We present a mechanism for the separation of strangeness from antistrangeness in the deconfinement transition. For a net strangeness of zero in the total system, the population of s quarks is greatly enriched in the quark-gluon plasma, while the s¯ quarks drift into the hadronic phase. This separation could result in ‘‘strangelet’’ formation, i.e., metastable blobs of strange-quark matter, which could serve as a unique signature for quark-gluon plasma formation in heavy-ion collisions. PACS: 25.70.Np, 12.38.M

Greiner, Carsten

Koch, Peter

Stöcker, Horst

English

Hochschulschriftenserver - Universität Frankfurt am Main

PHYSICAL REVIEW LETTERS Separation of Strangeness from Antistrangeness in  the Phase Transition from Quark to Hadron Matter:  Possible Formation of Strange Quark Matter in Heavy-Ion Collisions Carsten Greiner, Peter Koch, and Horst Stöcker Insrirut für  Theoretische Ph.r.rik,  Johann Wolfgang Goethe Unic.ersität, 0-6000  Frankfurt um  Main, West Germanj (Received 10  November 1986; revised manuscript received 25 March 1987) We present  a mechanism  for the separation of  strangeness from antistrangeness in the deconfinement transition.  For  a  net  strangeness of  Zero  in  the total  system, the population  of  s  quarks is greatly en- riched  in the  quark-gluon  plasma,  while  the  .F  quarks drift  into the  hadronic  phase.  This separation could result  in  "strangelet"  formation, i.e., metastable blobs of  strange-quark matter, which could serve as a unique signature for quark-gluon plasma formation in  heavy-ion collisions. PACS nurnbers:  25 70.Np, 12.38.Mh It  has recently been  proposed  that quark matter with finite net strangeness might be a meta~table'.~  or even an absolutely  stable3x4 state of  strongly  interacting matter at finite chemical potential and Zero temperature.  Such "strangelets,"  i.e., blobs of multistrange quark matter, if detected, would most probably be the only form of quark matter not subject to rapid decay.  3.4 On  the  other  hand,  it  was  also  shown  that  equal amounts  of  strange  and  antistrange quarks  are abun- dantly  produced  in  a  hot  quark-gluon  plasma  (QGP), created, e.g.,  in  the  early  Universe  or  in  high-energy heavy-ion collisions.  The strangeness saturates the phase space  in  a  baryon-rich  environment  after a  very  short equilibration time, t =  10 -'*  sec, which may actually be shorter than  the duration of  a  nuclear  co~lision.~-'  Of Course, in  heavy-ion  collisions the net strangeness of the QGP is  Zero  from  the onset.  Up to date, therefore all model  calculations (see,  for example, the work  of  Lee, Rhoades-Brown, and ~einz')  for the confinement phase transition  from  the  QGP into  the  gas  of  nonstrange, strange,  and  antistrange  hadrons  (HG) have  assumed that  the net  strangeness is  equal to Zero  in  each phase separately. However, in  the following we demonstrate that during the phase transition  there is a building up of a large an- tistrangeness  content  in  the  hadron  matter  while  the quark-gluon  plasrna  retains  a  large  net  strangeness excess-although  the  net  strangeness of  the combined QGP and  HG is  equal  to  Zero.  This  separation  will occur  only  when  the  system  carries  a  net  positive  (or negative) baryon number. Hence we  propose a  viable mechanism  for strangelet formation  in  initially  nonstrange  matter.  Such  nearly neutral  objects  would  be  most  fascinating  to  study. Strangelets-if  produced-  would  serve as a unique sig- nature for the formation of a QGP. The present approach relies on the ass~m~tion~-~~  that the relaxation times for chemical transmutations as well as the hadronization time are small compared to the life- time of  the mixed  phase in  nuclear collisions.  This as- sumption is supported by recent cal~ulations.~-'  Accord- ing to these studies617  the duration of  the phase transi- tion  is greatly enhanced by  the conservation of  the total entropy.  11,133'4 Thus, entropy  conservation  is  the first  constraint  for the  transition  process,  i.e.,  aV =  aQGpVQcp  +  D~~~V~~~. t-Iere  a  and  V  are the entropy densities and volumes of the  different  phases.  The  total  volume  is  given  by V =  VQGp  + Vhad The deconfinement  phase  transition  between  a  large number  of  mesons  and  baryon  resonances  and  nearly massless  quarks  and  gluons  is  taken  to  be  of  first  or- We have  assumed  isospin  symmetry, i.e.,  the chemical  potential  pUp  =pdOwn  =pq  =p  B/3.  The  Gibbs equilibrium  between  the two  phases  is  given  by  TQüp =  Thad  (thermal equilibrium), PqGP  =  Phad (mechanical equilibrium),  p&p  and  pQGP  =piad  (chemical equilibrium); p,  is  the chemical  potential  for  strange- ness,  which  controls  the strangeness content.  We em- phasize the significance of the last condition:  In a Gibbs phase equilibrium the chemical potentials  are continu- ous across the phase boundary whereas the correspond- ing densities are discorztinuous  (this has been discarded in Ref. 8). The requirement of total strangeness and baryon num- ber conservation yields two additional constraints Here the p,'s are the densities for the strange and non- strange quarks (i =s,S,q,q), kaons  (i  =K,K),  hyperons (i =  Y, F),  and nucleons and their resonances  (i =N,N), which, in  Boltzmann approximation for the strange par- ticles, are given by Only kaons and hyperons with strangeness s = 1  1  are taken  into  account  here.  We  estimate  the  effect  of heavier strange hyperons, using  Eq. (21, and find  nJnY @ 1987 The American Physical Society  1825 VOLCME  58,  NC.MBER  18  PHYSICAL REVIEW LETTERS  4 MA~  1987 =. 0.05-0.1  and nn/nv =: 0.005-0.001  for p,,  T in the hundred-megaelectronvolt region. The flavor composition of  strange hadrons and quarks > ields P~,iy  =  vq  PS, -+?  +  py.y- -  -Pq  -PJ?  (3) Ps,s  =  PS. Let us point out again that in the present approach the net  strangeness in  each separate phase  need  not vanish, although Smmi=0. On the contrary, we emphasize that this  would  be  inconsistent  with  the  Gibbs equilibrium conditions. The influence of  the strange particles on the equation of  state of  both phases and on the location of  the phase transition  is smallR  and is therefore neglected in  the fol- lowing.  We employ the bag model for the quark-gluon plasma and use a thermal gas of hadrons for the confined n~atter.~-'~  Interactions are neglected, i.e.,  u, =O.  The phase transition curves of  Refs.  11 and 12, which include a  large  number of  nonstrange mesons and baryons, are eniployed to study the evolution of the strangeness in  the present work. Baryon  number  and  entropy  conservation  force  the system to expand along the critical curve (T,p) by  con- verting plasma volume into hadron gas volume."  For a given  entropy and baryon  number, the temperature and the  baryochemical  potential  specify  the  volumes  occu- pied by the two phases.  I'  The strange chemical potential 11, needs to be specified in  addition to ensure  =0. Strangeness conservation leads to the following expres- 1  sion where  W,  =(rni/~)2~z(rni/~).  If  the hadron  phase  is eliminated  (Vhad=O) the  well-known  result5 p, =O  is recovered:  s and  S quarks are produced  in  pairs only. On the other hand, for vanishing QGP (VQGP=O) Zero net  strangeness leads to a  nonzero value of  the strange chemical  potential,5  p,#0:  Different  strange-particle production modes show up in the dorninance of  the asso- ciated production over the direct pair production at finite baryon density. During the coexistence of the QGP and HG, an addi- tional channel opens up for the strangeness:  Besides the associated production  and pair production  in  the hadron gas it is possible to have, for example, associated produc- tion  of a K meson  in  the sector of the hadron phase and the  s  quark  staying  in  the  QGP.  Consequently,  the strange quarks in  the plasma phase do acquire a chemi- cal potential p,  different from 0.  This leads to a ratio of s to F  quarks larger than  1  in  the QGP and to a dimin- ished  hyperon  abundance in  the hadronic  sector.  This phenomena  only  occurs  for  finite  net-baryon  densities, PB.  pBf 0.  For p,  =O,  i.e., vanishing net-baryon density, the transition  is  also completely  symmetric  for strange particles and antiparticles, i.e., p, =0 and s/F= I.  This is  shown in  Fig.  1  for temperatures and baryochemical potentials along the phase boundary of  Refs.  11 and 12 with  use of  different values of  the bag constant and of strange-quark mass. Observe  that  in  Fig.  I  (a), where  the  original  MIT bag-model constant is  used, s/S exceeds 10 for p~ =  150 MeV. Figure  I (b) shows the analogous result  obtained with a larger bag constant, BLf4=210  MeV.  Note that the ratio does not exceed 3 for this Parameter set.  Also shown is  the path that the system must take in  an isen- tropic expansion with o/A =  10.  We have used the isen- tropic  expansion  scenario"  based  on  the  simple  one- dimensional  model of  BjorkenI5 to simulate the dynam- I ics of the transition:  This treatment makes use of the as- sumption that the expanding quark-gluon plasma under- goes a  phase transition  at constant entropy and baryon number and, consequently,  constant o/A.  Thus we  get an impression of  the time dependence of  the process dis- cussed above.  Figure  l(c) shows the fraction of  strange quarks to all quarks present in the QGP as a function of pq. The same bag-model Parameters as in  Fig.  l (b) are used.  Note that f,  can exceed 0.5.  The path of an isen- tropic expansion with o/A is also demonstrated.  Figure 2 shows the time dependence of  the s/F ratio and of the fraction  of  strangeness  for  the  isentropic  expansion scenario shown in the previous figures.  Of special impor- tance is the fact that the accumulation of .r  quarks in the plasma phase grows with decreasing plasma volume (the fraction  K,  introduced  in  these figures, denotes the frac- tion rhe hadron gas volume occupies compared to the to- tal volume).  This opens up the possibility that s quarks may be bound not only in  hyperons and strange mesons: They could form strange quark clusters which  might be metastable objects. For small temperatures and  large ,U,,  the ratio p,/p, becomes  very  large even  for small  K,  although  the net strangeness  fraction  given  by f,  =(P,  -P~)/PB.~GP  be- comes very  small.  The ratio f, gives  the net  strange- quark  concentration  in  the  separating  quark  droplets. For K= 1 values of 0.85 for f, can be reached, i.e., about one strange quark per baryon number.  Rapid expansion can  therefore  result  in  the  formation  of  droplets  of strange-quark matter, which might be metastable. The  possibility  of  separating  strange  quarks  from antistrange quarks in  the QGP-HG transition  can  lead -towards  the late stage of  the phase transition-to  a tremendous enrichment of strange quarks in the QGP. A  fully  dynamical  scenario  of  the  phase  transition VOLUME  58,  NUMBER  18  PHYSICAL REVIEW LETTERS  4 MAY  1987 f, ' 0.4 - B"&  =  210 MeV m,  5  150 MeV CIA =  10  PS 0.3 -  PS -  3 FIG.  2.  The time  dependence  of  the  s/F ratio  and  of  the fraction  of  strangeness  for  the  isentropic-expansion  Scenario deinonstrated  in  the previous  figures.  Note  that the strange- ness  excess  becomes  largest  towards the  late  stage of  the ex- pansion.  Rapid expansion can therefore result in the forrnation of  droplets of  strange-quark matter, which  might  be  metasta- ble. B''~  =  210 MeV m,  =  150 MeV n-iust, in  addition to the equilibrium expansion  used  in Refs. 5-7,  include the following:  In the hadronic sector of  the mixed  phases the K +  are enriched  and the hy- perons  are  suppressed.  The mesons  are rnuch  lighter than the nucleons and their resonances, their velocity  is correspondingly higher, so the rapidly emitted particles, which also cool the system, are mainly the mesons.  They carry away entropy, energy, and antistrangeness.  There- fore, the whole system is being charged up with strange- ness,  and  this,  in  turn  also  enlarges  the  fraction  of strangeness in  the remaining quark droplets.  Because of this additional increase of the strangeness fraction f„  the quark droplets may have a lower energy per baryon than the hadronic phase.  This is  due to the lowering of  the Fermi  energy  by  the  increased  number  of  degrees  of freedom.  Now  in  an  isentropic  expansion  the  system FIG.  1.  The ratio of  strange to antistrange quarks in  the QGP as a function of the critical baryochemical potential along the  phase  transition. i.e., for  a continuously  varying tempera- ture.  Observe that in  (a), where the original  MIT bag-model constant  is  used,  s/F exceeds  10 for  PB =  150 MeV.  (b) The analogous  result  obtained  with  a  larger  bag  constant, B'I4=210 MeV.  Also  regarded  is  the path  which  the system must take in an isentropic expansion with  o/A  =10.  Note that the  ratio  does  not  exceed  3  for  this  Parameter Set.  (C) The fraction  of  strange quarks to all quarks present  in  the QGP as a function  of  PB.  The Same  bag-model  Parameters as in  (b) are used.  Note  that f,  can exceed  0.5.  The path  of  an isen- tropic expansion with o/A is also shown. VOLCPIIE  58,  NUMBER  18  PHYSICAL REVIEW LETTERS  4 MAI. 1987 TABLE I.  Energy density per baryon in the ground state for  timate of  the production  rate of  superstrange nuclei  we strange-quark matter at temperature  Zero for a given strange-  would  like  to refer  to the work  of  Kerrnan  and  Weiss. ness fraction f„  and a certain  bag constant and strange-quark  and Liu and Shaw.  l6 mass.  Note that we have used  U,  =O.  In the last row one finds  Additional  (nonstrange  and  strange)  mesons  and an estimate of  the corresponding hjperon mass with the above  baryon resonances should be  included  into the strangeness  fraction.  The underlined  numbers indicate  stable  The  factors for these  particles  can strange-quark matter with  respect  to strong decay towards the  make for  large contributions at the energy  densities of hadronic hyperon matter.  interest.  We would like to emphasize, though. that while 1;  0.1  0.3  0.5  0.7  1  our quantitative results may change. the qualitative con- B 114  ni T  clusions remain valid.  To improve the model, we will  in- (MeV)  (M~v)\ moves towards the energetically most favorable position, which, as was found at Zero temperature in Refs.  1-3, is the strangelet.  In Table I  we show the result for several values of  bag  constants.  Here the ground-state energy per baryon of  the quark matter with a given strangeness fraction  is  compared  to a simple estimate of  the corre- sponding  mass of  hadronic hyperon  matter.  Note, that for the original MIT bag constant quark matter is stable for all values of f,.  For the higher values B 'I4 =  160 and 180 ,MeV.  respectively.  only  quark matter with the net strangeness fraction f,  > 0.5 and f,  > 1, respectively,  is lower  in  energy per  baryon  than  the corresponding ha- dronic matter.  Therefore, once strangeness is built up in the plasma, it can stay in the quark phase.  Then it has a chance of  cooling down to form metastable cold droplets of strange-quark matter, which can only decay via weak interactions.  For  large  values  of  B 'I4 > 200  MeV, strange-quark matter  is  not  stable.  Indeed,  for  much larger bag constants, B 'I4 > 235  MeV, the strangeness separation mechanism proposed  here does not work, be- cause  associated  production  would  favor  the  hadronic hqperon matter state and thus strangeness would  be en- riched in the hadron side. Some cautionary  remarks are in  order.  In strangelet computations,  strange matter  is  absolutely  stable  only for large A > 10.  Metastable strangelets could, however, also exist for smaller A values.  But we would expect that the  probability  of  forming  large  plasma  droplets  in heavy-ion collisions will be small indeed.  For a rough es- corporate additional resonances and extend the strange- ness calculations to include quantum statistics.  Further- more, a generalized treatment of  the phase transition of the QGP to the hadron phase with initial net strangeness not equal to Zero is being developed.  The nonequilibrium aspects  of  this  transition.  meson  radiation  and  quark clustering,  need  to  be  studied  in  the  near  Future.  It should help our understanding of the possible  formation of strangelets in the deconfinement phase transition, be it in  the early  Universe  or  in  high-energy  heavy-ion  col- lisions. lS. A. Chin  and A. K.  Kerman, Phqs. Rev. Lett. 43,  1297 (1979); J. D.  Bjorken  and  L. D. McLerran. Phys. Rev. D  20. 2353 (1979). lE. Witten, Phys. Rev. D 30, 272 (1984). 3E. Farhi and R. L. Jaffe, Phys. Rev. D 30, 2379 (1984). %.  Baym and S. A. Chin, Phys. Lett. 62B. 241  (1976). 'P.  Koch, B.  Mueller,  and J. Rafelski. Phys. Rep. 142. 167 (1986):  P.  Koch,  J.  Rafelski,  and  W. Greiner.  Phys.  Lett. 123B, 151 (1983). and 145B, 142 (1984). 6~.  Kapusta and A. Mekjian, Phys. Rev. D 33. 1304 (1986). 'T.  Matsui, B.  Svetisky, and L. D. McLerran, Phys. Rev. D 34. 783. 2047 (1986). 8~.  S. Lee, M. J. Rhoades-Brown, and U. Heinz, Phys. Lett. 1748, 123 (1986). 9~uurk  Matter '83,  Nucl. Phys. A418 (1984); Quark Mutter '84, Lecture  Notes  in  Physics.  Vol.  221, edited  hy  H. Araki, J.  Ehlers.  K.  Hepp,  R.  Kippenhahn.  H.  A.  Weidenmüller, J. Zittartz, and W. