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ψ suppression in nuclear collisions
VoLume218, number 4
PHYSICS LETTERSB
2 March 1989
QUARK-GLUON PLASMA DIAGNOSTICS AND J / ~ S U P P R E S S I O N IN NUCLEAR C O L L I S I O N S Sibaji RAHA a and Bikash SINHA b Saha Institute of Nuclear Physics, 92, A.P. C, Road, Calcutta 700 009, India Variable Energy Cyclotron Centre, Bhabha Atomic Research Centre, 1/AF, Bidhan Nagar, Calcutta 700 064, India
Received 20 August 1988
The suitabilityof J/~gsuppression, observedin ultrarelativistic heavyion collisions,for detectingquark-gluonplasmais examined.
The possibility of creating a new state of matter, called the quark-gluon plasma (QGP), through ultrarelativistic heavy ion collisions seems very ripe [ 1 ], although how to decipher the presence of such a state is still an open question, there exist in the literature many plausible suggestions; nonetheless a recent idea by Matsui and Satz [2] relying on the suppression ofJ/t~ relative to the continuum dimuon spectrum in a QGP has generated tremendous interest. This is all the more so, as the results of the NA38 experiment with 200A GeV 160 beams on heavy targets do indeed show suppression in high transverse energy events [ 3 ]. Results for the 32S run are eagerly awaited and if, as is expected, the amount of J/~t suppression is found to increase, it would really be considered a strong indication for the formation of QGP. Given the momentous implications of the discovery of QGP, it is imperative to rule out all other probable (or even possible) mechanisms which may cause such a suppression. To this end, it should be remarked that even in hadron-nucleus collisions at high energy, processes were current wisdom does not expect the formation of QGP, the formation of J/tg is significantly more coherent than continuum dileptons. A phenomenologically useful way to characterize the amount of coherence in such production processes is to parameterize the total cross section a, ot for a particular channel in a hadron-nucleus (of mass number A ) collision as 0370-2693/89/$ 03.50 © Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
a~o, = aoA a,
( 1)
where ao is the corresponding hadron-nucleon cross section. Experimentally, f l ( J h g ) ~ 0 . 9 5 whereas fl(g+~tyon,) ~ 1 for (the invariant mass of the pair) Mu +0_ 1>3.5 GeV. Thus there exists a suppression of J/~g with respect to ~t+g~on, even in hA processes. (In an earlier work [4], we presented a space-time picture which, although rudimentary, quantitatively explained the origin of such a coherence.) While IAfll ~ 0.05 is certainly not enough to explain the observed suppression of J/~g in the NA38 experiment, the question naturally arises whether these numbers may naively be extrapolated to the heavy ion case. In particular, collective effects like the large temperature generated in ultrarelativistic nuclear collisions may substantially alter these numbers and in this letter we address ourselves to this very issue. The problem is admittedly a very difficult and involved one which must remain a future project; in the following we use a simplistic approach based on the model of ref. [4], which nonetheless suffices for our present purpose of demonstrating the idea only. As in ref. [4], let us start with the conventional wisdom [ 5 ] that in nuclei the quark degrees of freedom are essentially localised within regions of small volume with radius rN of about 0.5 fm, the rest of the nuclear volume being populated by mesons, etc. Taking these "little bags" as the nucleons, a resonance (whose radius is comparable to hadronic radii) should be formed not entirely within the struck nu413
Volume 218, number 4
PHYSICS LETTERS B
cleon but in the field of surrounding nucleons. The direct dileptons, on the other hand, are produced in a space-time volume 1 / M ( << typical hadronic radius). Thus there occurs an apparent decrease in the number of "effectively free" nucleons in the nuclear target for the J / ~ production process causing fl(J/~ll) to be < 1. To extend these considerations to the case where a large temperature may be generated one needs to estimate the effect of temperature on the radius o f the little bag. The radius of the bag, in zeroth approximation, is inversely proportional to the fourth root of the bag constant. One expects that with rising temperature, B should decrease, ultimately vanishing at T = Tc, the critical deconfinement temperature. Unfortunately, the variation of B with Tis to date an unsolved problem [6,7 ]. For our purpose, however, we may use the approximate result B(T)~B[1-(T/Tc)
