Dynamical fluctuation of compound multiplicity in nucleus-nucleus interactions at 4.5 AGeV Evidence of projectile dependence of azimuthal asymmetry

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1 Indian Journal of Pure & Applied Physis Vol. 45, Deember 2007, pp Dynamial flutuation of ompound multipliity in nuleus-nuleus interations at 4.5 AGeV Evidene of projetile dependene of azimuthal asymmetry Dipak Ghosh, Argha Deb, Subrata Biswas, Pasupati Mandal & Prabir Kumar Haldar ulear and Partile Physis Researh Centre, Department of Physis, Jadavpur University, Kolkata Reeived 3 June 2006; aepted 16 August 2007 Azinmuthal flutuations in ompound multipliity (pions + target protons) spetrum emitted from nuleus-nuleus interations initiated by 24 Mg-AgBr and 12 C-AgBr both at 4.5 AgeV have been studied. The data exhibit the existene of emission asymmetry in the azimuthal plane for both the interations. Asymmetry is found to depend on the number of ompound multipliity produed. Keywords: Relativisti nuleus-nuleus ollisions, Compound multipliity, Azimuthal asymmetry IPC Code: G01T 1 Introdution Various experiments have been performed mainly with the lepton-lepton, lepton-nuleus, hadronhadron, hadron-nuleus and nuleus-nuleus interations at relativisti and ultra relativisti energies to know the ultimate struture of matter. The observations from these experiments reveal the existene of non-statistial flutuations during multipartile prodution proess. The existene of intermittent type of flutuations speaks in favour of the presene of non-statistial flutuations in high energy interations. Hene, the non-statistial flutuations in partile density distribution have beome a subjet of major interest. A lot of methodologies have been developed to study the large non-statistial flutuations. Some well known physial phenomena like orrelation, intermitteny, et. may be onsidered as the manifestation of the fat that the prodution of pions is dominated by large flutuations arising out of dynamial reasons. Reently, flutuation studies have been reported for the pions in pseudorapidity spae 1-15.Azimuthal asymmetry is a very simple but useful tool for studying the non-statistial flutuations. The method of azimuthal asymmetry have been employed earlier in different types of interations. In the high energy nulear ollisions, investigations are arried out on the produed pions with a ommon belief that these partiles are the most informative about the ollisional dynamis and thus, ould be effetive in revealing the underlying physis of high energy relativisti interations. Limited attention has been given on the medium energy ( MeV) knoked out target protons, whih are also supposed to arry some information about the interation mehanism beause the time sale of emission of these partiles is of the same order ( s) as that of the produed partiles. These target protons, whih manifest themselves as grey traks in nulear emulsion, are the low energy part of the inter nulear asade formed in high energy interations. If the number of fast target fragments, generally, known as the grey partiles in emulsion media are ombined with produed pions, known as the shower traks in the same media, in a ollision, a new parameter named as ompound multipliity (n = n g + n s where n = ompound multipliity, n g = number of grey traks and n s = number of shower traks ) is formed whih an play an important role in understanding the reation dynamis in high energy nulear interations. However, the physis of nulear interations is ompletely known and therefore, all the available probes need to be thoroughly exploited towards meaningful analysis of experimental data. It is essential to analyze the behaviour of the ompound multipliity spetra thoroughly using the available tools in order to get more information about the inner dynamis of the partile prodution in high energy nulear interations. The objetive of this paper is to investigate the dynamial flutuations in the azimuthal angle distribution of ompound multipliity spetrum

2 960 IDIA J PURE & APPL PHYS, VOL 45, DECEMBER 2007 emitted from 24 Mg-AgBr and 12 C-AgBr interations both at 4.5 AGeV. We have also performed similar studies in ase of shower multipliity in our earlier publiation 23 for both the interations. 2 Experimental Details The data set used in this present analysis are obtained by exposing IKFI-BR2 emulsion plates by 24 Mg beam and 12 C beam with inident energy 4.5 AGeV at JIR Dubna, Russia. The sanning of the plates is arried out with the help of a high resolution Leitz metalloplan mirosope provided with semi automati sanning and measuring system. The sanning is done using objetive 10X in onjuntion with a 25X oular lens. To inrease the sanning effiieny, two independent observers sanned the plates independently. For measurement, 100X oilimmersion objetive was used in onjuntion with 25X oular lens. The measuring system fitted with it has 1 µ m resolution along the X and Y axes and 0.5 µ m resolution along the Z axis. The events were hosen aording to the following riteria: The inident beam trak should lie within 3 angles to the mean beam diretion of the pellile. It is done to ensure that we have taken the real projetile beam; the events, whih are within 20 µ m thikness from the top or bottom surfae of the plate, should be rejeted. It is done to redue the loss of traks as well as to redue the error in angle measurement; the events, primary beam traks of whih are observed to be a seondary trak of other interation should not be analyzed and are rejeted. Aording to the emulsion terminology 24, the partiles emitted after interations are lassified as: a. Blak partiles:- Blak partiles onsist of both single and multiple harged fragments. They are target fragments of various elements suh as arbon, lithium, beryllium et. with ionization greater than or equal to 10 I 0, I 0 being the minimum ionization of a singly harged partile. These blak partiles having maximum ionizing power are less energeti and onsequently, they are short ranged. Their range is less than 3 mm in emulsion medium. They have veloities less than 0.3 and energy less than 30 MeV, is the veloity of light in vauum. In the emulsion experiments, it is very diffiult to measure the harge of the fragments. So, identifiation of the exat nuleus is not possible. b. Grey partiles- They are mainly fast target reoil protons with energy up to 400 MeV. They have ionization 1.4 I 0 I< 10 I 0. These partiles have range greater than 3mm in emulsion medium and having veloities 0.7 V Shower partiles- The relativisti shower traks with ionization I less than or equal to 1.4I 0 are mainly produed by pions and are not generally onfined within the emulsion pellile. These shower partiles have energy in the GeV range. d. Projetile fragments- Along with these traks there are a few projetile fragments. In high energy nulear ollisions, the projetile beam whih ollides with the target nuleus also undergoes fragmentation. These partiles have onstant ionization, long range and small emission angle. They, generally, lie within 3 with respet to the main beam diretion. Great are should be taken to identify these projetile fragments. To ensure that the targets in the emulsion are silver or bromine nulei, we have hosen only the events with at least eight heavy ionizing traks of (blak + grey) partiles. i.e entral and quasi-entral events are taken. The events that have the number of heavy traks less than eight, are due to the ollision of the projetile beam with arbon, nitrogen and oxygen nuleus present in the emulsion. These types of events are alled CO events. For our present analysis, the ombination of grey and shower traks for formation of ompound multipliity has been onsidered. Aording to the above seletion proedure, we have hosen 800 events 25 of 24 Mg-AgBr and 800 events 26 of 12 C-AgBr interations both at 4.5 AGeV. The azimuthal angle (φ) is measured for eah trak with respet to the beam diretion by taking the readings of the oordinates of the interation point (X 0, Y 0, Z 0 ), the oordinates (X 1, Y 1, Z 1 ) at the end of the linear portion of eah seondary trak and the oordinates (X i, Yi, Zi) of a point on the inident beam. The variable used for this analysis is azimuthal angle (φ ). The experimental resolution of the azimuthal angle is of the order 5. ulear emulsion overs 4π geometry and provides very good auray in the measurements of angles of produed partiles and fragments due to high spatial resolution and thus, is suitable as a detetor for the study of flutuations in the fine resolution of the phase spae onsidered.

3 GHOSH et al.: DYAMICAL FLUCTUATIO OF COMPOUD MULTIPLICITY I UCLEUS-UCLEUS ITERACTIOS Method of Study To searh asymmetry in the distribution of ompound multipliity for both the interations in azimuthal angle spae, we have divided the whole azimuthal plane having 2π angular range into two equal angular intervals and the differene in the number of partiles emitted in the two intervals for eah of the events is found out. We repeat the proess and ontinue it by shifting the line of division over the azimuthal plane by 10 and by taking the differene in the number of ompound multipliity in the two halves, eah time. This proess is arried out till the position of the line of division is repeated. The maximum differene obtained for eah event is taken as n i, i, indiates the event. The probability of azimuthal asymmetry for the i-th event 27 is defined as: W i = n i / n i (1) where n i is the total number of ompound multipliity in the i-th event of the group of events in a partiular interval. For a group of m events in an interval, the probability of azimuthal asymmetry is then given as : W = i W i / m (2) To alulate the asymmetry parameter (W ), the whole data sample for both the interations, is divided into groups suh that all the events in a partiular group have equal or almost equal number of ompound multipliity. Then, W for different intervals for both magnesium and arbon interations have been alulated. For any partiular interval, the weighted average of = P is given by the relation: (3) where P represents the probability of getting an event with number of ompound multipliity. 4 Results and Disussion For studying the variation of the azimuthal asymmetry with the number of ompound multipliity, the alulated values of the probability W of azimuthal asymmetry and their orresponding weighted averages for experimental data sets in 24 Mg-AgBr and 12 C-AgBr interations both at 4.5 AGeV are given in Table1. We have plotted W against for the experimental data sets in [ 24 Mg- AgBr and 12 C-AgBr interations and they are shown in Figures1 and 2, respetively. The Figs 1 and 2 for both the data sets reveal that W depends on the interval. W dereases with the inrease of indiates that asymmetry dereases with the inrease of number of ompound multipliity. The observed asymmetrial behaviour is due to the statistial flutuations and inner dynamis of multipartile prodution has nothing to do with it. To ounter suh an argument and ensure that the observed asymmetrial behaviour is not due to Table 1 Values of the probability W of azimuthal asymmetry in different intervals in ompound multipliity distributions of 24 Mg-AgBr and 12 C-AgBr interations at 4.5 AGeV for both the experimental and randomized data sets Interation Experimental values (W ) Randomized values (W ) 24 Mg-AgBr (4.5 AGeV) 12 C-AgBr (4.5 AGeV) ± ± ± ± ± ± ± ± ± ±

