Multiple production in the Monte Carlo string fusion model

Physics Letters B 306 (1993) 312-318 North-Holland

PHYSICS LETTERS B

Multiple production in the Monte Carlo string fusion model N . S . A m e l i n 1,2, M . A . B r a u n 3 a n d C. P a j a r e s

Department of Pamcle Phystcs, Untversttyof Santtago de Compostela, E-15706 Santmgo de Compostela, Spare Received 13 January 1993 Editor: R. Gatto

The influence of the stnng fusion on the basic features of relativistic heavy-ion colhslons is stu&ed with the help of a Monte Carlo string fusion model. The model is based on the parton picture of strong interactions and includes the stnng fusion phenomenon. It is demonstrated that string fusmn leads to a considerable reduction of particle production with a relative enhancement of the baryon component in AA colhsmns at ultra-relatlwstlcenergies.

1. Introduction Global features o f particle p r o d u c t i o n in high energy heavy-ion colhsions seem to be described quite well within M o n t e Carlo models based on the ass u m p t i o n that in a collision colour strings are produced first, which afterwards decay i n d e p e n d e n t l y into the observed secondaries [ 1-7 ]. However, careful inspection reveals several discrepancies between experimental spectra [ 8,9 ] a n d the predictions o f the models. In particular, such models fail to reproduce the strange particle a b u n d a n c e at SPS energies, especially o f the strange antibaryons. This could be explained by string interaction: in ultra-relativistic heavy ion collisions the string density becomes so high that string colour fields begin to overlap a n d individual strings m a y fuse [10-15 ]. In this case one can expect higher abundances o f strange particles, antibaryons and even c h a r m e d hadrons. We present here a version o f the M o n t e Carlo string fusion model, in which the interaction o f no m o r e than two strings is taken into account. It is based on the p a r t o n picture o f strong interactions, and also on its properties following from the Regge f o r m a l i s m [ 16 ]. In this a p p r o a c h there is no formal difference l Alexander yon Humboldt Research Fellow. 2 On leave of absence from JINR, Dubna, Russian FederaUon 3 On leave of absence from St. Petersburg Umverslty, St. Petersburg, Russian FederaUon. 312

between hadron and nucleus collisions. Both cases are reduced to interactions o f partons wath given partonic distributions in the projectile a n d target. We consider strings o f different r a p i d i t y lengths, with their flavour a n d n o n - a b e h a n colour properties a n d the energy conservation fully taken into account. The theoretical background o f this numerical model can be found in ref. [ 17 ]. Here we only give its outlines and present our predictions for multiparticle p r o d u c t i o n in heavy ion experiments at SPS, R H I C a n d L H C energies.

2. Formation and fusion of strings At high energy a h a d r o n or nucleus collision is ass u m e d to be an interaction between two clouds o f p a r t o n s f o r m e d long before the collision. As was shown in ref. [ 16 ], the distribution in the n u m b e r o f p a r t o n s is directly connected with the values o f the m u l t i p o m e r o n vertices in the reggeon theory. In the eikonal a p p r o x i m a t i o n it takes the poissonian form

P(n) =exp( -7)7"/nI

(1)

with the m e a n n u m b e r o f partons 7 growing with energy x/~: 7=yoS 'J,

A=0.09,

yo=g/a°o 5,

g=l.8GeV

-1 .

Here ap is the p a r t o n - p a r t o n interaction cross section, which was assumed a constant:

0370-2693/93/$06.00@ 1993ElsevaerScaencePubhshersB.V

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ap=3.5 m b . The parton distribution in the impact parameter, relative to the center of the hadron to which they belong, is taken to be gaussian

F(bp) = (4n).)-'exp ( - b~/42)

(2)

with the mean radius proportional to the relative rapidity. For a hadron with rapidity Y

2 = o t ' ( Y - y ) , or'=0.21 GeV - 2 , where y is the patton rapidity. Accordingly, the gaussian form is also taken for the Pt distribution. The parton distribution in x=p+/P+, where p(P) is the parton (hadron) momentum, is assumed factorized except for the longitudinal momentum conservation U(XI,X2,...,Xn)=(~

