N U C L E A R PHYSICS A

ELSEVIER Nuclear Physics A610 (1996) 132c-138c

Baryon stopping and strange baryon enhancement in heavy ion collisions

A. Capella

Laboratoire de Physique Th@orique et Hautes Energies *, Universit4 de Paris XI, bgtiment 211, 91405 Orsay Cedex, France

I discuss a new mechanism of baryon stopping based on diquark breaking. I show that this component, which leads to baryon production near mid-rapidities, increases with A and with centrality faster than the inelastic cross-section. The consequences of this novel mechanism for strange baryon enhancement are discussed.

1. B A R Y O N S T O P P I N G

In the dual patton model (DPM) [1], as well as in most string models, the dominant hadronization mechanism in pp collisions consists in the production, via color exchange, of two quark-diquark strings. The diquark can fragment directly into a leading baryon, or can give a meson in the first string break-up and a baryon in subsequent ones. Usually, an effective baryon fragmentation function, which combines these two possibilities, is determined from pp data and then used in pA and A B collisions [2]. When doing so, the nucleon stopping in central A B collisions is too small. For instance, the net proton (p-/5) distribution in central S S has a pronounced dip at mid rapidities which is inconsistent with experiment [2]. Several attempts have been made to overcome this draw-back of independent string models. (For instance, with the introduction of double strings in VENUS [3]). In a recent paper by B. Kopeliovich and myself, we have shown that in nuclear collisions the diquark breaking (DB) component, increases with A and B and with centrality much faster than the diquark preserving (DP) one. Therefore, it is not possible to use the same effective baryon fragmentation function in pp collisions and in nuclear ones. One has to keep track separately of its D B and D P pieces and let their relative weights change with A and B in the way specified below. Note that in nuclear collisions we also have D B diagrams of the type shown in Fig. 1, not present in pp

collisiohs, in which the baryonic number follows a sea quark or gluon. This interesting possibility [5, 6] has been advocated in a recent paper by D. t(arzeev [7] as an important mechanism of baryon stopping. There is a controversy in the literature concerning the

* Laboratoire associ~ au Centre National de la Recherche Scientifique - URA D0063

0375-9474(96)$15.00, 1996 - Elsevier Science B.V. PII: S0375-9474(96)00349-1

A. Capella/Nuclear Physics A610 (1996) 132c-138c 133c

s-dependence of this component at high energies [5-7]. However, there is agreement on the fact that , at present energies, it behaves like l /v@. This implies that the baryon distribution behaves as l / v @ - the same distribution as a valence quark.

I turn next to the A-dependence ~ c of the D B component. Following [4] I

c split the nucleon-nucleon ( N N ) cross- c section into its diquark preserving and

~ diquark breaking components c~in = ~ C ~ ¢rDp -t- ~DB. I assume that once the

~ ~ ~ ' - ~ diquark has been destroyed in a colli- sion with one nucleon of the nucleus it cannot be reconstructed in further

Figure I : Diquark breaking component with collisions with other nucleons. The the baryon number following a sea quark or a N A cross-section involving n inelastic gluon. N N collisions is then given by

~ N A ~ ' = (~ ) E n ( ? ) ~ S B ~.~n-; T~(b) [~ - ~,~ T~(~)] ~ - ~ (~) DB,nk TM] i = l

Here TA(b) is the s tandard nuclear profile function at impact parameter b, nor- malized to unity. In (1) we have replaced the usual factor c ~ T~ corresponding

•

to the cross-section for n inelastic collisions by the product [ '~r i ~-1 \ i ) DB O'Dp T ~ : i = 1

(~'?n - ~SP) T](b). Indeed, only the term C~Sp T ] will contribute to the diquark pre- serving cross-section. Summing in n we have

°'DNBA(b) = En=lA o.NADB,nt [b~] = I -- [1 -- O'DB TA(b)] A (2)

Eq. (2) shows that the diquark preserving cross-section belongs to a class of process [8] which has only self-absorption (or self-shadowing). Obviously

N A Since (rDB < ¢in, it is clear from (2) and (3) that cDBNA increases faster with A than ~TDp. Actually, when ~DB is sufficiently small to neglect in (2) second and higher powers of

NA will increase linearly with A. This proves the result stated above that the CrDB, ~ D B

relative size of the D B component increases with increasing A. This result can be easily generalized to an A B collision. We have [9]

c~AB(b) ---- 1 -- (1 -- <rDB TAB(l))) AB (4)

where TAB(g) = f d2s TA(© TB(g--©. For ~DB sufficiently small we get from (4), after integration in impact parameter, AB = A B CrDB ~DB.