(2)
4] ,
which then implies yN(T)~yN[I_(T/Tc)4]
--1/4
(3)
Clearly, YN becomes infinite as T ~ T~, as it should in a QGP. Then, if the total nuclear volume remains the same, increase of 7N with T implies reduced internucleonic volume (which may be extracted from the nuclear saturation property [4,8] ) and this, in turn, would result in smaller values of ft. In addition to the above, another effect has to be taken into account. I f J / ~ ' s are produced in a hot medium, the c h a r m o n i u m masses are expected to be shifted to smaller values [ 9 ]. This will result in larger radii for J / V as can be readily seen from the following semi-classical analysis. The radius of J/~¢ is extracted [4] from the usual quarkonium model assuming a linear confining and a Coulomb type potential:
U( r) =sr-otcrf/r ,
(4)
where the string tension s is a function of T, vanishing at To. The bound state radius ra o f a QQ system is found by minimising the classical energy E ( r ) = 2 m q + 1/2mqr2 + U ( r )
(5)
w.r.t, r and demanding that at r = rB, E (rB) equals the mass of the resonance. It can be trivially shown [ 2 ], in the limit o f very small c~e~ 414
2 March 1989 (6)
r B ~ (mqS) -I/3 .
Having fixed mq and s at zero temperature, one can then calculate r a ( T ) from s ( T ) . In keeping with the spirit of this work, we relate s to B through the stringlike solutions of bag models [ 10 ]: socx/B ,
(7)
so that s ( T ) ~ s [ 1 - ( T / T c ) 4 ] I/2,
(8)
whence, we have rn( T) ~rB[1
-
( T / Z c ) 4 ] -1/6.
(9)
(From (9) one would expect ra to diverge at T = To. In reality, however, charmonia may still be formed at T > Tc because of the the possibility of forming coulombic bound states [2]. In the actual calculations reported below, we therefore do not use (9) but rather utilize the solution of (5) with (8). ) We may then employ the formalism of ref. [4] to calculate f l ( J / ~ ) and fl(~t+~tUo,~) for all temperatures o f interest T~< Tc, using formulae (3), (5) and (8). For the sake of brevity, we report here only the values of fl(~t+laUon~) for M , + ~ - ---3.1 GeV, the J/~t peak. With T~ = 200 MeV the current canonical value for the critical temperature, fl(~t + ~tUont) ~ 0.99-0.985 for all T u p t o 190 MeV. fl(J/~¢), on the other hand, decreases drastically with T, as can be seen from table 1, so that I Afll keeps increasing substantially with T. As we have neglected nuclear compression these numbers reflect only the effect of temperature and are therefore very conservative in the context o f actual heavy ion collisions. They should, therefore, be considered as being only indicative. Table 1 Variation of fl(J/~) (c.f. eq. ( 1) ) with temperature T. The critical temperature T¢ is taken to be 200 MeV. See the text. T (MeV)
PO/V)
IzXPl
120 140 160 170 180 185 190
0.93 0.92 0.91 0.89 0.85 0.79 0.55
0.06 0.07 0.08 0.10 0.14 0.20 0.44
Volume 218, number 4
PHYSICS LETTERS B
AS the effective number of free nucleons in the nuclear target (for hA processes) decreases, the probability of rescattering must increase proportionally, which may result in an increase of the average transverse momenta ( ( P v ) ) in hA collisions in the following manner: (PT)hA ~ (Pv)hNA J-/~,
(10)
so for continuum ~t+~t- pairs (PT),A should not be materially different from ( P T ) h N . For J/~g, however, (PT)hA should increase by about A°°5 and in hot surroundings this increase may be expected to be much larger (vide above). Thus the qualitative picture that emerges from these considerations is that even for nuclear collisions resulting in a global temperature T < To, the production of J / ~ may be suppressed relative to the continuum, the distribution of the J / v ' s produced being skewed to higher P~ values, thus mimicking even the Pv aspect [ 11 ] of the signal suggested. It should be remarked at this stage that since our initial work [ 4] several other authors have proposed various non-plasma scenarios for J / ~ suppression in nuclear collisions [12-16 ]. All these works rely on the inelastic scattering of J/~c's in the surrounding hot hadronic matter which may lead to disintegration of J/~c's, resulting in a net depletion. Among them, the