- Email: [email protected]
φ-Enhancement in nuclear collisions
Nuclear Physics B (Proc . Suppl .) 24B (1991) 273-27iß North-Holland
-ENHANCEMENT IN NUCLEAR COLLISIONS F. GRA5SI
instituto de Fisica-Departamento de Fisica Matemâti_a, Universidade die Sào Paulo, . C.P.20516, 01498 Sào Paulo- SP, Brazil, and H . HEISELBERG
Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green St ., Urbana, IL 61801, U .S .A. The observed enhancement of the ¢l(po + w) ratio in relativistic heavy ion collisions at CERN is explain:,?A as absorption of p and w's in the hadronsc matter created in the collisions . Production of 6 vector mesons in rescattering processes is unlikely and we suggest the enhancement of the 0 to continuum ratio is an artifact of the pt cutoff applied to the data . 1. INTRODUCTION An enhanced production of strange particles (K, A, 0 = (ss) . ..) has long been advocated as a signature for quark-gluon plasma formation! . A particular way to study this effect is to measure the ratio of the vector mesons? 0/(P0 + w) . lot ultra relativistic nuclear collisions not leading to quark-gluon plasma formation this is a small number because the production of vector me-sons with hidden flavor is inhibited (OZI rule). For example, ~/po - 1/20 in pp collisions from 24 GeV to 1.5 TeV lab energy and [0/Po]p,>Wev - 1/8 in pPt collisions at 200 GeV3. Contrarely, during the hadronization of a quark-gluon plasma, ~'s can be produced copiously via the coalescence of s and s quarks and so 0l (po + w) might reach ! eral times its value in ordinary - collisions . Recent estimate4 "_.' adicate that 0l(Po + w)IQop - (6 - 10) 0/(po + w)Ipa (in an opti-
mistic ,zenario). Recently, the NA38 collaborations has studied the d and po + to production in relativistic heavy ion collisions. They detect dimuons corning from 1) resonance decays,, e.g ., 0 -o p+ jr, 2) continuum processes, e.g ., qq -+ p+ is - (Drell-Yon) and 3) . bsCkground, e.g . 7t14 -4 Pf pl'. To reduce the background : which is very important at low invariant masses, cutoffs are introduced . only moon pairs with pt > pj`t GeV and ps > pTt GeV are kept : Two different sets of cutoffs were used : . 1 =11 GeV and ptut=1 .3 GeV and P." 1 =26 GeV or e ratios 0/(po + w) these cutoffs, the GeV. With pst=19 dimuons in designates the continuum and 0/c (where c transverse .4 GeV) increase with the the mass range 1.7-2
energy, Et , while (po+w)lc remains approximatively constant. Given that higher Et's are expected to correspond to more central collisions and higher particle densities,6 these observations could signal the appearance of a quarkgluon phase. In this work, we ward to show that these enha :ïcements can also occur in ordinary hadronic matter . Koch et al . have claimed that the observed enhancemen is ca-used by vector-meson production in rescattering~ We will show that rescattering is not able to produce any significant amount of vector mesons vakth pt and ps as measured by NA38 but that absorption and high pt enhancement can explain the data . 2. THE MODEL Let us consider the change per unit time and volume of the number of vector mesons, Nv of type V = po,w, ¢. A certain number of V's are created initially in primary collisions and may be modified later by absorption or production in secondary collisions occuring in the interaction region between the rezCâiog nuclei . The change in V mesons per volume and time is given by dNv dâa
_
E(('oj_varv)Pi(X)Pj(X) tj
-E, («.v-xv)Pi(X)PV(X),
(2.1)
where the first term corresponds to the creation of vector mesons V in (secondary) collisions between particles V in i and j and the second term to the absorption of
0920-5632/91/$03.50 ©, 1991 - Elsevier Science Publishers B.V. All rights reserved .
