numbers: 25.75.-q, 25.70.Pq

I. INTRODUCTION Most of the experiments on high energy hadron-nucleus and nucleus-nucleus collisions [1–5] were carried out to study the characteristics of multiparticle production, mainly for the forward emitted particles. During the last few years, the production of backward particles at relativistic energies has received considerable experimental and theoretical attention [6–12]. The primary reason for studying the emission of relativistic hadrons from nuclei in the backward direction is that in free nucleon-nucleon collisions such production is kinematically restricted. Emission of relativistic hadrons beyond this kinematic limit may then be evidence for an exotic production mechanism, such as production from clusters [8– 10, 13]. Baldin et al. [10] argued that simple Fermi motion could not account for such backward hadron emission. They stated that the dominant mechanism for such production was an interaction between the incident nucleons from the projectile and multinucleon clus∗

Electronic address: [email protected]

http://PSROC.phys.ntu.edu.tw/cjp

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c 2015 THE PHYSICAL SOCIETY ⃝ OF THE REPUBLIC OF CHINA

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MULTIPLICITIES OF FORWARD - BACKWARD . . .

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ters in the target, referred to as cumulative production. In this paper, we analyze the data on shower particles produced in both the forward (θlab < 90) and backward (θlab ≥ 90) hemispheres, where θlab is the emission angle in the laboratory system from the interaction of a 32 S projectile with a nuclear emulsion at 200 AGeV/c. The experimental multiplicity distributions of relativistic shower particles emitted in the forward (θlab < 90) and backward (θlab ≥ 90) hemispheres have been compared with the data generated with the computer code FRITIOF based on the Lund Monte Carlo Model [14, 15] for high energy nucleus-nucleus collisions. The FRITIOF model is useful in classifying particle emission into the forward hemisphere (FHS) and backward hemisphere (BHS). The modified FRITIOF code used in present work is based on the version 1.6 (10 June 1986) of authors B. Nilsson-Almquist and Evert Stenlund, University of Lund, Lund, Sweden [14, 15]. The modification was carried out by V. V. Uzhinskii, LIT, JINR, Dubna, Russia, in 1995. A large sample of 5000 32 S-emulsion events has been generated using the code, where the proportional abundance of different categories of target nuclei present in the emulsion material has been taken into account. The dependence of ⟨NsF ⟩ and ⟨NsB ⟩ on the projectile and target sizes are studied. The dependence of average forward shower particle multiplicity, ⟨NsF ⟩ and backward shower particle multiplicity, ⟨NsB ⟩ on heavilyionizing particles, Nh can be described by a linear relation in which the data are found to exhibit a positive correlation. Also the asymmetry factor (m = NsB − NsF ) m-distribution for different Ng intervals is studied, and the ratio NsF /NsB as a function of Ng is studied, which indicates a linear behaviour. Finally the scaling of the multiplicity distributions of the relativistic shower particles produced in both the forward and backward hemispheres is observed to obey the KNO scaling law.

II. EXPERIMENTAL TECHNIQUES In this experiment two stacks of Ilford G5 nuclear emulsion plates were exposed horizontally to a 32 S-beam at 200 AGeV from the Super Proton Synchrotron, SPS at CERN have been utilized for data collection. The scanning of the plates was performed with the help of a Leica DM2500M microscope with a 10X objective and 10X ocular lens provided with semi-automatic scanning stages. The method of line scanning was used to collect the inelastic 32 S-Em interactions. The interactions collected from line scanning were scrutinized under an optical microscope (Semi-Automatic Computerized, Leica DM6000M) with a total magnification of 10 × 100 using a 10X eyepiece and a 100X oil immersion objective. The measuring system associated with it has a 1 µm resolution along the X and Y axes and a 0.5 µm resolution along the Z-axis. The tracks associated with the interactions are classified in accordance with their ionization, range and velocity [16, 17]. The tracks having specific ionization g∗ (= g/go ) < 1.4 and relative velocity β > 0.7 are taken as shower tracks, where go is the Fowler and Perkins parameter for plateau ionization of singly charged relativistic particles. The number of such tracks in an event is represented by ‘Ns ’. Shower tracks producing particles are mostly pions, with a small admixture of charged K-mesons and fast protons. The secondary

