Nuclear Physics A544 (1992) 429c-434cNorth-Holland, Arnsf~erdam

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0375-9474/92/$05.00 O 1992 - Elsevier Science Publishers B.V . All rights reserved .

Scott ChaprnanNuclear Science Division, Lawrence Berkeley Laboratory, Berkeley, CA 94720 USA

stractFireball, firestreak and hadronic string models are shown to overpredict recent cen-

tral 15 AGeV Si+Au E802 spectrometer data by at least 70%. Claims in the literatureabout full nuclear stopping in Si+Au reactions are therefore premature. In fact, fits tothe spectrometer data indicate that up to half of the projectile nucleons may lose lessthan one unit of rapidity after traversing 5-10 fin of nuclear matter, implying possibly asurprisingly lop- stopping length of ~20 fm. Comparison of these same fits with E810,E814, and preliminary E802 dNcharged/di) data suggests, however, that there may be someinconsistencies among the various data sets, and therefore that additional data will beneeded to establish the degree of nuclear stopping at AGS energies.

1 . IntroductionIt is popularly believed that at the ACS "full stopping is realized [1], showing a be-

havior close to the Landau model[2] and to relativistic fluid dynamics[3], and the energydensity can reach values comparable to the critical values for QGP formation" [4] . flowever, as we pointed out in refs . [5, 6], the published E802 spectrometer data[7] cast doubton this belief, since in fact none of the present models is consistent with the full arrayof data. Moreover, unless the systematic errors of the spectrometer data are very large,these data are more indicative of a surprising degree of nuclear transparency. As we showbelow, however, no firm conclusion can be made on this important topic, since not allof the data sets are completely consistent. In this paper our aim is to clarify what arethe problems at present in drawing conclusions about nuclear stopping power in thesereactions .

In our letter[5] we discussed a model independent fit to the spectrometer data whichimplied that if systematic errors do not cause more than a 30% suppression of protonand pion yields, then 4-momentum and baryon conservation laws imply that at least 11out of 28 projectile nucleons suffer less than one unit of rapidity loss during the collision .In our subsequent paper[6], we gave the precise functional form of the fit used in theletter, and introduced three other fits which featured unexpectedly large n/p ratios in theprojectile region . Here we introduce a fifth 4-inomentuin-conserving fit which features amore realistic n/p ratio and can successfully reproduce the E810[8] data and extrapolations

*Tliis work was supported by the Director, Office of Energy ßesearcls, Division of Nuclear Physicsof the Office of Iligli Energy and Nuclear Physics of the U .S . Department of Energy under Contract No .DE-AC03-76SEr 00098 .

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S. Chapinan / Nuclear transparency in 15 AGeV Si+Au reactions?

of F814[0] leading neutron data (error,, are estimated by assuming . I GeV<T< .2GeV), butwhich overpredicts the currontly published E802 spectrometer data by 40%-70%, whilestill underpredicting preliminary E802 dNchctrqed1dq data[IO] . We conclude that unlikeE810, E814 and E802 diveharged1dq data, the E802 spectrometer data do not support theclaims of full nuclear stopping which are so prevalent in the literature [1,2,4,11-13] .

Is to the DateThe solid line in fig . I shows the results of, the generic fireball model outlined in ref.

[6] with pf, = 5po and -y,, = .5 . This fireball model produces more than a factor of 2 toomany protons, pions, and kaons (not shown) at mid-rapidity. No reasonable variation ofPer and/or -1,, significantly improves agreement with the data . In addition to the genericfireball, fig . I also shows results from die Landau hydrodynamic longitudinally expandingfireball[2] (dashed line) and the hydrocheinical spherically expanding fireball[I", 13] (dot-dashed line) . The longitudinal expansion of the Landau fireball results in reduced protonand pion peaks at midrapidity. This expansion, however, only shifts the problem to higherrapidities, where again the model produces a factor of 2 more protons than are seen inthe data . Even though the spherical expansion of the hydrochernical model provides apossible explanation for the difference in proton and pion slopes, the model again fails toreproduce the measured norms of these distributions . In fact, all of the fireball modelsconsidered here overpredict the measured proton and/or pion rapidity distributions byabout a factor of 2 .

50403020100

Fireballs

M,-8äa M,-M

Figure 1 . Landau hydrodynamic[2],hydrocheinical[12, 13], and generic[6]fireballs are compared to E802 proton andpion spectrometer data from 14 .6 AGeV/ccentral Si + Au reactions[ 7] . The bottompanels are for y = 1 .3 .

Firestreak and String Models504030

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Figure 2 . Firestreak[5, 6] (dashed),utile[14] (solid), and RQNID[ll](histogram) calculations are compared tothe sarne data as in fig . 1 . The bottompanels are the inverse slope parameters ofeqn . (1)[7] .

S. Chapman / Nuclear transparency in 15 AGeV Si+Au reactions?

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In fig . 2, we compare the firestreak[.5, 6] and two string models (Attila[14] andRQMD[11]) with the data. For the Firestreak and Attila, we have calculated Ti(y) byfitting the invariant distributions with exponentials

dl`=/dyd2ml = pi(y) exp(-(7nil - mi)/Ti(y))

( 1 )

in order to compare our curves to the published Ti (y) values.

Though the firestreakimproves on the fireball by showing "spectator" contributions, it still predicts a factorof 2 too many mid-rapidity protons and pions. The string models do a better job ofreproducing the overall ramp shape of dNp/dy, though they overpredict the number ofhigh rapidity protons by 50% . As for the pions, the string models again do better thanthe firestreak, though they still overpredict by 70% the dN,Jdy values reported by E802 .Comparing Attila to RQXID shows that rescattering does not significantly improve thestring model fits to the rapidity data . It should also be noted that the quark-gluon stringmodel recently proposed in ref.[4] similarly overpredicts the number of mid-rapidity pionsby at least 70%.

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ode Independent FitsHaving seen that none of the above equilibrium and nonequilibriurn models for nuclear

collision dynamics are able to reproduce the published spectrometer data, we consider nexta model independen .' . fitting procedure in order to isolate possible causes for the discrepancies . As in ref . [6], we begin by fitting the experimental 7;(y)[15] and (dN/dy)i(y)[7]data with simple functions which have reasonable extrapolations to phase space regionsoutside of the experimental acceptance (dot-dashed line of fig ., 3) . The invariant distribu-tions, fi = dNi/dyd'mi, are then completely determined if the exponential form of eqn.(1) is assumed, since

d1Vi /dy = 27rpi(y)Ti(J)(Ti(J) + ini) .

The exact functional forms of the fits that we used (for kaons as well) are given in ref. [6] .For the unobserved neutral mesons it is assumed that ::-° = (7r+ -F- r -)/2, Ii° = K+, andÎi° = K- . Charge conservation is enforced by demanding that the total number of finalprotons be Np = 14 -i- 79 - N,+ - Nl, + + N,,- + Nl;- . With Np fixed, the total number ofundetected neutrons is given by baryon number conservat ion, Nn, = 28 + 197 - Np. Thesefits allow us to take into account all of the observed energy in longitudinal and transversemotion as well as pion and kaon production .

The total outgoing longitudinal momentum Pz implied by these fits is easily calculatedby integrating 7nl sinh(y)fi over d2m.1 and y:

Pz =

~

dy2Ti2 + 2Tiini + na?(dNfdJ) i sinh(y)i_hadruns

E is simply found by replacing sinli(y) by cosli(y) . For the fit to the data shown by thedot-dashed lines in fig . 3, the integration over y gives Pz = 241 GeV/c and E = 455 GeV,whereas the total incoming energy and nlomentum are known to be PZ = 409 GeV/c

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S. Chapman / Nuclear transparency in 15 AGeV Si+Au reactions?

(= 28 x 141) and E = 595 Gel, (= 197 x .939 + 28 x 14.63) . More than a third of theinconvng momentum and a fourth of the energy are unaccounted for in this fit to thedata! If we assume that neither leptons nor photons carry a significant fraction of the4-momentum, then there must be some undetected hadrons somewhere which do carry it .The E802 collaboration has acknowledged that an undetected excess of low pjL particlescould result in a 25% normlization error of the dNIdy data[?, . To take into account theseand/or other possible systematic errors in the data, we proceed by multiplying each ofour (dNIdy)i functions by a = 1 .3 and find P,, = 322 GeV/c and E = 519 Gel. However,more than 85 GeV/c of momentum and 75 Get, of energy are still missing!

Either the systematic errors of the dA'ildy data are significantly larger than 30%,or else the "missing" 4-momentum must be carried by an unexpectedly large number ofundetected high-rapidity hadrons . The least transparent solution which does not overpredict any of the data by more than 30% is given by fitl of ref. [6] and is shown bythe dashed lines in fig . 3 . Less transparent solutions can of course be found by al-lowing more than a 30% discrepancy with the spectrometer data . An example of a fitof this kind is fits (solid lines in fig . 3), with fit parameters (see ref . [6]) given byOpro, Cproi Cspec, 6spec, 6 7r+, 67r- , Iftmesi ap, bpro(y<2 .25), bpro(y>2 .25)) = (2.25, 3.3, 93 .39,0.025, 1 .75, 1 .,'S5, 1 .4, W, 15, 125). Fit5 has an n/p ratio of 1 .3 for y > 1 .5 and 1 .62 fory < 1 .5 . From the bottom panels of fig . 3, it is evident that fits is only able to reproducehigh rapidity E810[8] and E814[9] data and simultaneously account for all of the initialmomentum by overpredicting the E8G2 spectrometer data by 40%-70% .

It was pointed out long ago[2] that the E802 spectrometer and dNhctrgedldq data seemto be inconsistent with one another. In fact as can be seen in fig . 4, our fits significantly

50

40

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0 et Independent Fits20

10

20

10

Figure 3 . A fit to the data. (dot-dashed),01 (dashed) and W (solid) are comparedto E802[7] data (doits), E810[8] negativesand (+) - (-) (dianwndo, and extrapolatedE814[9] protons (circles for T=.15GeV) .

100

80

C, 60lu90 40

20

Charged Particles

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Figure 4. FRI (dashed), fits (solid),Attifa[14] (dot-dashed) and RQMD[11](histogram) are compared to preliminaryE802 dArcharged1dy data,[10] .

underpredict dN~har9ed1dq even though they significantly overpredict the spectrometerdata . Only models like RQNID[11] which overpredict the spectrometer pious everywhereby at least 70% are able to accurately reproduce dNchar9ed/dq.

4. ConclusionWe conclude that none of the present models which assume complete nuclear stopping

and none of the nonequilibrium string models are consistent ïvith the published E802spectrometer data for central Si+Au collisions . If the normalization error of these datadoes not exceed 30%, then energy-momentum and baryon conservation alone requirethere to be an unexpected shoulder in the baryon spectrum in the region 2 < y < 3implying a high degree of nuclear transparency. On the other hand, results from E810[8]and E814[9] as well as preliminary dN~har9ed/dq data from E802 imply a high degree ofnuclear stopping in these reactions . These data seem to be inconsistent with one another,since no model or fit has been found which can reproduce all of the data while preserving 4-momentum conservation . Consequently, until these apparent inconsistencies are resolved,no firm conclusion can be drawn about the amount of nuclear stopping in central Si+Aucollisions at the AGS.

Acknowledgements : We are especially grateful to Matt Bloomer, Shoji Nagamiya,Flemming Videbaek, Sam Lindenbaum and Johanna Stachel for extensive discussions onthe AGS data.

e ere ces[1] T. Abbott et al (E802 collab), Phys . Lett . B197 (1987) 285 ; M. S . Tannenbaum etal, Nucl . Phys . A488 (1988) 555c ; P . Braun-Munzinger et al, Z . Phys. C38 (1988) 45; J .Stachel, Rappo~teur's talk, PANIC XII, International Conference on Particles andNuclei, MIT, 1990 (unpublished) .[2] J . Stachel, and P. Braun-Munzinger, Phys. Lett . B216 (1989) 1 ; Nucl. Phys. A498(1_989) 577c and private communication .[3] E . F. Staubo et al, Phys . Lett . B229 (1989) 351 .[4] N. S . Amelin et al, Phys. Rev. C44 (1991) 1541 .[5] S. Chapman and M. Gyulassy, Phys . Rev . Lett . 67 (1991) 1210 .[6] S . Chapman and la . Gyulassy LBL preprint 31475 (submitted to Phys. Rev. C).[7] T. Abbott et al (E802 collab), Phys . Rev. Lett . 64 (1990) 847; Phys . Rev. Lett . 66(1991) 1567.[8] W. A. Love et al (E810 collab), Nucl . Phys . A525 (1991) 601c.[9] J. Barrette et al (E814 Collaboration), Phys . Rev. Lett . 64 (1990) 1219 . Formore recent data, see J . Barrette et al ., E814 Collaboration, "Recent Results fromExperiment 814 at Brookhaven," these proceedings .[10] F . Videbaek, Proceedings of IIIPAGS (1990), p . 38 . BNL-44911 and priv . comm .[11] H. Sorge et al, Nucl . Phys . A525 (1991) 95c ; UFTP preprint 263 (1991) ; R.Mattiello et al, Phys . Rev. Lett . 63 (1989) 1159 .[12] G. Brown et al, Phys . Rev . C43 (1991) 1881 ; C. M . Ko et al, Phys . Rev. Lett . 66(1991) 2577.[13] C. h-I . Ko et al, Erratuni Phys . Rev . Lett . 67 (1991) 1811 .[14] X1 . Gyulassy, CERN-TH.4794, Proc . Balatonfured Conf. on Nuc. Phys . (1987) .[1 .5] M. A . Bloomer, MIT Ph .D thesis 1990 and private communication .

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