274
F. Grass, I:. IIAiselberg/ -~~~~:ance;I~rl:6'
(secondary) collisionswith particle i. p;,.i v are the corresponding particle densities. The absorption of vector-mesons is known from pho.,' : toabsorptien experiments: Qb° , c-- 8 - 10 mb, cr 25 - 33 mb. The production cross sections are smaller, .d = 1-2 mb. Furtypically 0.1-0.4 mb and app,thernore, there is a threshold for production of the heavy vector-mesons particularly wah large transverse momenta . The production of a massive V with p, :i- 19 GeV and pe >_ 1 .1 GeV requires a large cms energy of the two colliding particles which is not available in rescattering processes since most particles are created at midrapidities (y - 3) having small relative momenta . A detailed estimate? shows that production is small compared to absortion and we will therefore neglect it in the fo0o::"ing . We shall consider the one dimensional expansion in the z-direction of the hadronic gas. It is convenient to switch to variables like the rapidity y = z log(t + z)l(t - z) and proper time r = t2 -- z2 . A peoe(r) dN/,-dyd 2 sF oc 1/r dependence is obtained when hydrodynamics apply to the one dimensional expansion of a relativistic fluid8 as well as for one-dimensional free exuansaan For simplicity we take the hadrons tQ be evenly distr;buted transversely in a region of radius - R = 1 .2Aä3, i.r ., dN/dydâ ~ (dNld~)lT1Z . From eq . (2 .1), we obtain the time de,endence ofthe number of vector mesons d v (r3) dyv (ro) (ro/r1) -dù ~~o6 .v)I+R' dy where (mob,v) is the vector meson absorption cross section times the relative velocity of the two scatterers averaged over the components of the hadronic gas and averaged over the momenta of the colliding particles. The initial time ro is the formation time of the main components (7r, p) of the hadronic gas; the heavier vector mesons should be formed earlier due to the uncertainty principle. To is generally assumed to be ti 1 fm/c but might be larger,9 ro - 3 fraic. The final time =T; when a vector meson stops scattering is when it lea%;es the interaction region, i.e., ry = Rlve where ve is thz transverse velocity. The hadronic gas nay, however, freeze-out at an earlier time since three-dimensional expansion will take place around rr ^= R/c . Are expect that for the vector mesons (,.. .) = 1 - 1.5 GeV; so the two times are not very +fferent (if c. - cb/_q) . However, given the uncertitudcs on ib, >> and the aâ b, s, we take in what follouvs, (rol7y)(°b-Olf-' _ xv to be a single unkrown f
nuclear collisions 5 â4
FIGURE 1 as function of Ee/Azl3 (eq . 2.3) for various 0/(po +w) values of xO/xpo+,, (see text). The NA38 data for 0 is shown Ly filled squares and for 5 by filled Mangles. parameter in the range 10,1] . The hadronic density dNldy will increase with centrality of the heavy ion collision and we assume as in1G a linear relationship dN/J!! - aEe . The parameter a for the O+U case, can be estimated from the O+Uli and S+VV events of NA3411 . We find (including neutrais and correcting for resonance decay") a - 1.5 GeV-1 for O+U . We can now write the 01'(ß'o + w) ratio as: No ( ,rf
(2 .2)
NP+W(rP
No (To)
JP+W(rO)
gÜ
â;
(2 .3)
that the initial production ratio NO(ro)/NW+PO(To) does not depend on Er and has the same vaiue in pp, pA or nuclear collisions . That would e.g., be the case if the production in primary collisions was a superposition of independent nucleon-nucleon collisions . Since the Nh3g data is taken at midrapidity, we expect that ab"rption in the pU dzta is negligible and that 0"po +w)(E.)h(. := coast = 1VO(ro)/ .N.+PO(To)Indeed, 0/(po +w)(Ee )Ipu is founds to be only slightly dependent on Ee . The results of eq. (2.3) for O-U and 5-U are shown together with the NA35 data in figure 1 . The theoretical curve with xolx,+,, = 1 .7 Tiffs the data for 0 and 5 reasonably but is sensitive to changes (*30 °ia in figure 1) in 1f one inserts the nucleon absorption cross sections in nuclei (o,b,v) given earlier, however reduced by a factor of 2/3 as given by the additive quark model isecause the absorption is predominantly We
assume
F. Grossi, it . lfeiselberg/l~-enhancement in nuclear collisions
275
absorption)
Nv _ Nr exp[(llpu - R(Et))(rni`e - m)] . R% NPu
FIGURE 2 Ratio Qi/c as a function of Et/Ax/ 3 (eq. 3.1) for xo (or Oa6s ti 0) . on mesons, this corresponds to rjr/ib = 2 - 3, which lies within the uncertainty of the estirnatesobtained with To= 1-3 fm/c and vp = R/c, ti 4-6 fm/c as discwscd above, 3.