conclusion of ref. [15 ] that the measured suppression may be understood if the hadronic densities are as large as indicated by the CERN data is similar to our contention that high temperature may provide an explanation. Except for ref. [ 12 ], however, theA-dependent effects, which is the starting point of our analysis, have so far been neglected by other authors. Thus our work rests on a somewhat different philosophy - the space-time aspect of the production process. The approach ofref. [ 12 ] is akin to ours in spirit, inasmuch as these authors also start with the A-dependent results of hA data. They begin with the feature of the hA data that there exist two components of J / ~ ' s in such collision processes - the usual fl~ 0.95 for low Xv, while large Xv corresponds to fl~0.7, fl for the continuum dileptons, however, shows no appreciable dependence on XF. The authors ofref. [ 12 ] did not attempt to explain this observation but rather used these results. They concluded that in order to explain the observed suppression in the NA38 events
2 March 1989
[3 ] one needs a large fraction of the more coherent component of the J/~'s. In the context of our model, we can understand the Xv dependence of fl quite naturally. We can visualize the low-Xv J / ~ ' s as originating from the stopping of one q (or el) from the incident hadron while the bulk of the incoming momentum is carried offby the spectator partons from the projectile. In such cases there is no appreciable deposition of energy (or, in other words, no thermalisation) and the zero-temperature results of ref. [4] apply, giving f l ( J / ~ ) -0.95. On the other hand, there are also events where the incident hadron deposits all its energy in a small volume which may become thermalised (reminiscent of the "hot spot" picture in hA collisions). By momentum conservation, this "hot spot" moves with a large longitudinal momentum and i f J / t f s are formed by qCl annihilation inside these "hot spots", they would populate the large-Xv domain. In these circumstances the effective fl(J/t~) would reflect the effect of the temperature, as discussed above. So would, indeed, fl(~t+~tUon,) for the la+p. - pair at large Xv (originating from the "hot spot") except that we have already seen that fl(~t+~t - ) is remarkably insensitive to temperatures almost upto Tc. Thus one may understand why f l ( J / ~ ) is a function of Xv while fl(~t+ ~t- ) is apparently not. We are therefore inclined to interpret the conclusion of ref. [ 12] favouring a larger fraction of the more coherent component of J / ~ in AA processes as requiring high temperatures to be generated in these cases, consistent with our point of view. To summarize, we do not doubt the suppression of J / ~ ' s in a QGP. There are, however, many unsolved problems in the multiparticle production processes in nuclear collisions which must be understood before the J / ~ suppression can be made into a "telltale" signature of QGP. Within the premises of our model, nonetheless, we may safely believe in having witnessed the precursor phenomenon (larger spatial extent of quark degrees of freedom than in the ground state of normal nuclei) to the formation of Q G P and the search must continue. The authors would like to acknowledge helpful comments from the participants at the International Conference on Physics and Astrophysics of QuarkGluon Plasma (ICPA-QGP'88). February 1988, 415
Volume 218, number 4
PHYSICS LETTERS B
B o m b a y , a m o n g w h o m A. R o m a n a , F. Close, L. M c L e r r a n , A. C a p e l l a a n d E.V. S h u r y a k m u s t be especially m e n t i o n e d . R.A. S a l m e r o n d e s e r v e s o u r g r a t i t u d e for his i n t e r e s t in this p r o b l e m a n d his illuminating comments. N o t e a d d e d . A f t e r the s u b m i s s i o n o f this letter, we b e c a m e a w a r e o f r e c e n t d a t a o n ( p x ) hA for J / ~ [ 17 ] as well as kt+~t - [ 18], w h i c h c o u l d be c o m p a r e d to the p r e d i c t i o n s o f eq. ( 1 0 ) a b o v e : 2 (PT)oPt~J/v
~ 1.57
(GeV/c) 2
w h i l e ( P ' 2r ) p p ~ J / v ~ 1.23 ( G e V / c ) 2. Similarly, ( P v2) ~ - w ~ + ~ -
~ 1.59 ( G e V / c ) 2
w h i l e ( P v2) n - p ~ t + ~ t - ~ 1.44 ( G e V / c ) 2. T h e s e v a l u e s yield f l j / v ~ 0 . 9 7 a n d fl,+~_ ~ 0 . 9 9 3 which, o b v i o u s l y , are well w i t h i n a c c e p t a b l e ranges.