1--

Xt

b!t(X,)

(3)

with the single-parton distributions obtained from the Regge theory [ 18 ]: u~(x)=u~(x)=x

-°5 ,

u,~(x)=x

1-~

wath a cutoff at small x: X>Xmxn=mt/P+. Here v, s and vv denote valence and sea quarks and diquarks, respectively. Without string fusion partons are assumed to interact only once. This corresponds to a finite formation time or, in the language of Feynman diagrams, to the contribution of non-planar diagrams only. With the partonic parameters chosen as described above the model describes well the NN inelastic cross sections [ 17 ]. For nuclear collisions the nuclear patton wave function is taken as a convolution of the parton distribution within a nucleon and the distribution of nucleons in the nucleus. The latter was chosen in the Woods-Saxon form

p(r) = p o / [ 1 +exp ( r - ro) / a]

(4)

with

ro=l.19A~/3+l.61A-l/3fm,

opposite colour fluxes. The longitudinal and transverse momenta of the quarks at the ends of the string determine in a unique way the string kinematic characteristics. Only u-, d and s-quarks are considered. The probability to find a strange sea quark pair inside the nucleon was suppressed by a factor 0.29 as compared to a non-strange sea quark pair. The average number and density of strings are presented in table 1 for central pp, SS and AuAu collisions. The string density increases 1.5 times for pp interactions and 3 times for SS and AuAu collisions with the rise of energy from 19.4 to 6300 A GeV and reaches 28.4 strings per fm 2 in AuAu collisions at LHC energies. Thus the probability for the strings to overlap becomes considerable. Following ref. [ 15 ] we assume that strings fuse when their transverse positions come within a certain interaction area of the order of the string proper transverse dimension or, in the language of the present paper, the parton-parton cross section ap. With strings occupying different rapidity intervals, their fusion may take place only when these intervals overlap. The introduction of string fusion is quite simple in the presented parton picture. It is described by allowing that partons may interact not only once but several times, the number of interactions being the same for the projectile and target partons. The inelastm multiple patton interaction is then taken to correspond to a formation of a fused string with the quantum numbers supplied by the interacting partons. The energy-momentum of the fused string is evidently the sum of the energy-momenta of the daughTable 1 Model predlcnons for the number of stnngs (upper numbers) and their densities (fm-2) (lower numbers) in central pp, SS and AuAucolhslons. Colhsmn (GeV)

pp

SS

AuAu

4.2 13

123 33

1302 9.8

200

7.2 1.6

215 5.4

2008 15.1

6300

15.4 2.2

430 10.7

3780 28.4

19.4 a=0.54fm.

According to our picture a parton-parton inelastic interaction leads to creation of a colour string. Since both the projectile and target should remain colourless, colour strings have to be formed in pairs with

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ter strings. The colour charges of the fusing string ends sum into the colour charge of the resulting string ends according to the SU (3) composition laws. In particular two triplet strings fuse into a triplet and a sextet string with the relative probabilities ½ and ] respectively. A triplet and an antitriplet string fuse into a singlet state (realized as a diffractive event) and an octet string with the respective relative probabilities and ~. No other strings were considered in the present calculations. Fused strings have differently favoured ends composed of the flavours of daughter strings. Due to the fusion the total number of strings in a given transverse area becomes limited, so that one expects a substantial reduction in particle production [ 15]. However details of produced particle spectra depend on the way the new strings with more colour decay.

Q~31 = 4 ,

3 June 1993 Q~61=~,

Q~81=3.

It follows that

Kts I ~K[6] ~2.5Kt31 .

(6)

We use the ordinary triplet string decay algorithm of Artru and Mennessier [21 ] with the following parameters obtained from comparison to e + e - experimental data [22 ]: - the single qq string in the model decays via q-q or q(t-qq production with the relative probabilities Pqq/Pq=O.085 ,

Ps/Pu(a) =0.29 ;

- the probability of the decay depends exponentially on the area A swept by the string, according to the invariant area decay law P = 1- e x p ( - b t 3 1 A ) , bt31 =At ~ wf=0.4 GeV -2 ;

(7)

f 3. S~ing

We assume a quasi-classical picture of the decay of colour strings in which pairs of oppositely coloured partons are produced in the string colour field, which neutralizes this field and leads to string breaking. The new sextet and octet strings are supposed to break with the production of two (anti)quark complexes with the same colour charges Q and - Q as those of the ends of the string. The created (anti)quarks have arbitrary favours and masses chosen as the corresponding constituent masses. The probability rate for the constant colour field of two opposite colour charges Q-O` to create a parton pair with the same colour charges Q-O. and transverse mass Mt for unit string length and time is taken in the spirit of the Schwinger expression for the probability to create an e+e - pair in a constant electromagnetic field [ 19,20,11 ]: w ~ K~NIexp ( -- zcM2/KtNI ) .

(5)

Here [N] denotes an SU (3) representation of dimension N; K is the string tension and it has been assumed that new strings have the same transverse areas as the triplet one. The string tension K is proportional to the quadratic Casimxr operator Q2 for the corresponding representation: 314

the transverse momentum distribution for patrons is taken in the gaussian form with the total transverse momentum of the quark pair equal to zero:

-

decay

f(Pt)Pt dp~ ~ exp ( - or t3 l p~ )Pt dpt, ott31 = 5 GeV -2 ;

(8)

the last decay of the string is determined by its rest mass: Ms=M~+AM, where Mh is the corresponding hadron mass and A M = 0.36 GeV. The strange quark and diquark suppression parameters extracted from comparison to experiment [22] can be obtained by the proper choice of the quark masses: Mu,d=0.23 GeV, Ms=0.35 GeV, Mqlq2 =Mql + M ~ . The string tension of the ordinary strings is taken as Kt31 =0.2 GeV 1. We assume that [ 6 ] - and [ 8 ]-strings have the same invariant area decay law (7) and Pt distribution (8) with parameters b and a that can be calculated from (6) and the known quark masses: -

btsl ~b[6] ~2b[31 ,

ot[8] ~,~og[6]~ 1-25ot[31 .

(9)

After the decay two new QQ strings are treated in the same manner and decay into more QQ strings, until we arrive at objects with masses comparable to hadron masses which are identified with observable hadrons by combining into them the produced flayours with statistical weights.

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PHYSICS LETTERS B

K K+~ p X a ~ z 3

Z~

I

[ • [6]-STR:~(Z~G~V) [ i 2 ~[3]-STRII~ES(IGeV)2

] |

A F~ "~

K- K+ ~- p X

Fig. 1. The hadromc content of the decay of octet and sextet strings relaUve to the number of lr- Blackshaded columns correspond to the octet and sextet stung decay. Gray shaded columns correspond to the decay of two tnplet stnngs.

I

8

I

O •

6 Z

|

2[3]-STRINGS(llGeV) [8] - STRING(22 GeV)

I

Oo

4

o

o

o

o

°@•@••• @

2

0 @o

@

0

-3

-6

i

o Y !

3

i

i

~Oo.ooo ~ 1 0 -2 Z

o

213]-5~IN3S(ll~g)

•

[ al - BTRIhE(22C,e¥)

o'4

o'8

o oeo

~•

1'2

The calculated decay spectra of the fused strings are presented in figs. 1 and 2 in which relative particle production rates for the [ 6 ] - and [ 8 ]-strings and distributions in rapidity y Pt for the [ 8 ]-string are compared to the ordinary qq string with the same invariant energy v / ~ = 2 2 GeV. (The latter distributions for the sextet string are practically the same as for the octet one because of the approximate equality o f their quadratic Casimirs). One can observe that in the fused string more baryons and antibaryons, especially strange, are produced, while the number o f kaons stays practically unchanged as compared to ordmary strings. The strange baryon enhancement in the octet string is accompanied by a simultaneous reduction of charged particle production (fig. 2). As for the average pt, it grows very little as a consequence of (9). From fig. 2 one can conclude that its average value for the [8 ]-string has grown only by 10% as compared to the [3 ]-string.