EFFECTS OF LARGE p,-ENHANCEMENT
If ;rector mesons are not produced in secondary collisions but only absorbed, one would expect that the ratio of vector mesons with respect to the continuum de creases as Et increases because a hadronic gas of higher density is produced, leading to stronger absorption . This is not what was found by NA38 and we will show that this may be connected to the Cronin eFeet kenhancement of particle production at large p, as the target size A in VA colfisions or Et ?n nuclear collisions increases) and the fact that a cut in transverse momentum is applied to the data . Vice parametrize the pi-distribution as dN/dp, oc exp(-Pra t), where rn, is the transverse mass
of the particle with mass m. This seems to be a form that fits the pt -distributions well for most mesons at 200 i GeV lab energy (see e.g . 12 for s, 13 for O's, 10 for the J/q+'s) . with 0 t, 5.5 GeV -1 . The slope parameter R doos, however, decrease slightly with increzsing A in pA collisions or F, in nuclear collisions . Hence the measured ratio Nv%N, with a p, cutoff is a factor ti exp(-D(Et)(mÉ°°- ire)) smaller than the ratio without cutoff . Assuming the latter :o be the same as in pU collisions -ind :hat #(B, = 0) - pxu we obtain (not including
(3.1)
WA8012 measures the p, slopes for aro and {rinds a decrease of the slope R or an increase of the "temperature' T= 1/S with centrality frorn app=:r.atc!y 100 MeV to 220 MeV; this corresponds to a decrease in ß by aQ = Q(Et = 0) - p(E,az) = 0.8 going from peripheral to central collisions . In the same way; for the J%*, NA38 findl' that (p,) increases with E, from - 2 Gw to , 1.2 -10.05 GeV; since A = rr,r ; 2 % pt >z for heavy particles, this gives 0,0 - 1.5 f 0.25 GeV- ' . With L.ß - 1 - 2,GeV -1 . The V/c ratio of eq . 3.1 is thus enhanced by a factor -1 .5-3 .5 when going from peripheral to central collisions . As seen in figure 2 this estimate of the enhancement is in agreement will. the h!A38 data for 0/c for which absorption is small. The côserved (pa + w)lc ratio however is almost constant as seen in figure ct because absorption is significant. Including absorption we find from eqs. 2 .3 and 3.1 .pu INr:Fr," iw
ro r1
n
We parametrize Q(Et) from data on J/4F for which if =" m;ra/2(pt) z . We take (pt) lyu as (pt)Ippçw GeV/c15 and get Onu - 5 GeV_ t . Moreover, froml 4 eve have the following parametrization (p,)~~~cty - t GeV +0.003Et from which we extract Q(Et) . Though these numbers are taken from data on the J/0 they apply approximately to lighter mesons as well as discussed above. The results of eq . (3 .2) and the experimental points for rß mesons are shown in fig.2 and thosefor po+w in fig .3 . (We have assumed the same p(&/A2/3 ) dependence for 0-U and 5-U collisions lacking knowledge of %s000w) . For 0/c, the simplest assumption . i.e. to (pt s-u neglect absorption (xA = i) fits the data reasonably for 0 with no free parameters ; note that no strangeness enhancemert is needed . The fit is not as good for S; this could be because our relation fnr t;( F.', l A`i°) coo; dc .-Vied from 0 data and assumed to be the same for S as well . For (po -t-s.:)/c. the theoretical cüive with xPo+,. = iï .F fits reasonably the 0 and S data . This is consistent with our earlier results since the data for 0/(po + w) were fitted with xd/x,+. -1 .7 and thosefor 0 over continuum by x# - 1 . Therefore data for (po + w) oves continuum
F. Grassi, H. Heiselberg/O-enhancement in nuclear collisions
276
REFERENCES 1. P. Koch, 8. Müller, and J. Rafelski. Phys . Rep. 142 (1986)1 . 2. A. Shor . Phys. Rev. Lett .54 (1985)1122 : 3. J. Badier et al . Phys. Lett . 122B (1983) 441 . 4. P. Koch, U. Heinz, and J. Pild-t . Phys. Lett . B243 (1990) 149 ; Z .Ph,s .C 47 (1990) 477. 5. J. P. Guillaud et al . (NA38), Nucl . Phys. A525 (1990) 449c .
oU_ -
. ZI . . .