416
2 March 1989
References [ 1 ] See, e.g., B. Sinha and S. Raha, eds., Proc. Intern. Conf. on Physics and astrophysics of quark-gluon plasma (ICPAQGP '88) (Bombay, February 1988) (World Scientific, Singapore), to be published; Nucl. Phys. A 461 (1987) 1. [2] T. Matsui and H. Satz, Phys. Lett. B 178 (1986) 416. [3]A. Romana, in: Proc. Intern. Conf. on Physics and astrophysics of quark-gluon plasma (1CPA-QGP '88) (Bombay, February 1988), eds. B. Sinha and S. Raha (World Scientific, Singapore), to be published. [4] S. Raha and B. Sinha, Phys. Lett. B 198 (i987) 543. [5] G.E. Brown, Nucl. Phys. A 374 (1982) 630c. [6] E.V. Shuryak, Phys. Rep. 61 (1980) 71. [ 71 B. Muller and J. Rafelski, Phys. Lett. B 101 (1980) 111. [8 ] A.K. Chaudhuri, S. Raha and B. Sinha, Phys. Lett. B 208 (1988) 513. [ 9 ] T. Hashimoto, O. Miyamura, K. Hirosi and T. Kanki, Phys. Rev. Lett. 57 (1986) 2123. [ 10] K. Johnson and C.B. Thorn, Phys. Rev. D 13 (1976) 1934. [ 11 ] F. Karsch and R. Petronzio, Phys. Lett. B 193 (1987) 105. [12] A. Capella, J.A. Casado, C. Pajares, A.V. Ramallo and J. Tran Thanh Van, Phys. Lett. B 206 (1988) 354. [ 13 ] J. Ftacnik, P. Lichard and J. Pisut, Phys. Lett. B 207 ( 1988 ) 194. [ 14] C. Gerschel and J. Htifner, Phys. Lett. B 207 (1988) 253. [ 15 ] S. Gavin, M. Gyulassy and A. Jackson, Phys. Lett. B 207 (1988) 257. [ 16l R. Vogt, M. Prakash, P. Koch and T.H. Hansson, Phys. Lett. B207 (1988) 263. [ 17 ] J. Badier et al., Z. Phys. C 20 ( 1983 ) 101. [ 18] P. Bordalo et al., Phys. Lett. B 193 (1987) 373.
PHYSICS LETTERSB
2 March 1989
QUARK-GLUON PLASMA DIAGNOSTICS AND J / ~ S U P P R E S S I O N IN NUCLEAR C O L L I S I O N S Sibaji RAHA a and Bikash SINHA b Saha Institute of Nuclear Physics, 92, A.P. C, Road, Calcutta 700 009, India Variable Energy Cyclotron Centre, Bhabha Atomic Research Centre, 1/AF, Bidhan Nagar, Calcutta 700 064, India
Received 20 August 1988
The suitabilityof J/~gsuppression, observedin ultrarelativistic heavyion collisions,for detectingquark-gluonplasmais examined.