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tracks having specific ionization in the interval 1.4 < g∗ ≤ 10 are known as grey tracks. The numbers of such tracks in a star are designated by ‘Ng ’. This corresponds to protons with velocity in the interval 0.3 ≤ β ≤ 0.7 and range ≥ 3.0 mm in the emulsion. The present work in based on these shower tracks only. Grey tracks are associated with the recoiling protons and have an energy range of (30–400) MeV. The sum of the number of grey and shower tracks in such an interaction is known as the compound particle multiplicity, and their number in a collision is represented by Nc = Ng + Ns . Black tracks are mainly the fragments emitted from an excited target. The secondary tracks having specific ionization g∗ > 10 are classified as black tracks, represented by ‘Nb ’. This corresponds to protons of relative velocity β < 0.3 having a range in the emulsion of R < 3.0 mm. The particles producing black tracks are mainly the fragments emitted from the excited target. This ionization corresponds to protons with energy range < 30 MeV. The black and grey tracks taken together are said to be heavily ionizing tracks. Thus these tracks correspond to g∗ ≥ 1.4 and β ≤ 0.7. Their number in a star, Nh = (Nb + Ng ) is a characteristics of the target. There is a limitation with nuclear emulsion that the exact identification of the target is not possible, since the medium of the emulsion is heterogeneous and composed of H, C, N, O, Ag, and Br nuclei. The events produced due to the collisions with different targets in nuclear emulsion are usually classified into three main categories on the basis of the multiplicity of heavily ionizing tracks [18, 19]. In the present work we have categorized the events on the basis of Nh multiplicity as: The events with Nh in the range 2 ≤ Nh ≤ 7 are classified as collision with a group of light nuclei (CNO, ⟨AT ⟩ = 14), and Nh ≥ 8 are classified as collision with a group of heavy nuclei (AgBr, ⟨AT ⟩ = 94). And the events with all Nh values are classified as collisions with the emulsion. So, according to this selection procedure, we have chosen 330 events of 32 S-Em, 200 events of 32 S-AgBr events, and 130 events of 32 S-CNO interactions at 200 AGeV.

III. RESULTS AND DISCUSSIONS III-1. Multiplicity Distributions The experimental multiplicity distributions of relativistic shower particles produced in the forward (θlab < 90) and backward (θlab ≥ 90) hemispheres in the interaction of a 32 S projectile with CNO, AgBr, and Em are shown in Fig. 1 (a–c) and Fig. 2 (a–c), respectively, along with the corresponding FRITIOF data. It has been found that the multiplicity distribution of relativistic shower particles for a given projectile in both the forward and backward hemispheres slightly changes with the target size. It can be concluded that increasing the target size leads to a slight shift of the distribution toward high multiplicity events in both the forward and backward hemispheres. The experimental data in the forward hemisphere has been found to be analogous to the FRITIOF data. However, it deviates from the experimental data in the backward hemisphere, i.e., the peak appears at lower values in the FRITIOF data as compared to the experimental data, which is because of the low multiplicity of relativistic shower particles produced in the backward hemisphere

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in the FRITIOF generated data.

FIG. 1: Multiplicity distributions of relativistic shower particles produced in forward hemispheres in the interaction of (a) 32 S-CNO, (b) 32 S-AgBr, and (c) 32 S-Em at 200 AGeV, along with the FRITIOF data.

