7 8 (7 ).6 2 9 -6 3 3 (20 0 4 )
^ UP i
strong azimuthal fluctuations of pions produced in nuclear interactions at a few GeV/n
Dipak G hosh*, Argha D eb , Swarnapratim Bhattacharyya, Keya Dutta (Chatlopadhyay) and Jayita (ihosh Nuclear and Particle Physic.s Rcsarch Centre,
Depaitment o f Physics. Jadavpui University, Kolkala-700 ()'^2. India E-mail dipakghnsh JnCi^yahno com
R eceived 29 January 200^, d tre p te d 6 Au^nu^t 2003
Ab'Jtriict This paper pre,sents a detailed .study on the azimuthal flucfcjations oi the pions produced in nucleai emulsion from high energy iciativistic interactions initiated by “’O-AgBr at 2 lAG cV , ‘K'-AgBr interactitins at 4 5 AGcV and ^‘‘Mg -A gBr interactions at 4 SACJeV The outcome n( ilijs analysis signifies the existence of strong a/imulhal a.symmelry in the multipion pioduetion process A.synmieiry is also found to depend on iht‘ number of pions produced.
Kevword.s Azimuthal asymmetry, pionisation, relativistic nucleus-nucleus collisions l‘Vrs Nos. 25 75 q, 24 f>() Ky
1. Introduction
K' know the ultimate structure o f matter, various experim ents have been performed m ainly with lepton-lepton, lepton-nucleus, h.idi on -h a d ro n , h a d r o n - n u d e us an d n u c l e u s - n u d e us miciaclions at relativistic and ultra relativistic energies. The observations from these experim ents reveal the existence o f non- siatisiical fluctuations during the m ultiparticle production.So ihc analysis o f non-statistical fluctuations are b elieved to throw light on the inner dynam ics o f particle production process. Thus, the study o f non-statistical fluctuations during multiparticle pioduclion IS o f major interest today. A lot o f m ethod ologies have been d e v e lo p e d to stu d y th e la r g e n o n -s ta tis tic a l ihiciualions. S o m e w ell k n o w n p h y sic a l p h en om en a like
^^’r id a tio n , in te r m it te n c y , m a y b e c o n s id e r e d as the nianifestation o f the fact that the p rod uction o f p ions are
^li^minated by large flu c tu a tio n s a risin g out o f d ynam ical Over the last few years, a lot o f investigations have done on correla tio n [1-lO J and in term ittent type o f
‘^Liciualionsl 1 M 6 ] .
Non-statislicai fluctuations m ay be a m anifestation o f quark
"luon plasma (QGP) phase transition w hich might occur at ulira-
^^htfivistic n u c le u s - n u c le u s c o l lis i o n s and n eed sp e c ia l
^ ponding Author
attention. A very sim ple but useful tool to study non-slatislical fluctuations, is azimuthal asymmetry. Few publications on this are available in the literaturel 1 7 -2 3 1. H ow ever, the physics o f nuclear interactions is not yet co n clu siv e and it is the high time to take advantages o f modern Ux)ls for understanding o f the fluctuations arising out o f dynam ical reasons. This paper reports a study on azimuthal asym m etry o f the pions produced m nuclear em u lsion from high en ergy relativistic interactions initiated by ‘^*0-AgBral2.1 A G e V , ^^"-AgBr interactions at 4.5 A G eV and ^**Mg A gB r interactions at 4.5 AGeV.
Though at relativistic energy, chance o f QGP phase transition is most unlikely, the study o f non-statislical fluctuations at this energy, helps to make a com parison o f the nature o f dynam ical fluctuations with that at ultra relativistic energy. This compari.son helps us to gel a clear idea about how the fluctuation pattern changes as the energy and projectile are varied.
2. Experimenlal details
The data are obtained by exp osin g lllford G5 em ulsion plates e x p o s e d to b eam o f en er g y 2.1 G eV at B E V A L A C BERKF:LEY[24) and the data o f AgBr interactions and ^"^Mg -A gB r in teractions are ob tain ed by e x p o sin g NIKF'I B R 2 em ulsion plates at 4.5 A G eV from JINR, Dubna, Russia 125,26J.
© 2 0 0 4 1ACS
6 3 0 D ip a k G h o s h e t a l
A Leitz Ortholux m icroscope with a lOX objective and 25X ocular len s provided with a B row er stage is used to scan the initiated interaction plates and a L eitz M etaloplan m icroscope with a lOX objective and lOX ocular lens provided with a sem i
autom atic scanning stage is used to scan the A gB r and -A gB r plates. Each plate is scanned by tw o independent o b se r v e r s to in c r e a se th e s c a n n in g e f f ic ie n c y . T h e final m easurem ents are done using an oil-im m ersion lOOX objective.
The m easuring system fitted with it has Ipm resolution along the X and Y -axes and 0..S )j,m resolu tion alon g the Z -axis.
A fter scann ing ,the ev e n ts are ch o se n according to the follow ing criteria:
(i) The incident beam track should lie within 3^^ from the main beam direction in the p ellicle. It is done to ensure that w e have taken the real projectile beam .
(ii) Events sh ow in g interactions within 2 0 pm from the top and bottom surface o f the p ellicle are rejected. This is done to reduce the loss o f tracks as w ell as to reduce the error in angle m easurem ent.
(iii) T he tracks o f the in cid en t particle, w hich in du ce interactions, are fo llow ed in the backward direction to ensure that it is a projectile beam starting from the beginning o f the p ellicle.
A ccording to the em u lsion term in ology |2 7 |, the particles em itted after interactions are classified as :
(a) B lack particles : B lack particles con sist o f both sin gle and m u ltip le ch a rg e d fr a g m e n ts.T h e y are target fragm ents o f various elem en ts like carbon, lithium, beryllium e tc with ionization greater or equal to 10 being the m inim um ionization o f a sin g ly charged particle. The range o f black particles in the em ulsion m edium is less than 3 mm. T hey have v elocities less than 0.3c. w here c is the v elo city o f light in vacuum.
E nergies o f these particles are generally less than 30 MeV. In the em ulsion experim ents, it is very difficult to m easure the charges o f the fragments. S o identification o f the exact nucleus is not p ossib le.
(b) Grey particles: They are mainly fast target recoil protons with energy upto 4 0 0 MeV. Ionisation pow er o f grey particles lies b etw een 1.4 to 10 7^. Their ranges are greater than 3 mm. T hese grey particles have velocities lying betw een 0 .3 c to 0.7c.
(c) Show er particles : T he relativistic show er tracks with ionization / less than or equal to 1.4 are m ainly produced by p ions (rc'*’, rr , TtP) and arc not generally con fined w ithin the em u lsion p ellicle.T h ese show er particles have en ergy in G eV range.
(d) The projectile fragm ents are different class of tra^
with constant ionization, long range and small cmissu^
angle.
To en sure that the targets in the em u lsion are silvci bromine n uclei, w e h ave ch osen on ly the events with at eight heavy ion izin g tracks o f (black+grey) particles. / e cemr and quasi-ccntral even ts are taken. The events that have number o f heavy tracks less than eight, is due to the collision u- the projectile beam with carbon, nitrogen and oxygen nudeu present in the em u lsion . The.se types o f events are called C Nf even ts.
A cc o r d in g to the a b o v e s e le c tio n procedure, vve hj\^
chosen 7 3 0 events o f '^’O -A gB r interactions at 2.1 AGcV |24 800 events o f ^^C-AgBr interactions at 4.5 A G eV 12(S| and K(x events of-"^Mg - AgBr interactions at4.5A G eV [29]. Theemissioi angle (Q ) and azim uthal angle ( 0 ) are m easured for each imd by taking readings o f the coordinates o f the interaction pum Zq) , coordinates (X ,, K,, Z^) at the end o f the Iimlm! portion o f each secondary track and coordinate (X^, K, ' / ) ot:
point on the incident beam . In case o f show er panicles, tii-, v a r ia b le u se d is p s e u d o r a p id ity and it is defined
?7 = “ ln (ta n 0 /2 ) .T h e u n c e r ta in ty in th e measurement n em ission angle w hich is very es.sential for this studv exceed s 0.1 mrad. N uclear em u lsion covers geomeiiy :ti\
provides very good accuracy in the m easurem ents of aniileso produced particles and fragm ents due to high spatial resnluiK'r and thus, is suitable as a detector for the study o f fluctuatmn in the fine resolution o f the phase space considered.
3. Method of analysis
To study the fluctuations in azimuthal plane, Takibaev's mctlrv f30] is fo llo w ed here. A ccord ing to this m ethod, we divide (h.