The possibility of creating a new state of matter, called the quark-gluon plasma (QGP), through ultrarelativistic heavy ion collisions seems very ripe [ 1 ], although how to decipher the presence of such a state is still an open question, there exist in the literature many plausible suggestions; nonetheless a recent idea by Matsui and Satz [2] relying on the suppression ofJ/t~ relative to the continuum dimuon spectrum in a QGP has generated tremendous interest. This is all the more so, as the results of the NA38 experiment with 200A GeV 160 beams on heavy targets do indeed show suppression in high transverse energy events [ 3 ]. Results for the 32S run are eagerly awaited and if, as is expected, the amount of J/~t suppression is found to increase, it would really be considered a strong indication for the formation of QGP. Given the momentous implications of the discovery of QGP, it is imperative to rule out all other probable (or even possible) mechanisms which may cause such a suppression. To this end, it should be remarked that even in hadron-nucleus collisions at high energy, processes were current wisdom does not expect the formation of QGP, the formation of J/tg is significantly more coherent than continuum dileptons. A phenomenologically useful way to characterize the amount of coherence in such production processes is to parameterize the total cross section a, ot for a particular channel in a hadron-nucleus (of mass number A ) collision as 0370-2693/89/$ 03.50 © Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
a~o, = aoA a,
( 1)
where ao is the corresponding hadron-nucleon cross section. Experimentally, f l ( J h g ) ~ 0 . 9 5 whereas fl(g+~tyon,) ~ 1 for (the invariant mass of the pair) Mu +0_ 1>3.5 GeV. Thus there exists a suppression of J/~g with respect to ~t+g~on, even in hA processes. (In an earlier work [4], we presented a space-time picture which, although rudimentary, quantitatively explained the origin of such a coherence.) While IAfll ~ 0.05 is certainly not enough to explain the observed suppression of J/~g in the NA38 experiment, the question naturally arises whether these numbers may naively be extrapolated to the heavy ion case. In particular, collective effects like the large temperature generated in ultrarelativistic nuclear collisions may substantially alter these numbers and in this letter we address ourselves to this very issue. The problem is admittedly a very difficult and involved one which must remain a future project; in the following we use a simplistic approach based on the model of ref. [4], which nonetheless suffices for our present purpose of demonstrating the idea only. As in ref. [4], let us start with the conventional wisdom [ 5 ] that in nuclei the quark degrees of freedom are essentially localised within regions of small volume with radius rN of about 0.5 fm, the rest of the nuclear volume being populated by mesons, etc. Taking these "little bags" as the nucleons, a resonance (whose radius is comparable to hadronic radii) should be formed not entirely within the struck nu413
Volume 218, number 4
PHYSICS LETTERS B
cleon but in the field of surrounding nucleons. The direct dileptons, on the other hand, are produced in a space-time volume 1 / M ( << typical hadronic radius). Thus there occurs an apparent decrease in the number of "effectively free" nucleons in the nuclear target for the J / ~ production process causing fl(J/~ll) to be < 1. To extend these considerations to the case where a large temperature may be generated one needs to estimate the effect of temperature on the radius o f the little bag. The radius of the bag, in zeroth approximation, is inversely proportional to the fourth root of the bag constant. One expects that with rising temperature, B should decrease, ultimately vanishing at T = Tc, the critical deconfinement temperature. Unfortunately, the variation of B with Tis to date an unsolved problem [6,7 ]. For our purpose, however, we may use the approximate result B(T)~B[1-(T/Tc)
(2)
4] ,
which then implies yN(T)~yN[I_(T/Tc)4]
--1/4
(3)
Clearly, YN becomes infinite as T ~ T~, as it should in a QGP. Then, if the total nuclear volume remains the same, increase of 7N with T implies reduced internucleonic volume (which may be extracted from the nuclear saturation property [4,8] ) and this, in turn, would result in smaller values of ft. In addition to the above, another effect has to be taken into account. I f J / ~ ' s are produced in a hot medium, the c h a r m o n i u m masses are expected to be shifted to smaller values [ 9 ]. This will result in larger radii for J / V as can be readily seen from the following semi-classical analysis. The radius of J/~¢ is extracted [4] from the usual quarkonium model assuming a linear confining and a Coulomb type potential:
U( r) =sr-otcrf/r ,
(4)
where the string tension s is a function of T, vanishing at To. The bound state radius ra o f a QQ system is found by minimising the classical energy E ( r ) = 2 m q + 1/2mqr2 + U ( r )
(5)
w.r.t, r and demanding that at r = rB, E (rB) equals the mass of the resonance. It can be trivially shown [ 2 ], in the limit o f very small c~e~ 414
2 March 1989 (6)
r B ~ (mqS) -I/3 .