The values of ⟨NsF ⟩, DF and DF /⟨NsF ⟩ in the forward hemisphere for 32 S at 200 AGeV are given in Table I. Also the values of ⟨NsB ⟩, DB , and DB /⟨NsB ⟩ in the backward hemisphere are also presented in the same table. Here DF and DB are values of dispersions of relativistic shower particles in forward and backward hemispheres respectively. For the sake of comparison, the values of ⟨NsF ⟩ and ⟨NsB ⟩ for 32 S at 4.5 AGeV [20] and 28 Si at 14.6 AGeV are also shown in the table. It has been found from the table that the values of ⟨NsF ⟩ and ⟨NsB ⟩ increase with the projectile mass and energy, whereas the values of DF /⟨NsF ⟩ and DB /⟨NsB ⟩ remain almost constant for the two projectiles 32 S at 200 AGeV and 28 Si at 14.6 AGeV. Also, for the sake of comparison with the generated FRITIOF data, the corresponding values for the FRITIOF data are given in the Table I. III-2. Asymmetry Factor The asymmetry factor (m = NsB −NsF ), m distribution of relativistic shower particles produced in 32 S-Em interactions at 200 AGeV for different Ng intervals, i.e., Ng = 0, Ng = 1, Ng = 2, Ng = 3, Ng = 4, Ng = 5, 6, and Ng ≥ 7 are shown in Figure 3. It has been found from the figure that the m distribution is almost similar for different Ng intervals, whereas a sharp peak is observed for Ng ≥ 7.

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FIG. 2: Multiplicity distributions of relativistic shower particles produced in the backward hemispheres in the interactions of (a) 32 S-CNO, (b) 32 S-AgBr, and (c) 32 S-Em at 200 AGeV, along with the FRITIOF data. TABLE I: Values of ⟨NsF ⟩, ⟨NsB ⟩, and D/⟨N ⟩ in the forward and backward hemisphere at 200 AGeV. Incident Energy (GeV)

Types of Interaction

DF

⟨NsB ⟩

DB

DB /⟨NsB ⟩

14.58 ± 0.48

—

—

0.46 ± 0.03

—

—

18.99 ± 0.16

8.86 ± 0.21

0.46 ± 0.01

3.13 ± 0.08

2.53 ± 0.11

0.77 ± 0.03

69.54 ± 0.40

21.46 ± 0.58 0.30 ± 0.008 18.93 ± 0.24 8.08 ± 0.35

0.42 ± 0.01

Si-Em

32

14.6

28

200

32

S-Em

Backward hemisphere

DF /⟨NsF ⟩

S-Em

4.5

FRITIOF

Forward hemisphere ⟨NsF ⟩

(60.43 ± 0.78) (56.15 ± 0.82) (0.92 ± 0.02) (5.36 ± 0.10) (5.01 ± 0.08) (0.93 ± 0.03)

III-3. Variation of ⟨NsF ⟩ and ⟨NsB ⟩ with Projectile Mass The values of the average multiplicity of shower particles produced in the forward hemisphere ⟨NsF ⟩ are strongly dependent on the projectile mass number Ap . Fig 4 (a) shows the variation of ⟨NsF ⟩ on the projectile mass number Ap , the values of the other experimental data have been taken from the references [21, 22]. The solid line shows the linear fit to the data, and is given by the fitting equation as: ⟨NsF ⟩ = (−1.97 ± 0.82) + (2.54 ± 0.54)Ap . Fig. 4 (b) shows the variation of ⟨NsB ⟩ on the projectile mass number Ap , and it is found to show a linear behaviour. The values of the other experimental data have been

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N g=0 N g=1 N g=2 N g=3 N g=4 N g=5,6 N g>= 7

0.24

0.20

0.16

dn/dm

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0.12

0.08

0.04

0.00 10

20

30

40

50

60

m = (N

70 B s

80

90

100

110

F

- Ns )

FIG. 3: Asymmetry distribution for different Ng intervals in

32

S-Em interaction at 200 AGeV.

FIG. 4: Variation of ⟨NsF ⟩ and ⟨NsB ⟩ with projectile mass number, Ap .