4 Et
À2/3
13
10
FIGURE 3 Ratio (po + w)lc as a function of Et /A2'3 (eq. 3.2) for varices values of should he reproduced by $,+,, = 1/1 .7 - 0.6 . 4. SUNAMÀkY The absorptior, i: nuclear matter (which decreases .N~,, with Et) and the pt cutoff (whi,..h increases N~ and with Et) may explain the NA38 data . No strangeness eahânce~mcnt is needed ; on the contrary we vxpo .t that the creation of high pt mesons at midrapidity in secondary collisions is rare_ ACKNOWLEDGEMENTS This work was supported by F.A.P .E .S .H . in Brazil and NSF grant PHY89-21025.
6. G. Baym, G. Friedman, and H . Heiselberg . HiPAGS Proc . of "Workshop on heavy ion physics°, Brookhaven, March 5-7, 1990, ed . 0. Hansen ., p. 102. 7. F. Grassi and H . Heiselberg . Univ . of Illinois, P-915-61 ; to appear in Phys . Lett . B. 8. .i . D. Bjorken. Phys. Rev. D27 (1983) 140. 9. T. Csörg6, J. Zimi'rlyi, J. Bondorf, and H. Heisel berg . Phys . Lett . B222 (1989) 115. 10 . 5 . Gavin and M, . Gyulassy. Phys . Lett . 8214 (1988) 241; S. Gavin, M . Gyulassy and A. Jackson, Phys . Lett . B207 (1988) 257.
11 . J. Schukraft et al . r ;~ s~iass), Z. Phys. +08 (1988j 59 ; Nuci . Phys . A498 (,~989) 403c ; Nucl . Phys . B353 ' (1991)1. 12 . R. Santo et a!_ (WA80), Nucl . Phys . A498 (1989) 391c . 13 . C. Daum et al . Nucl . Phys . B186 (1981) 205 .
14 . M . C. Abreu et al . (WA38) Z. Phys . C. 38 (,ï988) 11' - Nucl . Phys. A498 (1989) 249c. 15 . J. Bi.rlldr et zl . Z . Phys C 20 (1983)101.
-ENHANCEMENT IN NUCLEAR COLLISIONS F. GRA5SI
instituto de Fisica-Departamento de Fisica Matemâti_a, Universidade die Sào Paulo, . C.P.20516, 01498 Sào Paulo- SP, Brazil, and H . HEISELBERG
Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green St ., Urbana, IL 61801, U .S .A. The observed enhancement of the ¢l(po + w) ratio in relativistic heavy ion collisions at CERN is explain:,?A as absorption of p and w's in the hadronsc matter created in the collisions . Production of 6 vector mesons in rescattering processes is unlikely and we suggest the enhancement of the 0 to continuum ratio is an artifact of the pt cutoff applied to the data . 1. INTRODUCTION An enhanced production of strange particles (K, A, 0 = (ss) . ..) has long been advocated as a signature for quark-gluon plasma formation! . A particular way to study this effect is to measure the ratio of the vector mesons? 0/(P0 + w) . lot ultra relativistic nuclear collisions not leading to quark-gluon plasma formation this is a small number because the production of vector me-sons with hidden flavor is inhibited (OZI rule). For example, ~/po - 1/20 in pp collisions from 24 GeV to 1.5 TeV lab energy and [0/Po]p,>Wev - 1/8 in pPt collisions at 200 GeV3. Contrarely, during the hadronization of a quark-gluon plasma, ~'s can be produced copiously via the coalescence of s and s quarks and so 0l (po + w) might reach ! eral times its value in ordinary - collisions . Recent estimate4 "_.' adicate that 0l(Po + w)IQop - (6 - 10) 0/(po + w)Ipa (in an opti-
mistic ,zenario). Recently, the NA38 collaborations has studied the d and po + to production in relativistic heavy ion collisions. They detect dimuons corning from 1) resonance decays,, e.g ., 0 -o p+ jr, 2) continuum processes, e.g ., qq -+ p+ is - (Drell-Yon) and 3) . bsCkground, e.g . 7t14 -4 Pf pl'. To reduce the background : which is very important at low invariant masses, cutoffs are introduced . only moon pairs with pt > pj`t GeV and ps > pTt GeV are kept : Two different sets of cutoffs were used : . 1 =11 GeV and ptut=1 .3 GeV and P." 1 =26 GeV or e ratios 0/(po + w) these cutoffs, the GeV. With pst=19 dimuons in designates the continuum and 0/c (where c transverse .4 GeV) increase with the the mass range 1.7-2