w hole azim uthal plane having 2 n angular range into tv o cqua angular intervals and the d ifferen ce in the number of shown particles em itted in the tw o intervals for each o f the c\cntM^
found out. W e repeat the p rocess and continue it by shiliini the line o f d ivision over the azim uthal plane by 10*^ and b) taking the d ifferen ce in the number o f show er particles in ihi tw o halves, each time. T his process is carried out till the posiuor o f the line o f d ivision is repeated. T he m axim um difference obtained for each event is taken as , /, indicates the cveni The probability o f azimuthal asym m etry for the i-ih event defined as
w here is the total num ber o f .shower tracks in the i-th event o f the group o f even ts in a particular interval. For a group"' m events in an interval, the probability o f azimuthal asymffl"''^
is given as
W = ' ^ W , / m . (3)
Strong azimuthal fluctuations o f pions produced in nuclear interactions etc
631To calculate the asym m etry parameter ( vv ) the data sample jividcd into groups such that all the even ts in a particular ' )up have almost equal num ber o f sh ow er tracks. Then, w c
\lfulate W different intervals for the data set o f ,xv‘’cn. For any particular interval, the w eighted average o f
\ IS given by
N s = ’ (3)
inh'idction N s Ns Expcrim eiilal Randomized
value ( w ) value ( w )
1-5 3.5 1.00± 05 0 88
6-8 7 0 0 6 9 ± .0 4 0 64
'"O-AiiUr 9 - n 10 9 0 58± 01 0 59
>: 1 A(icV)
12-18 16.14 0 .5 7 ± .0 6 0 .4 9
19 - 23 21 50 0 ,5 3 ± 01 0 50
fable 2. Values o f the probability w o f azimuthal asymmetry in different intervals for '^C-AgBr in teraction s at 4 5 AGeV foi both the
^^pciimenial and randomised data sets
•''leiaction N s N.S Experimental Randomized
value ( v v ) value ( i v )
1-5 3 4 4 0 .8 0 i.0 2 0 .7 9
6 -1 0 7 82 0.71 ± .0 ‘) 0 54
'-'('AgBr n - 1 5 12.32 0 6 0 ± .0 7 0 49
'■‘ S A(ieV)
16-18 16,75 0 .5 8 ± .0 5 0 52
19-29 2 1 .9 0 0 .4 9 ± .0 4 0 37
2.1 A G e V , ‘^ - A g B r interactions at 4.5 AG eV and -'‘Mg -AgB r interactions at 4.5A G eV , respectively.
Itible ,t. Values of the prohabiliiy w ol a7imuthal a.symnicliy in itiffciem Ng intervals for ‘^M g-Agllr inteiaetions ul 4 5 A fieV for both Hie cxperimcnlal anU lanclomised data .set.s
where represents the probability o f getting an event with
\ number o f shower tracks.
4. R esu lts and d iscussion
]0 study the variation o f the d egree o f azimuthal asymmetry
„ith the number o f show er tracks, w e have divided the total nun,bet of events into m ultiplicity sub-groups. The subgroups .iieehoseri such that each sub-group contains sufficient number ,)l events and the variation o f m ultiplicity within a group, is not Mgnificant. The m ultiplicity ranges for the three data sets arc
^hown in Tables I, 2 and 3 r e sp e c tiv e ly . A s the sh ow er nniliiplicity varies a little within a particular sub-group, w e have iiilailaied the w eighted m ean m ultiplicity ( ) o f each sub- emup using eq. (3). For every sub group o f the three data sets iliL-degicc of azimuthal a.symmetry (vv ) is calculated using cq.
ij) The calculated values o f w are Tabulated in Tables 1 ,2 ,ind ^ for high energy, interactions initiated by “’O -A gBr at
hihli- I. Vfilucs of the probability w of azimuthal asymmetry in different
~ in ic iv a ls for ‘K )-A gB r in teraction s at 2 1 A (jcV for both the v\('i.iiint'nial a n d landoimsed data sets.
Interaction Ns Ns Experimental
value ( vv )
Randomized value ( w )
1-6 3 67 .80± 05 75
7 -1 0 8 34 64± 02 56
^■^IHg-AgBr (4.5A(jeV)
11-15 12 79 54± 01 ,44
16-21 18 45 41± 07 37
22-12 26 IS 33± 01 31
We have plotted w against with the experim ental data sets o fo x y g en in Figure I, carbon in I'lgurc 2 and magnesium in Figure 3. The figures corresponding to all data sets reveal that
F igu re 1. R epiesetils the plot o f the p iob ab ility w of azim uthal asymmetiy in different intervals for '^>()-AgBr interactions at 2 1 AfieV for boih ihe cxpciimental and randomised data sets
F ig u re 2. R epresents the plot o f the probability w azimuthal asymmetry in different intervals for ‘^C-AgBr interactions at 4.5 AGeV for both the experimental and randomised data sets
632 D ip a k G h o s h e t a l
the d egree o f asym m etry for show er tracks depend on the m ultiplicity interval. vj7 decreases with the increase o f indicating that asymmetry decreases with the increase in number o f show er multiplicity.
Table 4. Values o f p and q per degree o f freedom for *^0-AgBr mten i at Z.IACieV, *^C'- A gBr interaction s at 4.5 AGeV and
interactions at 4.5AGeV. -Agli
Interactions P
M
'H)-AgBr (2.1 AGeV) 1.43 - 34
'^C-AgBr(4 5AO eV) 1.13 ' 2.5
^^Mg-AgBr(4 .lAGeV) 1 55 - 45
'^S-AgBr(2(X)AOeV) 1 90 - .33
'<‘O -A gBr(60A (!eV ) 1.98 - 34
F ig u r e 3. R epresents the plot o f the p robab ility w o f azim uthal asymmetry in different intervals for AgBr interactions at 4 5 AOeV for both the experimental and randomised data sets
It m ay happen that the observed asym m etrical behaviour is d u e to the sta tistica l flu c tu a tio n s and inner d y n a m ics o f m ultiparticle production has nothing to do with it. To counter such an argum ent and to ensure that the observed asym m etrical b eh a v io u r is not d u e to sta tistic a l flu c tu a tio n s , w e h ave redistributed all the particles o f each event randomly throughout the considered phase space interval and the sam e analysis has b een performed. ^ calculated from the random ized data sets o f oxygen , carbon and m agnesium have also been plotted against in Figures 1, 2 and 3, respectively. T he results for the random ized data sets, show that the probability o f azimuthal asym m etry for all the points differ appreciably from that o f the experim ental values (considering the error bars ). In fact, the azim uthal asym m etry for random ized even ts is less than that o f experim ental events. Such an ou tcom e ob v io u sly confirm s the e x iste n c e o f non-statistical fluctuations in particle production p ro ce ss.
We have tried to fit the vj7 vs, plot in a form W = p . ^ and noted that for every fit, X ^ /D O F (D egrees o f freedom ) is less than 1.
T he values o f p and q obtained from best fits for the data sets o f ’^O'AgBr interactions at 2,1 A GeV, AgBr interaction at 4.5 A G eV and ^ M g -A gB r interactions at 4 ,5 A G eV are given in Table 4. We see from this table that the values o f p obtained from best fit o f o x y g en data and those from carbon data and m agnesium data arc not the sam e and so also the case for q valu es.
The value o f in fact, determ ines how rapidly the azimuthal asym m etry d ecreases w ith the num ber o f sh ow er p articles.
Larger the value o f 4^, m ore rapidly the VF decreases.
From the table, it can be .said that the rate o f decrenicm i azimuthal asymmetry is fastest in case o f ^^Mg-AgBr intcraaion and slow est in ca se o f ^^C-AgBr interactions.
It is useful to com pare our results with that obtained hnn the p io n is a tio n o f '^“S -A g B r in te r a c tio n s and
interactions at ultra-relativistic high energiesf23]. In this as, also the degree o f azim uthal asym m etry decreases w ith ihi increase o f .shower m u ltip licities and is consistent with ou fin d in g s. T he va lu es o f p and q ob tain ed from these lu interactions are also sh ow n in Table 4. From the table, u is mvi that the values o f p are alm ost the sam e for the two inierai. tn n at ultra-relativistic high en ergies.T h e sam e statement is valid i case o f q values too.
It is also to be noted from Table 4 that the q values t
‘^’0 -A g B r interactions at 6 0 A G eV and 2.1 A G eV arc same \i in te re stin g p oin t is that fo r - ‘^M g-A gB r interactions .uk
*^C-AgBr interactions, the values o f r/ are different though thei energies are sam e.
5. Conclusion
To con clud e w e m ay write
(i) T h e production o f sh ow er particles is asymmeiiu azimuthal plane.
A sym m etry d ecreases with the increase in nuinbei o shower multiplicity.
At low er energy, this asym m etry depends on the and energy o f the p rojectile and at ultra-relativisi energy, this asym m etry is alm ost independent ot ihein T h e decrem ent o f the degree o f azimuthal asymmein is independent o f en ergy for the sam e projectile H o w ev er for the sam e energy o f different projectile'' the degree o f azim uthal asym m etry decreases tasii?' for the heavier projectile.
(ii)
(iii)
(iv)
(V)
Acknowledgments
T h e authors are grateful to Prof, P.S.Y oung , Missis‘’iPI'‘
University, U .S.A and PtX)f. K.D.Tolastov o f JINR, Dubna, for providing them with the ex p o sed and d eveloped emulsi^’”
Strong azimuthal fluctuations o f pious produced in nuclear interactions etc
633used for this analysis.W e also like to acknow ledge the -'^.'^^al help sanctioned by the U niversity Grant C om m ission OiM of India) under their C O SIST programme.
in
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