4. N u m e r i c a l results

[3] --,.[B]

+

3 June 1993

,'6

2

Pt (C-eV/c) Fig. 2 Rapidity and transverse momentum d:stributlons of charged particles from the decay of an octet string (open c:rcles) and from two triplet strings (sohd circles).

In summary, the simulation procedure consists of three parts. (1) The determination of the geometry of the collision and the definition of the initial state o f the interacting objects. At this stage relative positions o f the nuclear centres, posations of the nucleons inside the nuclei and partons inside the nucleons are determined. Pairs of interacting partons are pinned down. (2) String formation. The simulation of longitudinal and transverse m o m e n t a of the interacting partons and computation of the kinematical characteristics o f the strings. (3) String decay and multiparticle production. N o rescattering of partons or hadrons is included in this version. The effect of string fusion is most pronounced in interactions with heavy nuclei where the number of strings is large. So we present here the results of Monte Carlo simulations for the nucleus-nucleus interaction in our model with string fusion.

4. I. Reductwn of parncle production Due to fusion the string density cannot grow infinitely, so a substantial reduction in mulUplicities may 315

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be expected. In fig. 3 we show rapidity distributions for A u + A u at 200 and 6300 A GeV, simulated with and without fusion. One observes strong reduction in multiplicities in the model with fusion. In particular, in Au + Au collisions at 200 and 6300 A GeV, the parUcle density in the central region decreases with the inclusion of fusion 1.9 and 2.5 times respectively. Such a reduction was predicted in the simplified version of the fusion model [ 15 ]. The estimates made in that paper pointed to an even stronger decrease in the multiplicities. For that, one should keep in mind that in the present calculations only two strings merge at most. With high string density, fusion of three and more strings seems quite probable, which will diminish the multiplicities still further.

4.2. Strange baryon enhancement As expected, string fusion leads to a considerable strange antibaryon enhancement. It is demonstrated m figs. 4 and 5 for heavy ion collisions at SPS energies. For S + S central collisions at 200 A GeV the production of A's increases 1.5 times in the fusion model in comparison to the model without fusion. For A u + A u interactions the growth is approximately 4 times. It should be noted that no significant change in K ° production occurs with the inclusion of fusion. Some reduction in the number of strange mesons can

3 June 1993

09

''''l''''l''''l''''l''J'l''''l''''l'''

o MODEL(NOSTRING FUSION) MODEL • NA35DATA •

0.6

S+S 200 AGeV

Z 03

-1

0

1

2

3

4

5

6

Y Fig 4. The rapidity distribution o f A m central S + S collisions at the SPS energy calculated in the model with (solid squares) and without (open cnrcles) fusion in comparison with Na35 experimental data [9] (sohd circles).

an~nl*,.,i,,,*l,nnnl.,l,lnn.nl.,,nl~,J.

o MODEL(NOSTRINGFUSION) • MODEL

Au+Au 200 AGeV 3 2

-1

0

i

2

3

4

5

6

7

Y 7000

.... i

6000 5000

: Au+Au

,

o • [] •

....

, ....

, ....

Fig. 5 T h e r a p l ~ t y d l s t n b u t x o n o f z i i n c e n t r a l A u + A u colhsIons at the SPS energy calculated in the model with (solid squares) and without (open circles) fusion.

MODEL(NO STRINGFUSION)200AGeV MODEL200AGeV MODEL(NOSTRINGFUSION)6300AGeV MODEL6300AGeV

"~ 4000

even be noticed in Au + Au collisions at SPS energies (fig. 6).

~,I, ,o HU H

3000

~7[i

,=,"

%

El L3

2000

[3 [3

o. . . . . . ~ ..... ,~" •'° , , , , , • o

1000

-10

-5

0

.~ -~,

5

5. Conclusions 10

Y Fig. 3 Charged particle rapidity distribution for A u + A u co]hslons with (solid symbols) and without (open symbols) string fusion.