energy, Et , while (po+w)lc remains approximatively constant. Given that higher Et's are expected to correspond to more central collisions and higher particle densities,6 these observations could signal the appearance of a quarkgluon phase. In this work, we ward to show that these enha :ïcements can also occur in ordinary hadronic matter . Koch et al . have claimed that the observed enhancemen is ca-used by vector-meson production in rescattering~ We will show that rescattering is not able to produce any significant amount of vector mesons vakth pt and ps as measured by NA38 but that absorption and high pt enhancement can explain the data . 2. THE MODEL Let us consider the change per unit time and volume of the number of vector mesons, Nv of type V = po,w, ¢. A certain number of V's are created initially in primary collisions and may be modified later by absorption or production in secondary collisions occuring in the interaction region between the rezCâiog nuclei . The change in V mesons per volume and time is given by dNv dâa
_
E(('oj_varv)Pi(X)Pj(X) tj
-E, («.v-xv)Pi(X)PV(X),
(2.1)
where the first term corresponds to the creation of vector mesons V in (secondary) collisions between particles V in i and j and the second term to the absorption of
0920-5632/91/$03.50 ©, 1991 - Elsevier Science Publishers B.V. All rights reserved .
274
F. Grass, I:. IIAiselberg/ -~~~~:ance;I~rl:6'
(secondary) collisionswith particle i. p;,.i v are the corresponding particle densities. The absorption of vector-mesons is known from pho.,' : toabsorptien experiments: Qb° , c-- 8 - 10 mb, cr 25 - 33 mb. The production cross sections are smaller, .d = 1-2 mb. Furtypically 0.1-0.4 mb and app,thernore, there is a threshold for production of the heavy vector-mesons particularly wah large transverse momenta . The production of a massive V with p, :i- 19 GeV and pe >_ 1 .1 GeV requires a large cms energy of the two colliding particles which is not available in rescattering processes since most particles are created at midrapidities (y - 3) having small relative momenta . A detailed estimate? shows that production is small compared to absortion and we will therefore neglect it in the fo0o::"ing . We shall consider the one dimensional expansion in the z-direction of the hadronic gas. It is convenient to switch to variables like the rapidity y = z log(t + z)l(t - z) and proper time r = t2 -- z2 . A peoe(r) dN/,-dyd 2 sF oc 1/r dependence is obtained when hydrodynamics apply to the one dimensional expansion of a relativistic fluid8 as well as for one-dimensional free exuansaan For simplicity we take the hadrons tQ be evenly distr;buted transversely in a region of radius - R = 1 .2Aä3, i.r ., dN/dydâ ~ (dNld~)lT1Z . From eq . (2 .1), we obtain the time de,endence ofthe number of vector mesons d v (r3) dyv (ro) (ro/r1) -dù ~~o6 .v)I+R' dy where (mob,v) is the vector meson absorption cross section times the relative velocity of the two scatterers averaged over the components of the hadronic gas and averaged over the momenta of the colliding particles. The initial time ro is the formation time of the main components (7r, p) of the hadronic gas; the heavier vector mesons should be formed earlier due to the uncertainty principle. To is generally assumed to be ti 1 fm/c but might be larger,9 ro - 3 fraic. The final time =T; when a vector meson stops scattering is when it lea%;es the interaction region, i.e., ry = Rlve where ve is thz transverse velocity. The hadronic gas nay, however, freeze-out at an earlier time since three-dimensional expansion will take place around rr ^= R/c . Are expect that for the vector mesons (,.. .) = 1 - 1.5 GeV; so the two times are not very +fferent (if c. - cb/_q) . However, given the uncertitudcs on ib, >> and the aâ b, s, we take in what follouvs, (rol7y)(°b-Olf-' _ xv to be a single unkrown f