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taken from the references [21, 22]. The solid line shows the linear fit to the data represented by an equation of the form: ⟨NsB ⟩ = (−4.37 ± 1.03) + (3.61 ± 0.74)Ap . III-4. Variation of NsF /NsB as a function of Ng Fig. 5 shows the variation of the ratio of the forward and backward particles with the Ng produced in the interactions of 32 S-Em at 200 AGeV. The experimental data has been fitted with a well-known Gaussian distribution, shown by the dotted line in the figure. The Gaussian distribution is a statistical probability function which has a simple and appealing physical interpretation. We have calculated the values of χ2 /DOF (where DOF means degrees of freedom) for the fit, the width, and the peak of the distribution. The values are found to be 0.54, 9.30, and 2.12, respectively. Since the χ2 /DOF value is less than 1. This indicates that the confidence level of fitting is high and the distribution has been fitted nicely.

FIG. 5: Variation of NsF /NsB with Ng .

III-5. Correlations As we know, the only quantity by which a projectile may communicate with the target fragmentation region is the energy transferred. In the photo emulsion technique, it is customary to take the multiplicity of the heavily ionizing particles, Nh as in indirect measure

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of this quantity. It is therefore interesting to investigate the variations of ⟨NsF ⟩ and ⟨NsB ⟩ with Nh . Fig. 6 shows the multiplicity correlations of relativistic shower particles emitted in the forward and backward hemisphere as a function of the heavily ionizing particles, Nh , in the interactions of 32 S-Em at 200 AGeV. For comparison the results from the FRITIOF model are also plotted in the same figure. These correlations can be fitted by a positive linear dependence shown by the fitting equations below. ⟨NsF ⟩ = (60.12 ± 2.85) + (1.36 ± 0.25)Nh ⟨NsF ⟩ = (66.22 ± 2.44) + (2.24 ± 0.21)Nh ⟨NsB ⟩(12.22 ± 0.91) + (0.78 ± 0.09)Nh ⟨NsB ⟩(0.09 ± 0.01) + (1.01 ± 0.05)Nh

Experimental, FRITIOF, Experimental, FRITIOF.

FIG. 6: Variations of (a) ⟨NsF ⟩ with Nh and (b) ⟨NsB ⟩ with Nh in 32 S-Em interactions at 200 AGeV along with the FRITIOF data.

In Fig. 6 it has been shown that the experimental values for both ⟨NsF ⟩ and ⟨NsB ⟩ increase linearly with Nh up to some limit, after that it remains constant, and that may be because of the low statistics, whereas the corresponding FRITIOF data show a linear increase over all Nh values. Analysis of these curves in Fig 6 and their fitting may reveal some important features. Especially, the average multiplicity of relativistic shower particles emitted in the forward hemisphere depends strongly upon the number of heavily ionizing particles, Nh , but the average multiplicity of backward shower particles depends weakly upon the number of heavily ionizing particles Nh .

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The correlations between the multiplicity of relativistic shower particles emitted in the backward and forward hemisphere are one of the most sensitive sources of information on the mechanism of particle production in both the forward and backward hemispheres. Fig. 7 shows the relations between (a) ⟨NsF (NsB )⟩ with NsB and (b) ⟨NsB (NsF )⟩ with NsF for 32 SEm interactions at 200 AGeV, which evidently reveals a linear relation and is represented below by the following relations, for the sake of comparison the corresponding FRITIOF results are also plotted in the same figure with a linear relation given. ⟨NsF ⟩ = (39.38 ± 2.49) + (1.57 ± 0.12)NsB ⟨NsF ⟩ = (41.16 ± 3.85) + (2.98 ± 0.25)NsB ⟨NsB ⟩ = (5.59 ± 1.22) + (0.17 ± 0.02)NsF ⟨NsB ⟩ = (0.06 ± 0.002) + (0.08 ± 0.001)NsF

Experimental, FRITIOF, Experimental, FRITIOF.