316

We have presented a Monte Carlo string fusion model based on the parton picture ofhadron and nucleus collisions. The model intends for simulations of multiple particle production in hh, hA and AA collisions at ultra-high energies.

Volume 306, number 3

20

,,,i,

PHYSICS LETTERS B

,,,i,,,,|.,J,l,.,

K° 16

S

ample, the M o n t e Carlo string m o d e l [24] reproduces NA35 data [9 ], particle p r o d u c t i o n in pp and p + S collisions (except the shape o f the r a p i d i t y distribution for A particles) a n d nonstrange particle distributions in S + S collisions at 200 A GeV, b u t underestimates the n u m b e r o f strange particles observed in NA35 [ 9 ] a n d WA85 [ 8 ] in central colhsions b y factors 2:2:4 for K °, A a n d A. String fusion gives a clear possibility to explain this effect.

,i,,,,i,,,,I,

o

MODEL(NOSTRINGFUSION)

•

MODEL AGeV

~12

Z "~

3 June 1993

8 4 0

, , ,_1 ,~.,.,~ ~. . . .

i ....

i ....

l,

2

3

4

,-,'-~..,, I , , Acknowledgement

-1

0

1

5

6

7

Y Fig. 6. The rapidity distribution of K ° in central Au + Au colhslons at the SPS energy calculated in the model with (sohd squares) and without (open circles)fuslon. The m a i n results o f our study can be s u m m a r i z e d as follows: ( a ) A large n u m b e r o f interacting p a r t o n s are prod u c e d in ultra-relativistic heavy ion colhsions, which leads to a very high string density, their overlapping and, probably, fusion. ( b ) According to our picture, fusion o f two [3] colour strings either creates the same [ 3 ] colour string ( m a i n l y between d i q u a r k s ) or forms new [6 ]- and [ 8 ]-strings. They decay faster a n d p r o d u c e relatively m o r e baryons, especially strange ones. (c) As a result o f this, string fusion leads to a considerable b a r y o n e n h a n c e m e n t in central n u c l e u s nucleus collisions, a c c o m p a n i e d b y a simultaneous reduction o f the total multiplicity, especially the meson multiplicity. The m o d e l thus predicts a much slower growth o f the particle density in the m i d r a p idity region than the D P M without fusion [23 ]. ( d ) Transverse m o m e n t u m distributions do not practically change with the inclusion o f string fusion, because a larger total transverse m o m e n t u m as fav o u r e d by the increased string tension is distributed a m o n g a greater n u m b e r o f particles. It should be n o t e d that no p a r t o n a n d h a d r o n final state rescatterings have been included in the model. Most existing M o n t e Carlo string models include seco n d a r y h a d r o n rescattering, which allows to obtain a good agreement with the global experimental data on h e a v y ion collisions at SPS energies b u t does not perm i t to describe strange particle production. F o r ex-

The authors are grateful to the General Direction o f the Scientific and Technical Investigation ( D G I C Y T ) o f Spain a n d the Alexander y o n H u m b o l d t F o u n d a t i o n for the financial support.

References

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[20] A. Casher, H. Neunberg and S. Nussmov, Phys. Rev. D 20 (1979) 179. [21 ] X. Artru and G. Mennesaer, Nucl. Phys. B 70 (1974) 93, X. Artru, Phys. Rep. 97 (1983) 147. [22]P. Mattig, Phys. Rep. 177 (1989) 141, and references therem.

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[23] A. Capella, C. Menno and J Tran Thanh Van, Nucl. Phys. A544 (1992) 581e. [24 ] N.S. Arnelin, L P. Csernal, K.K. Gudlma, V.D. Toneev and S Yu. Slvoklokov, Soy J. Nucl. Phys. (1992), m press; N.S. Amelln, E.S. Staubo and L.P. Csernal, Nucl. Phys. (Proc. Suppl.) B 24 (1991) 269.