Nuclear Physics B (Proc . Suppl .) 24B (1991) 199-206North-Holland

H. J . CRAWFORD

Space Sciences Laboratory, University of California, Berkeley, CA 94720

Mukesh S . DESAI and Gordon L . SHAW

Department of Physics, University of California, Irvine, CA 92717

1 . INTRODUCTIONThe possibility that S-drops may not only be

metastable 1-12 but would be absolutely stable if theywere large enough s, would have consequences of thegreatest importance . While it may require an as-trophysical event 13-20 to produce strange matter ofsufficient size for absolute stability, we can considerproducing smaller, metastable S-drops at presentlyavailable fixed-target heavy-ion accelerators at BNLand CERN. The accelerator experiments are com-plementary to the important astrophysical investiga-tions 13-'23. It was suggested earlier 3,7,9,11 .12 to lookfor the formation of relatively Small A strange mat-ter ( S-drops ) in relativistic heavy-ion collisions . Itwas proposed 12 that these small metastable S-dropscould he isolated and rapidly grown to a large sta-ble ,zïze . The present paper 24 continues the work ofLiu and Shaw 7 on the production probability of S-drops fruia a hot quark-gluon droplet via the mecha-nism of fragmentation and recombination under bestguess scenarios . The spirit of this work its to providea simple framework in which to calculate productionprobabilities given various values of the relevant pa-

0920-5632/91/$03 .50 © 1991 - Elsevier Science Publishers B.V .

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PRODUCTION OF DROPS OF STRANGE MATTER IN FIXED-TARGET HEAVY-ION COLLISIONS

The theoretical possibility that strange matter is more stable than nuclear matter has enormous impli-cations . It has been suggested to search for the possible formation of metastable strange matter withrelatively small baryon number A, S-drops, in present fixed-target relativistic heavy-ion collisions at BNLand CERN. In this paper we estimate the sensitivity required for the above experiments to be successful .These estimates of the production ( and lifetimes ) of S-drops as a function of A, strangeness, S, andelectric charge, Z, should be useful in designing and evaluating searches for S-drops, 'AZ. For example,the production estimates for metastable S-drops with AN30 indicate that they could be detected withdedicated experiments having high sensitivity. Furthermore, specific searches for metastable S-drops withZ < 0 would have the advantage of low intrinsic background .

rameters . The results presented here should be usefulin designing and evaluating future accelerator searchesfor S-drops.

In this paper we address the question of the pro-duction probability of S-drops, SAZ, and the neces-sary experimental sensitivity required to detect themin relativistic heavy-ion fixed-target collision experi-ments . The production ofS-drops which have lifetimesra greater than 3 - 10-s sec is investigated for small A(AN30), where we find their production to be exper-imentally accessible . Specific searches for metastableS-drops with Z < 0 would have the advantage of lowintrinsic background coming mainly from anti-nucleiand free quarks 25 . Included here are features suchas the `cooling' of the S-drop (where we introduce theconcept of the `super compound state') . Although,admittedly, our calculations are rough they will nev-ertheless serve to indicate the viability of the present-day high sensitivity experiments in search of this ex-otic form of matter .

2 . CALCULATIONSOur basic scenario for producing the S-drops is sum-

200 H.J. Crawford et al ./ Production of drops ofstrange matter in fixed-target heavy-ion collisions

marized in Fig. 1 . The spirit of this paper is to makevery simple physical esü~liaï,es for each of the steps .

(o) A relativistic large heavy-ion Abeam collides with

a fixed-target heavy nucleus to form large hot non-equilibrium quark-gluon, QG, drop . We assume thatthe QG-drop is formed in the cms system consisting ofequal numbers of beam and target nucleons . There isprobably a threshold for producing the QG-drop bothin size, .AO , and in beam energy, E°b . Above thesethresholds, we will take the probability for formingthe QG-drop, PQG, as :

0

0PQG = Pec '

(Abeam - Abeam) * O(Elab - Elab)

(1 )

where Pcc is the probability of having a central colli-sion ; we take P,, = 0.1 .

(a) The next step is the fragmentation of the largeQG-drop of size 2Abeam into smaller QG-drops, againin non-equilibrium states . Perhaps a similar breakupis described by van Hove 28. The probability of thisspatial factor, Pap , to produce a drop of size A will betaken as:

P,p = A/2Abeam M

where we expect this ratio to be much less than 1 .Perhaps we need a Au or Pb beam to produce theinitial QG-drop, and as we will see below, only smallQG-drops with A from 10-30 can be expected to haveappreciable probabilities of producing an S-drop.