In the numerical calculations, we take GDB : 7 rob, corresponding to a 20 % weight of the D B component in pp collisions ((r~P~ : 32 mb). Using eq. (4) one then finds tha t this weight has increased to about 40 % in central S S collisions and is as large as 64 % in central Pb Pb. Clearly, the presence of such an increasingly important component,

134c A. Capella/Nuclear Physics A610 (1996) 132c-138c

producing baryons with a l / v @ distribution, will have a dramatic effect in the baryon stopping. This is illustrated in Fig. 2. First we see that this component has a small effect in pp and peripheral SS collisions. (Note, however, that here the description of the data is bet ter without the D B component. This is due to the fact that we have used for the D P component the total baryon fragmentation function determined in ref. [2] from a fit of pp data). In the case of central SS collisions the effect of the D B component is already very large. The pronounced dip obtained without this component is largely filled-in, in agreement with experiment. The predicted curve for Pb Pb collisions shows a flat distribution at mid rapidities. Such a shape has been recently confirmed by the NA49 and NA44 collaborations [10].

Note tha t the l / v @ baryon number distributions of the D R component implies that dN/dy behaves as s -1/4 at y* = 0. Since the D P component drops much faster with s, the baryon distribution at mid rapidities at RHIC will be dominated by the D B

/ . a r ~ 7 , , P b P b - - - * n - ' h component , with a predicted net nucleon number : (alv/ay)y.=o _~ 10.

10 I ~ P b - P b ( *0 .2 ) / ~

8 ~ ~ cent ra l / !1 Ii :"" ............................................. "k ##

C -, , b 6 ~ :i t ,

• \ Z , s - s ' " . " - /% "-"~ I /~k~, 1 ' , c e n t r o l I//~, ,

b 4

,,,,,,,-t ~ 2"

0 . . . ~ ~ . 0 1 2 3 4 5 6

Y Figure 2 : Rapidity distribution of the p-/~ difference in AA collisions at v'~ = 20 GeV. The thick dashed curve is the result of ref. [2] for central SS collision without the diquark breaking mechanism. The thick solid curve shows the result of the calculation [4] including the diquark breaking component. The full circles are the data points from [16]. The same for peripheral SS' collisions is shown by the thin solid and dashed curves and the square points. Here the theoretical curves are for N N collisions, normalized to the data. The dot ted curve shows our prediction for central Pb-Pb collision scaled down by a factor 1/5. It corresponds to nucleon minus antinucleon - rather than to proton

minus antiproton.

A. Capella/Nuclear Physics A610 (1996) 132c-138c 135c

2. S T R A N G E B A R Y O N E N H A N C E M E N T

A comprehensive study of strangeness enhancement in DPM has been published recently [11] [12]. The observed yield of strange particles in central SS collisions is obtained with two main modifications of the model : a) qq-~-~ pairs from the nucleon sea are introduced with the same weight needed in the string breaking process. This mechanism is very similar to string fusion and produces baryons and antibaryons in pairs ; b) final state interaction of secondaries is introduced. In particular the two body and quasi two body reactions Ir + N -* K + A, ... , are found to account for most of the observed A enhancement. On the contrary, string fusion by itself has very little effect on A production due to the small A/A experimental ratio [13]. (In the presence of final state interaction the effect of string fusion can be larger due to possible annihilation of A's with nucleons).

In the calculations of [11] [12] the new mechanism of baryon stopping described in section 1 is not present. As a consequence the nucleon yield, needed to evaluate the final state interaction, is ill determined (see Fig. 2). In [12] this problem was solved in a very crude way by introducing some extra, ad-hoc, stopping in order to reproduce the central S S data. However the extrapolation to central Pb Pb is not safe. Moreover, the stopping mechanism in section 1 is a source of extra A's produced near mid-rapidities. Indeed, in the D B diagram of Fig. 1 the probability to produce a A is proportional to 3 As (i.e. three times larger than in the DP component) since the strange quark can be any of the three quarks that form the baryon. When the baryon number follows a valence quark the corresponding enhancement is 2As. (In the numerical calculations, I assume that the relative weights of these two par ts of the DB-component are given by purely probabilistic arguments). I~ is therefore necessary to reexamine the results of [11] [12] in the presence of the new stopping mechanism. I shall consider only A production. The results for kaons and A's are practically unchanged by the presence of the D B component. The results [14] for central S S and Pb Pb collisions are given in Tables 1 and 2 and compared with available data. In the absence of final state interaction the contribution from string fusion is normalized in such a way as to reproduce the measured value of the A/A ratio [13] and turns out to be very small. In the presence of final state interaction, on the contrary, the string fusion contribution is computed according to refs. [11] [12]. As discussed there, this calculation gives the maximal possible value of this contribution and probably overestimates it. We see from Table 1 that, in SS, the results without final state interaction are close to the NA36 data. The NA35 data, on the contrary, require full final state interaction and are atso rather well reproduced. Table II shows that the corresponding predictions for Pb Pb collisions (i.e. without and with final state interaction) are dramatically different. The result with final state interaction give a rapidity density of 23 to 30 A's per unit rapidity at y* = 0. This prediction practically coincides with the one given in [12] and is in agreement with preliminary data [15] presented by the NA49 collaboration at this conference.

Finally, although we have only considered A and A production, it is clear that

136c A. Capella/Nuclear Physics A610 (1996) 132c-138c

s t r ing fusion plus final s ta te interact ions such as rr 4- A -+ K 4- E, ... will also produce

an enhancement of the o ther s t range baryons and ant ibaryons.

Table 1 A rap id i ty d i s t r ibu t ion in central S S collisions at 200 GeV/c per nucleon. Columns 1 and 2 are the values without final s ta te interact ions - respectively wi thout and with sea qq-q--q pairs (see main text) . Columns 4 and 5 are the corresponding values wi th final s ta te interact ion. The NA35 values are read from Fig. l l b of [17] and those of NA36

from Fig. 14 of [18] wi th the p± acceptance correction given in eq. (1) ( the value with

an as ter ix is for y* = 1.25).

(dN/dY)NAa6 (dN/dY)NAa5 y, (dN/dy)~SoT~ ss--+, ss--+, s s + a ( dN/ dy)~ith .~,i

0 0.72 0.78 0.97 ± 0.14 1.5 1.9 2.2 ± 0.3 0.5 0.72 0.77 0.97 4- 0.12 1.4 1.8 2.1 4- 0.3

1 0.71 0.75 0.86 4- O.lO 1.4 1.7 2.1 4- 0.3 1.5 0.67 0.70 0.76 4-0.12" 1.4 1.6 2.2 4- 0.3 2 0.61 0.62 1.2 1.3 1.4 ± 0.2

Table 2 Same as Table 1 for central Pb Pb collisions at 160 GeV/c per nucleon.

y. (dN/dy),pb Pb--+A Pb Pb--+A fsl (dN/dy)~ith f~i

0 7.7 8.4 23 31

0.5 7.4 8.1 22 30 1 6.5 6.8 20 25 1.5 4.9 5.0 16 19 2 2.9 2.9 8.8 9.1

R E F E R E N C E S

I. For a review see A. Capella, U. Sukhatme, C. I. Tan and J. Tran Thanh Van, Phys.

Rep. 236 (1994) 225. 2. A. Capella, A. Kaidalov, A. Kouider Akil, C. Merino and J. Tran Thanh Van, Z.

ffir Physik C70 (1996) 507. 3. K. Werner, Phys. Rep. 232 (1993) 87. 4. A. Capella and B. Kopeliovich, Phys. Left. B, in press. 5. G. C. Rossi and G. Veneziano, Nucl. Phys. B123 (1977) 507.

A. Capella/Nuclear Physics A610 (1996) 132c-138c 137c

6. B. Z. Kopeliovich and B. G. Zakharov, Z. Phys. C43 (1989) 241. 7. D. Kharzeev, Can gluons trace baryon number ?, CERN-TH/95-343. 8. A. Blankenbecler, A. Capella, C. Pajares, A. V. Ramallo and J. Tran Thanh Van,

Phys. Lett. B 107 (1981) 106. 9. C. Pajares and A. V. Ramallo, Phys. Rev. D31 (1985) 2800.

10. P. Seyboth (NA49 co11), Proceedings XXXI Rencontres de Moriond, Les Arcs, France (1996). D. Zachery (NA44 coll.) Ibid.

11. A. Capella, Phys. Left. B364 (1995) 175. 12. A. Capella, A. Kaidalov, A. Kouider Akil, C. Merino and J. Tran Thanh Van,

Z. Physik C, in press. A. Capella, A. Kaidalov, A. Kouider Akil, C. Merino, J. Ranft and J. Tran Thanh Van, Proceedings XXX Rencontres de Moriond, Les Arcs, France (1995).

13. S. Abatzis et al (WA94 coll), Phys. Left. 354 (1995) 178. S. Abatzis et al (WA 85 coil), Phys. Left. B359 (1995) 382. M. A. Mazzoni et al (WA 97 coll), Proceedings XXV International Symposium on Multiparticle Dynamics, Starg Lesn~, Slovakia (1995). R. Lietava (WA97 coil), Proceedings XXXI Rencontres de Moriond, Les Arcs, France (1996).

14. A. Capella, Strangeness enhancement scenarios : fireball or independent strings ?, preprint LPTI-IE Orsay 96-30, hep-ph 96-05216.

15. NA49 collaboration : these Proceedings. 16. NA35 Collaboration : tI. StrSbele et al, Nucl. Phys. A525 (1991) 59c. 17. T. Alber et al (NA 35 toll), Z. Phys. C64 (1994) 195. 18. E. G. Judd (NA36 toll), Nucl. Phys. A 590 (1995) 291c.