nuclear collisions 5 â4
FIGURE 1 as function of Ee/Azl3 (eq . 2.3) for various 0/(po +w) values of xO/xpo+,, (see text). The NA38 data for 0 is shown Ly filled squares and for 5 by filled Mangles. parameter in the range 10,1] . The hadronic density dNldy will increase with centrality of the heavy ion collision and we assume as in1G a linear relationship dN/J!! - aEe . The parameter a for the O+U case, can be estimated from the O+Uli and S+VV events of NA3411 . We find (including neutrais and correcting for resonance decay") a - 1.5 GeV-1 for O+U . We can now write the 01'(ß'o + w) ratio as: No ( ,rf
(2 .2)
NP+W(rP
No (To)
JP+W(rO)
gÜ
â;
(2 .3)
that the initial production ratio NO(ro)/NW+PO(To) does not depend on Er and has the same vaiue in pp, pA or nuclear collisions . That would e.g., be the case if the production in primary collisions was a superposition of independent nucleon-nucleon collisions . Since the Nh3g data is taken at midrapidity, we expect that ab"rption in the pU dzta is negligible and that 0"po +w)(E.)h(. := coast = 1VO(ro)/ .N.+PO(To)Indeed, 0/(po +w)(Ee )Ipu is founds to be only slightly dependent on Ee . The results of eq. (2.3) for O-U and 5-U are shown together with the NA35 data in figure 1 . The theoretical curve with xolx,+,, = 1 .7 Tiffs the data for 0 and 5 reasonably but is sensitive to changes (*30 °ia in figure 1) in 1f one inserts the nucleon absorption cross sections in nuclei (o,b,v) given earlier, however reduced by a factor of 2/3 as given by the additive quark model isecause the absorption is predominantly We
assume
F. Grossi, it . lfeiselberg/l~-enhancement in nuclear collisions
275
absorption)
Nv _ Nr exp[(llpu - R(Et))(rni`e - m)] . R% NPu
FIGURE 2 Ratio Qi/c as a function of Et/Ax/ 3 (eq. 3.1) for xo (or Oa6s ti 0) . on mesons, this corresponds to rjr/ib = 2 - 3, which lies within the uncertainty of the estirnatesobtained with To= 1-3 fm/c and vp = R/c, ti 4-6 fm/c as discwscd above, 3.
EFFECTS OF LARGE p,-ENHANCEMENT
If ;rector mesons are not produced in secondary collisions but only absorbed, one would expect that the ratio of vector mesons with respect to the continuum de creases as Et increases because a hadronic gas of higher density is produced, leading to stronger absorption . This is not what was found by NA38 and we will show that this may be connected to the Cronin eFeet kenhancement of particle production at large p, as the target size A in VA colfisions or Et ?n nuclear collisions increases) and the fact that a cut in transverse momentum is applied to the data . Vice parametrize the pi-distribution as dN/dp, oc exp(-Pra t), where rn, is the transverse mass
of the particle with mass m. This seems to be a form that fits the pt -distributions well for most mesons at 200 i GeV lab energy (see e.g . 12 for s, 13 for O's, 10 for the J/q+'s) . with 0 t, 5.5 GeV -1 . The slope parameter R doos, however, decrease slightly with increzsing A in pA collisions or F, in nuclear collisions . Hence the measured ratio Nv%N, with a p, cutoff is a factor ti exp(-D(Et)(mÉ°°- ire)) smaller than the ratio without cutoff . Assuming the latter :o be the same as in pU collisions -ind :hat #(B, = 0) - pxu we obtain (not including
(3.1)
WA8012 measures the p, slopes for aro and {rinds a decrease of the slope R or an increase of the "temperature' T= 1/S with centrality frorn app=:r.atc!y 100 MeV to 220 MeV; this corresponds to a decrease in ß by aQ = Q(Et = 0) - p(E,az) = 0.8 going from peripheral to central collisions . In the same way; for the J%*, NA38 findl' that (p,) increases with E, from - 2 Gw to , 1.2 -10.05 GeV; since A = rr,r ; 2 % pt >z for heavy particles, this gives 0,0 - 1.5 f 0.25 GeV- ' . With L.ß - 1 - 2,GeV -1 . The V/c ratio of eq . 3.1 is thus enhanced by a factor -1 .5-3 .5 when going from peripheral to central collisions . As seen in figure 2 this estimate of the enhancement is in agreement will. the h!A38 data for 0/c for which absorption is small. The côserved (pa + w)lc ratio however is almost constant as seen in figure ct because absorption is significant. Including absorption we find from eqs. 2 .3 and 3.1 .pu INr:Fr," iw
ro r1
n
We parametrize Q(Et) from data on J/4F for which if =" m;ra/2(pt) z . We take (pt) lyu as (pt)Ippçw GeV/c15 and get Onu - 5 GeV_ t . Moreover, froml 4 eve have the following parametrization (p,)~~~cty - t GeV +0.003Et from which we extract Q(Et) . Though these numbers are taken from data on the J/0 they apply approximately to lighter mesons as well as discussed above. The results of eq . (3 .2) and the experimental points for rß mesons are shown in fig.2 and thosefor po+w in fig .3 . (We have assumed the same p(&/A2/3 ) dependence for 0-U and 5-U collisions lacking knowledge of %s000w) . For 0/c, the simplest assumption . i.e. to (pt s-u neglect absorption (xA = i) fits the data reasonably for 0 with no free parameters ; note that no strangeness enhancemert is needed . The fit is not as good for S; this could be because our relation fnr t;( F.', l A`i°) coo; dc .-Vied from 0 data and assumed to be the same for S as well . For (po -t-s.:)/c. the theoretical cüive with xPo+,. = iï .F fits reasonably the 0 and S data . This is consistent with our earlier results since the data for 0/(po + w) were fitted with xd/x,+. -1 .7 and thosefor 0 over continuum by x# - 1 . Therefore data for (po + w) oves continuum
F. Grassi, H. Heiselberg/O-enhancement in nuclear collisions
276
REFERENCES 1. P. Koch, 8. Müller, and J. Rafelski. Phys . Rep. 142 (1986)1 . 2. A. Shor . Phys. Rev. Lett .54 (1985)1122 : 3. J. Badier et al . Phys. Lett . 122B (1983) 441 . 4. P. Koch, U. Heinz, and J. Pild-t . Phys. Lett . B243 (1990) 149 ; Z .Ph,s .C 47 (1990) 477. 5. J. P. Guillaud et al . (NA38), Nucl . Phys. A525 (1990) 449c .
oU_ -
. ZI . . .
4 Et
À2/3
13
10
FIGURE 3 Ratio (po + w)lc as a function of Et /A2'3 (eq. 3.2) for varices values of should he reproduced by $,+,, = 1/1 .7 - 0.6 . 4. SUNAMÀkY The absorptior, i: nuclear matter (which decreases .N~,, with Et) and the pt cutoff (whi,..h increases N~ and with Et) may explain the NA38 data . No strangeness eahânce~mcnt is needed ; on the contrary we vxpo .t that the creation of high pt mesons at midrapidity in secondary collisions is rare_ ACKNOWLEDGEMENTS This work was supported by F.A.P .E .S .H . in Brazil and NSF grant PHY89-21025.
6. G. Baym, G. Friedman, and H . Heiselberg . HiPAGS Proc . of "Workshop on heavy ion physics°, Brookhaven, March 5-7, 1990, ed . 0. Hansen ., p. 102. 7. F. Grassi and H . Heiselberg . Univ . of Illinois, P-915-61 ; to appear in Phys . Lett . B. 8. .i . D. Bjorken. Phys. Rev. D27 (1983) 140. 9. T. Csörg6, J. Zimi'rlyi, J. Bondorf, and H. Heisel berg . Phys . Lett . B222 (1989) 115. 10 . 5 . Gavin and M, . Gyulassy. Phys . Lett . 8214 (1988) 241; S. Gavin, M . Gyulassy and A. Jackson, Phys . Lett . B207 (1988) 257.
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