Having fixed mq and s at zero temperature, one can then calculate r a ( T ) from s ( T ) . In keeping with the spirit of this work, we relate s to B through the stringlike solutions of bag models [ 10 ]: socx/B ,
(7)
so that s ( T ) ~ s [ 1 - ( T / T c ) 4 ] I/2,
(8)
whence, we have rn( T) ~rB[1
-
( T / Z c ) 4 ] -1/6.
(9)
(From (9) one would expect ra to diverge at T = To. In reality, however, charmonia may still be formed at T > Tc because of the the possibility of forming coulombic bound states [2]. In the actual calculations reported below, we therefore do not use (9) but rather utilize the solution of (5) with (8). ) We may then employ the formalism of ref. [4] to calculate f l ( J / ~ ) and fl(~t+~tUo,~) for all temperatures o f interest T~< Tc, using formulae (3), (5) and (8). For the sake of brevity, we report here only the values of fl(~t+laUon~) for M , + ~ - ---3.1 GeV, the J/~t peak. With T~ = 200 MeV the current canonical value for the critical temperature, fl(~t + ~tUont) ~ 0.99-0.985 for all T u p t o 190 MeV. fl(J/~¢), on the other hand, decreases drastically with T, as can be seen from table 1, so that I Afll keeps increasing substantially with T. As we have neglected nuclear compression these numbers reflect only the effect of temperature and are therefore very conservative in the context o f actual heavy ion collisions. They should, therefore, be considered as being only indicative. Table 1 Variation of fl(J/~) (c.f. eq. ( 1) ) with temperature T. The critical temperature T¢ is taken to be 200 MeV. See the text. T (MeV)
PO/V)
IzXPl
120 140 160 170 180 185 190
0.93 0.92 0.91 0.89 0.85 0.79 0.55
0.06 0.07 0.08 0.10 0.14 0.20 0.44
Volume 218, number 4
PHYSICS LETTERS B
AS the effective number of free nucleons in the nuclear target (for hA processes) decreases, the probability of rescattering must increase proportionally, which may result in an increase of the average transverse momenta ( ( P v ) ) in hA collisions in the following manner: (PT)hA ~ (Pv)hNA J-/~,
(10)
so for continuum ~t+~t- pairs (PT),A should not be materially different from ( P T ) h N . For J/~g, however, (PT)hA should increase by about A°°5 and in hot surroundings this increase may be expected to be much larger (vide above). Thus the qualitative picture that emerges from these considerations is that even for nuclear collisions resulting in a global temperature T < To, the production of J / ~ may be suppressed relative to the continuum, the distribution of the J / v ' s produced being skewed to higher P~ values, thus mimicking even the Pv aspect [ 11 ] of the signal suggested. It should be remarked at this stage that since our initial work [ 4] several other authors have proposed various non-plasma scenarios for J / ~ suppression in nuclear collisions [12-16 ]. All these works rely on the inelastic scattering of J/~c's in the surrounding hot hadronic matter which may lead to disintegration of J/~c's, resulting in a net depletion. Among them, the conclusion of ref. [15 ] that the measured suppression may be understood if the hadronic densities are as large as indicated by the CERN data is similar to our contention that high temperature may provide an explanation. Except for ref. [ 12 ], however, theA-dependent effects, which is the starting point of our analysis, have so far been neglected by other authors. Thus our work rests on a somewhat different philosophy - the space-time aspect of the production process. The approach ofref. [ 12 ] is akin to ours in spirit, inasmuch as these authors also start with the A-dependent results of hA data. They begin with the feature of the hA data that there exist two components of J / ~ ' s in such collision processes - the usual fl~ 0.95 for low Xv, while large Xv corresponds to fl~0.7, fl for the continuum dileptons, however, shows no appreciable dependence on XF. The authors ofref. [ 12 ] did not attempt to explain this observation but rather used these results. They concluded that in order to explain the observed suppression in the NA38 events
2 March 1989
[3 ] one needs a large fraction of the more coherent component of the J/~'s. In the context of our model, we can understand the Xv dependence of fl quite naturally. We can visualize the low-Xv J / ~ ' s as originating from the stopping of one q (or el) from the incident hadron while the bulk of the incoming momentum is carried offby the spectator partons from the projectile. In such cases there is no appreciable deposition of energy (or, in other words, no thermalisation) and the zero-temperature results of ref. [4] apply, giving f l ( J / ~ ) -0.95. On the other hand, there are also events where the incident hadron deposits all its energy in a small volume which may become thermalised (reminiscent of the "hot spot" picture in hA collisions). By momentum conservation, this "hot spot" moves with a large longitudinal momentum and i f J / t f s are formed by qCl annihilation inside these "hot spots", they would populate the large-Xv domain. In these circumstances the effective fl(J/t~) would reflect the effect of the temperature, as discussed above. So would, indeed, fl(~t+~tUon,) for the la+p. - pair at large Xv (originating from the "hot spot") except that we have already seen that fl(~t+~t - ) is remarkably insensitive to temperatures almost upto Tc. Thus one may understand why f l ( J / ~ ) is a function of Xv while fl(~t+ ~t- ) is apparently not. We are therefore inclined to interpret the conclusion of ref. [ 12] favouring a larger fraction of the more coherent component of J / ~ in AA processes as requiring high temperatures to be generated in these cases, consistent with our point of view. To summarize, we do not doubt the suppression of J / ~ ' s in a QGP. There are, however, many unsolved problems in the multiparticle production processes in nuclear collisions which must be understood before the J / ~ suppression can be made into a "telltale" signature of QGP. Within the premises of our model, nonetheless, we may safely believe in having witnessed the precursor phenomenon (larger spatial extent of quark degrees of freedom than in the ground state of normal nuclei) to the formation of Q G P and the search must continue. The authors would like to acknowledge helpful comments from the participants at the International Conference on Physics and Astrophysics of QuarkGluon Plasma (ICPA-QGP'88). February 1988, 415
Volume 218, number 4
PHYSICS LETTERS B
B o m b a y , a m o n g w h o m A. R o m a n a , F. Close, L. M c L e r r a n , A. C a p e l l a a n d E.V. S h u r y a k m u s t be especially m e n t i o n e d . R.A. S a l m e r o n d e s e r v e s o u r g r a t i t u d e for his i n t e r e s t in this p r o b l e m a n d his illuminating comments. N o t e a d d e d . A f t e r the s u b m i s s i o n o f this letter, we b e c a m e a w a r e o f r e c e n t d a t a o n ( p x ) hA for J / ~ [ 17 ] as well as kt+~t - [ 18], w h i c h c o u l d be c o m p a r e d to the p r e d i c t i o n s o f eq. ( 1 0 ) a b o v e : 2 (PT)oPt~J/v
~ 1.57
(GeV/c) 2
w h i l e ( P ' 2r ) p p ~ J / v ~ 1.23 ( G e V / c ) 2. Similarly, ( P v2) ~ - w ~ + ~ -
~ 1.59 ( G e V / c ) 2
w h i l e ( P v2) n - p ~ t + ~ t - ~ 1.44 ( G e V / c ) 2. T h e s e v a l u e s yield f l j / v ~ 0 . 9 7 a n d fl,+~_ ~ 0 . 9 9 3 which, o b v i o u s l y , are well w i t h i n a c c e p t a b l e ranges.
416
2 March 1989
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