4 962 IDIA J PURE & APPL PHYS, VOL 45, DECEMBER 2007 Fig.1 Plot of the probability W of azimuthal asymmetry against intervals for both experimental and randomized data in 24 Mg-AgBr interations at 4.5 AgeV statistial flutuations, we have redistributed all the partiles of eah event for both the interations randomly throughout the onsidered phase spae interval and the same analysis has been performed. W alulated from both the randomized data sets of magnesium and arbon have also been presented in Table 1. We have plotted ΥW against for the randomized data sets in 24 Mg-AgBr and 12 C-AgBr interations and they are also shown in Figs1 and 2, respetively. The results for the randomized data sets show that the probability of azimuthal asymmetry for most of the points differ appreiably from that of the experimental values (onsidering the error bars) for both heavier ( 24 Mg ) and lighter ( 12 C) projetile. In fat the azimuthal asymmetry for randomized events is less than that of experimental events. Suh an outome obviously onfirms the existene of nonstatistial flutuations in ompound multipliity distribution. From Table1, it is evident that for the probability W depends upon the number of ompound multipliity. We have plotted the probability W against for the experimental data of heavier ( 24 Mg ) and lighter ( 12 C) projetile and they are shown in Figures 3 and 4, Fig.2 Plot of the probability W of azimuthal asymmetry against intervals for both experimental and randomized data in 12 C- AgBr interations at 4.5 AGeV Fig. 3 Plot of the probability W of azimuthal asymmetry against intervals for the experimental data of 24 Mg-AgBr interations along with the power law best-fit urve

5 GHOSH et al.: DYAMICAL FLUCTUATIO OF COMPOUD MULTIPLICITY I UCLEUS-UCLEUS ITERACTIOS 963 Fig. 4 Plot of the probability W of azimuthal asymmetry against intervals for the experimental data of 12 C-AgBr interations along with the power law best-fit urve Table2 Values of p and q for ompound multipliity in 24 Mg- AgBr and 12 C-AgBr interations both at 4.5 AGeV Interation p q 24 Mg-AgBr (at 4.5 AGeV) C-AgBr (at 4.5 AGeV) respetively. The W - plots reveal that the experimental data sets follow a power law of the form: W = p. q (4) The values of p and q are obtained from best fit urve of W versus plot for both the interations and the values are presented in Table 2. We have noted for 2 every fit in W vesus plot χ / DOF (degrees of freedom) is less than 1. It is seen from Table 2 that the values of p and q obtained from the best fit urves of ompound multipliity data emitted from magnesium and arbon are not the same. In fat,the value of q determines how rapidly the azimuthal asymmetry dereases with the number of ompound multipliity. Larger value of q indiates the value of W dereases more rapidly. The rate of derement of azimuthal asymmetry is faster in ase of 24 Mg-AgBr interations than that in ase of 12 C-AgBr interations for ompound multipliity (Table 2). Thus the above analysis indiates the following interesting results: 1. Compound multipliity, for both 24 Mg-AgBr and 12 C-AgBr interations, are emitted asymmetrially in azimuthal angle spae. 2. The degrees of asymmetry depend on the number of ompound multipliity and it dereases with the inrease of number of multipliity. 3. The values of p and q for ompound multipliity in heavier ( 24 Mg) projetile are greater than that for lighter ( 12 C) projetile. This suggests that the variation depends on the projetile mass at the same inident energy. 4. However, for the same inident energy 4.5 AGeV, for ompound multipliity the degree of azimuthal asymmetry dereases faster for the heavier projetile than that of lighter projetile. Aknowledgement We thank Prof. K D Tolstov of JIR, Dubna, Russia, for his extreme generosity in providing us with the exposed and developed emulsion plates for this work. Referenes 1 Bialas A & Peshanski R, ul Phys B, 273 (1986) Abreu P et al. (DELFI Collab), Phys Lett B, 247 (1990) Ajinenko I V et al. (A22 Collab), Phys Lett B, 235 (1990) Adamovih M I et al. (EMU01 Collab), Phys Rev Lett, 65 (1990) Akesson T et al. (HELIOS Emul Collab), Phys Lett B, 252 (1990) Alberty J & Bialas A, Z Phys C, 50 (1991) Bushbek B et al., Phys Lett B, 215 (1988) Braunshweig et al. (TASSO Collab), Phys Lett B, 231 (1989) Derado I et al. (EM Collab), Z Phys C, 47 (1990) Derado I et al., Z Phys C, 54 (1992) Ghosh D et al., Phys Rev C, 52 (1995) Ghosh D et al., Phys Lett, 41 (1998) Sengupta K et al., Phys Lett B, 236 (1990) Ohs W & Woseik J, Phys Lett B, 214 (1988) Ohs W, Phys Lett B, 247 (1990) Sarkar S & Goswami T D, Indian J Pure & Appl Phys, 40 (2002) 539.

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