FIG. 7: Variation of (a) ⟨NsF ⟩ with NsB and (b) ⟨NsB ⟩ with NsF in 32 S-Em interactions at 200 AGeV along with the FRITIOF data.

From the figures and the fitting equations it may be noticed that a strong correlation between ⟨NsF ⟩ and NsB may be seen for both the experimental and FRITIOF data. However, the FRITIOF data shows a greater increase than the experimental data, due to reasonable statistics.

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III-6. KNO Scaling Koba-Nielsen-Olesen (KNO) scaling [23] is a well established empirical law for multiparticle production in p - p collisions. Koba, Nielsen, and Olesen have predicted that the multiplicity distributions of the produced particles in high-energy hadron-hadron collisions should obey a simple scaling law known as KNO scaling when expressed in terms of the scaling variable Z (= N/⟨N ⟩). If Pn (s) represents the probability for the production of n √ charged particles in an inelastic hadron-hadron collision at a centre of mass energy s, then the multiplicity distributions in high energy collision obey a scaling law: ( ) σn (s) 1 N Pn (s) = = Ψ σinel (s) ⟨N ⟩ ⟨N ⟩ 1 = Ψ(Z), (1) ⟨N ⟩ where σn (s) is the partial cross-section for the production of n charged particles, σinel is the total inelastic cross-section and ⟨N ⟩ is the average number of charged particles produced. The KNO scaling thus implies that the multiplicity distribution is universal and Ψ(Z) is an energy independent function at sufficiently high energies when expressed in terms of the scaling variable Z. KNO scaling behaviour for the forward and backward multiplicity distributions is also observed in nucleus–nucleus collisions [24, 25]. Fig 8 shows the multiplicity distributions of forward and backward particles emitted in 32 S emulsion interactions at 200 AGeV which may be described by a KNO scaling law. These distributions may be represented by a universal function of the form: Ψ(Z) = AZ exp(−BZ).

(2)

From Fig. 8 it can be seen that the experimental data of forward and backward particles emitted in 32 S emulsion interactions at 200 AGeV lie on a universal curve within the statistical errors, and seem to satisfy the scaling function. The best fitting parameters A and B used in Eq. (2) are found to be 3.68 ± 0.02 and 1.62 ± 0.01, respectively. The values of the corresponding χ2 /DOF are found to be 0.38, which indicates that the fitting is good for both the forward and backward multiplicity distributions.

IV. SUMMARY AND CONCLUSIONS On the basis of the results presented, the following conclusions may be drawn: 1. The multiplicity distribution of relativistic shower particles for a given projectile in both the forward and backward hemispheres slightly changes with the target size. So, increasing the target size leads to a slight shift of the distribution toward high multiplicity events in both the forward and backward hemispheres. The experimental data in the forward hemisphere has been found to be analogous to the FRITIOF data. However, it deviates from the experimental data in the backward hemisphere.

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FIG. 8: Forward and Backward Particle Multiplicity Distribution in terms of KNO Scaling in 32 S-Em interactions at 200 AGeV/c.

2. The average multiplicity of shower particles produced in the forward and backward hemisphere is strongly dependent on the projectile mass number Ap . 3. The multiplicity correlations of relativistic shower particles emitted in the forward and backward hemisphere as a function of heavily ionizing particles, Nh , has been found to show a linear relation. 4. The experimental data of the forward and backward particles emitted in 32 S emulsion interactions at 200 AGeV lie on a universal curve within the statistical errors, and seem to satisfy the scaling function.

Acknowledgement We would like to express our thanks to Professor P. L. Jain of SUNY at Buffalo, USA for providing the exposed and developed emulsion plates for the present analysis. The corresponding author of this paper Mir Hashim Rasool acknowledges Dr. Shakeel Ahmad for his help in generating events using the FRITIOF model.

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