(b) The small QG-drop will cool mainly by mesonemission. From the results of Liu and Shaw 7, we takethe main process for the buildup of s quarks (and de-crease in electric charge) in the drop to form an S-dropSAZ to be the emission of K+ and KO mesons, and wewill ignore baryon emission in our specific calculationsbelow.

(c) Following the strong process of cooling and for-mation of the S-drop, there follows a rapid furthercooling by emission of gammas of perhaps the last100 MeV of excitation (again see van Hove 26). Weintroduce, below, the concept of the super compoundstate, SCS, to understand this .

(d) Finally, using the Berger-Jaffe mass formula, towe examine the energy levels of each state 'AZ to

see which ones wiil live long enough for the relevantexperiments to detect them .We define the production probability Pprod as :

Pprod = PQG ' Psp ' Paum ' Peool

where P,u,n is the probability for a given A and Z ( ;,sldS not detected) in step (b) and Pcool is the probabilityfor cooling in step (c), and these will be calculatedbelow.2.1 . Quark contentP(SAZ) : Probability for the Formation of an S-

drop, SAZ.Let us consider the relativistic heavy-ion central col-

lision in which a hot quark-gluon (QG) droplet maybe formed with baryon number, A, and electric chargeZi -- 0.5A . Here the subscript indicates the initialstate of the droplet, assumed to be quite hot and toundergo an evolution to the S-drop state . We expect Ato represent some fraction of the baryon numberof thetarget and projectile . This QG-droplet will have 3Au and d valence quarks and many sea quark pairs uû,dd, and ss . Some of the quarks will leave the QG-dropin the form of mesons and baryons in a strong interac-tion process, altering the strange quark content of thedrop as well as lowering its energy content . This wascalculated in some detail by Liu and Shaw 7 who con-cluded that for small A there is an appreciable proba-bility of leaving the S-drop with â strangeness fractionnear the energy minimum required for metastability,namely, n,mi,, " 0.8A . Further, the dominant processof reaching this state was through the removal of squarks through meson emission . This will form thebasis of our simplified model.We first calculate the strange quark content of the

drop . To do this, we need a way to estimate thenumber of strpzige quarks left in the S-drop by me-son emission from the initial QG state . The strangequarks are carried off by K- and K° mesons, whilethe anti-strange quarks are carried off by K+and K°mesons, with the net number of s quarks left in thedrop as n, = (K+ -1- K°) - (K- + K°) where the Ksrepresent the number ofeach type ofmeson. From therecent E802 investigations 27,28 ofSi+Au at BNL, we 24

H.J . Crawford et al./Production of drops ofstrange matter in fixed-target heavy-ion collisions

large QG-drop

-r !s

IC's

(c)

low-excited S-drop

estimate n� the average number of strange quarksproduced in step (b) of Fig . 1, to be O.1A . As thecollision energy increases, we expect the mean mesonmultiplicity to increase due to increase contributionsfrom the sea quarks 29, but the size of the drop willremain much the same since it is formed Prim--rily ofvalence quarks . Thus, as the lab energy Elab increasesfrom the BNL value of 14.5 GeV%Abeam to the CERNvalues of SO GeV/Abeam and 200 GeV/Abeam� we canreasonably expect the strange quark concentration to

increase from our BNL value of n, s~ 0.1A, becomingperhaps as large as n, -- 0.2A.29

To investigate how a, piece of nuclear matter with

this quark mixture would evolve, we turn to theBerger-Jaffe mass for.mula 1ß . There are two param-eters in the Berger-Jaffe mass formula, m� the massof the strange quark, and co, the energy per baryonfor a large A strange matter . There is a sensitivityto these parameters 10,12-30 but for purposes of this

paper we chose optimistic but reasonable values of

eo = 880 MeV and m. = 150 Me'V 31 . We find thenthat the number of s-quarks, n.i� , at the energy min-

imum, in S, Z space for a given A is n.min = 0.8A .

FIGURE 1 .

smaller QG-drops

-~O Q OI

(ug), (ds)leave s in

drop

metastableS- drop

Highly schematic scenario for producing small, metastable S-drops as described in Section 2 .

201

However, we have just seen that the average collision

leaves a, drop whose s quark content is quite far fromthis value. Presumably a drop with such low s quark

content would simply dissolve into normal hadrons.The drop formation process is statistical in nature and

there are fluctuations in the s quark content around

this average value that could lead to events in whichthe drop is near the n, required fc,r metastability.

Assuming Poisson statistics, we calculate the prob-

ability for a given strange quark content n. using

( )(4)

Wepresent in Table 1 the probability ofgetting a drop

of n,,ni,, = 0.8A as a function of A and âwerage values

of n, between O.1A and 0.2A . We conclude from this

table that we should concentrate further efforts in our

discussion about detectability on values of AN30 .

Once having formed our residual S-drop, the drop

may evolve via a variety of stfuag aad weak processes

depending on its charge as well as on n. . To find the

charge distribution of our drops, we now look at the

process by which charge is removed in the emission of

the strange mesons . Note that we are assuming that

202 113. Crawford et al . /Production ofdrops of strange matter in fixed-target heavy-ion collisions

pion emission leaves the net charge unchanged on theaverage. When an s quark pairs with a u quark itremoves one unit of charge ; when it pairs with a dquark the charge is not altered . If ns is the numberof s-quarks left in the drop then on the average thenumber of u-quarks that paired off with an s will beii, = n,/2.0 . We take our protodrop to have an ini-tial charge Zi = 0.5A before accounting for the mesonemission process . ( In this model the charge on thedrop cannot increase beyond Zi.) To arrive at an S-drop having a given Z we need, say, nu = Zi - Z num-ber of u-quarks to pair off with s. Again, assumingPoisson statistics, we have :

We define:

2.2. MetastabilityAt this point we have computed the probability dis-

tribution in SAZ, Eq. (3) above. The next step is toconsider the lifetimes of these SAZ drops with respectto both strong and weak processes to see which livelong enough for observation. The basis for these cal-culations will be ine Bergen-Jaffe mass formula 1° usedabove, as described in reference 12.We estimate the decay rates for weak decay pro-

cesses using the following formulas 12 : for /3 decay,

roz_1

103( AE(20eV) )SS-1

and, for weak non-leptonic decor; 32,

hos=1 ~ lop( AE(20eV))25-1'

First, we only consider S-drops SAZ which are sta-ble against strong neutron decay. Second, we se-lect those S-drops which have no charge change asin Eq.(7) with lifetimes T >_ 3 - 10' 8 sec . The weaknonleptonic decays, Eq.(8), occur very rapidly. How-ever, the small energy release w-ll go off as -y rays(see Sec.2.4) and thus r-*]? not affect the spectrometerexperimentii which detect Z and A but not S . In appli-cation of these equations, we assume that the S-drops

have rapidly reached their ground states via energyemission as discussed below in Section 2.4 .

2 .3 . Production probabilities for observable S-dropsWe now can calculate the production probabilities

P(SAZ) for SAZ using Eq.(6) for those S-drops whichhave /3-decay lifetimes > 3 - 10'8 sec . a s discussed inSection 2.2 . The values of S and Z have also beenrestricted by taking account of strong neutron decay.Furthermore we consider values of Z which satisfy thegreater of either IZI < 0.2A or IZI < 3.0 , for highervalues of positive Z the intrinsic background will belarge and thus make it difficult to detect large positiveZ S-drops, while for lower negative Z the probabilityP(SAZ) is low. From Table 1 we see that for A > 40.0the probability is too low to be observable for the ex-isting experiments . But for A < 30 it is appreciableenough for the present-day experiments to look forthese metastable states . Results for A = 10 are shownin Table 2 for n, = O.IA suggested for the BNL case(for more details see Ref. 24). We have included theA =10 calculations, although the formalism may notbe applicable for this small an A. Note that the prob-ability of forming a positively charged drop with Z =1 to 3 is less than three orders of magnitude greaterthan for forming a negatively charged drop with Z =-1 to -3 when the probabilities are summed over themetastable n, combinations . This will prove relevantwhen discussing experimental detectability in Section3.

2.4 . Cooling of S-drop to its ground stateHere we calculate P,, the probability for rapidly cool-

ing of the initially formed S-drop, SAZ, to near itsground state (step (c)) . As discussed above, we haveassumed that the drop A was formed via the initial in-teractions among equal numbers ofprojectile and tar-get nucleons in a high energy nucleus-nucleus collision.Thus, for a lab energy Elab = Tab GeV/Abca�a the cmsenergy of the S-drop is Ei = A (ylab/2) GeV. Theinitial S-drop that is formed in an excited state willdecay into its `ground' state through various processesthat could be allowable from energetic considerations .For an co = 880 Mer' and m, = 150 MeV we find aground state energy of Eo

910A MeV in the mass

Plnu)e'n°(rau)n �

(5)(nu) 1.

P(SAZ) = P(nu)P(n'). (6)

H.J. Crawford et al./Production ofdrops -,-f strange matter in fixed-target heavy-ion cotisions

Table 1 : Probability P(n�� ;,, ) of obtaining n.in = 0.8A for different A and n, .

Table 2 : Probability P(SAZ) for A=10.0 and n, = OJA.

In Table 2 : P�, m is the total probability for a given Z . Included above are only thoze S and Z for which theweak lifetimes of the metastable S-drop is greater than 3 -10'8 sec . Strong neutron decay also constrainsthe range of S and Z. Furthermore the Z values have been restricted to the greater of the followingconditions : 145 3 or 145 0.2A .

A n.in na = MA P(n.,,nin ) na = 0.15A P(n�nin) na = 0.2A P(n,min)10 8 1.0 9.1 .10-6 1.5 1.4 .10-4 2.0 8.6- 10-415 12 1.5 6.0 -10'8 2.3 3.7 .10-6 3.0 5.5-10-'20 16 2.0 4.2-10-10 3.0 1.0 .10-7 4.0 3.8 -10- '530 24 3.0 2.3- 10-14 4.5 8.5-10-11 6.0 1 .9-10-840 32 4.0 1.3-10-l' 6.0 7.5- 10-14 8.0 1.0-10-1950 40 5.0 7.5- 10-23 7.5 6.8- 10-17 10.0 5.6-10-1360 48 6.0 4.5 - 10'27 9.0 6.3 . 10'29 12.0 3.1-10'1570 56 7.0 2.7 - 10'31 10.5 6.0- 10-23 14.0 1.8 -10';780 64 8.0 1.7 -10'35 12.0 5.7 -10-26 16.0 1.0-10-1990 72 9.0 1 .0 .10-39 13.5 5.4- 10-29 18.0 6.0 -10-22100 80 10.0 6.3- 10-44 15.0 5.2- 10-32 20.0 3.5 -10-24

ZS

-3 -2 -1 0 1 2 3

-11 7.8 -10'1° 1.1-10-s 1 .4 -10-s 1.6 -10'9 1.4 -10 9 1.0 -10'9 5.7 -10'io

-10 6.6 -10'9 1.1-10'8 1 .5 - 10'8 1 .8-10-, 1.8 -10'8 1.4 -10'8 8-5-10'

-9 4.7 -10'8 8.4- 10-8 1 .3- 10-7 1 .7- 10-7 1.9 .10-7 1.7 -10" 1.1 .10-7

-8 2.7- 10-7 5.4 -10" 9.5- 10-7 1.4 - 10-s 1.8-10" 1.8 .10-6 1.3 -10-s

-7 1.2 -10-s 2.8-10-6 5.6- 10-6 9.6- 10-6 1.4 -10's 1.6 -10'S 1.4 -10's

-6 14.1 .10-6 1.1-10' 2.6 -10" 1 5.2 -10-5 R.6 -10-5 11.1 . 10-4 11.1 .10-4

-5 9.5- 10-6 3.0-10-' 8.5 -10's 2.0- 10-4 4.1-10-4 6.6- 10-4 7.9 -10`

-4 1.3-10-' 4.2-10-3

1 P,u,n 1 2.8 -10'S 4.4 -10'S 1 1.2 -10-4 1 2.6- 10-4 15.1- 10-4 17.9- 10-4 5.1 -10'3

204 H.J. Crawford et al . /Production of drops ofstrange matter in fixed-target heavy-ion collisions

r-ge from 10 < A <_ 30 near the energy minimumin Z, S space . Thus, we are interested in calculatingthe probability for rapid cooling of the S-drop fromthe ini'ial energy E; to year its ground state value byemission of an amount of energy whose maximum isset by AE,nax = Ei - Eo.Now we calculate the probability that the excited

protodrop having energy E; will emit energy DE ina short enough time (by meson and baryon emission)to have its further evolution dominated by rapid -r

emission and then by the weak decay processes, Wewill assume that the probability P,,.l to cool to withina window dE, of our ground state is simply :

Pool =dE,1AE�,ax

We estimate dE, to be the excitation energy atwhich rapid gamma emission dominates. Here we in-troduce the concept of the Super Compound State,SCS, in which the t nergy dE, i,- shared among manyexcited quark configurations . This is in analogy withthe compound state in moderate and large A nucleiwhere at low excitation energies, y emission dominatesover neutron emission. In the SCS, neutron emissionis greatly inhibited by the further requirement that 3quarks with the correct energy, spin ; flavor and colormust combine before emission is possible . Thus wesuggest that a value (less than mass of pion) dE,100 MeV is reasonable for the SCS to decay by a rapidseries of -y emissions to the ground state configurationof the quarks which can then decay by the weak in-teraction. We use this value of dE, with Eq.(9) toestimate Pcocl in Table 3 .

3 . RESULTS AND DISCUSSIONThe search for the production of small metastable

S-drops at present fixed-target heavy-ion facilities at,BNL and CERN is of the greatest importance . Twoexperiments have been recently approved at BNL 33

which will be searching for S-drops in their stud-ies, E864 34 and E878 35. A recent proposal, SP-SLC P259, 36 to search for neutral S-drops has beenpresented at CERN, and other potential experimentswere discussed in a discussion meeting on "Strange

Table 3 : Probability of cooling, Pcool, to within dE, of100.0 MeV for various A and ylab .

matter" held there 37. Arguments were made thatthe present fixed target heavy-ion facilities presenta "Window of opportunity in searching for S-drops"since future higher energy heavy-ion colliders may beworse both from a production and detection perspec-tive. It is with all this in mind that we have presentedhere a very simple framework in which to calculateproduction probabilities and detection for S-drops inthese experiments now being implemented or now be-ing designed . Although our calculations are rough,the results presented in Tables 1-4 should be of use indesigning and evaluating searches for this exotic andpotentially important form of matter. (Furthermore,the calculations have been presented in a transparentmanner so that the reader might in any of the severalstages substitute an "improved" version .)We now calculate the production probability Pprod

defined in Eq. (3) where P�,�, is tabulated in Table2 for n, = 0-1A , Pcocl in Table 3 . For larger ft, seeRef. (24) . We have evaluated P,p for Abeam = 30 . Ourresults for Pprod are given in Table 4 for various ylab-

We observe from Table 4 that an experiment de-signed to look for S-drops st BNL and CERN shouldhave a sensitivity of detecting rates smaller than oneS-drop produced in 107 collisions. The rates for smallA (less than 30) look favorable. Specific searches formetastable S-drops with Z e 0 have the advantageof a much lower intrinsic background (e.g., Z = -3would have no intrinsic background) and yet have onlyless than a factor of a thousand smaller production

..A -ydab ~' Pc1 n.n 14 .5 15.6- 10-315 .0 1 14 .5 3.7 -10-320 .0 14 .5 2.8- 10-310 .0 60 .0 2.2- 10-315 .0 60.0 1 .5- 10-320.0 60.0 1 .1 .10-310.0 200.0 1.1 .10-315.0 200.0 7.3- 10-420.0 200.0 5.5- 10-4

H.J. Crawford et al . /Production ofdrops of strange matter in fixed-target heavy-ion collisions

rate than the corresponding case with Z > 0 .Experiments at CERN would have the advantage

over those at BNL in that the larger expected n, atthe higher E(ab gives an increase in production rates .However, there will be a decrease in collision timesat CERN energies whose consequences are hard to es-timate, so that it is crucial to do these searches forS-drops at all available energies .

Table 4: Probability for the production of an S-drop,Pprod, as given by Eq . (3).

ACKNOWLEDGEMENTSWe thank Jon Engelage, Peter Lindstrom, Michael

Shin, and Peter Sondereggi:r for helpful discussions.This work was supported in part by the United StatesDepartment ofEnergy Division of Nuclear Physics un-der Grant DE-AC03-76SF-0098 .

205

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206 H.J . Crawford et al./Production ofdrops of strange matter in fixed-target heavy-ion collisions

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32 . This is correctly normalized to A° decay (ratherthan the 61= 3/2 suppressed K+ in Ref. (12) ) .

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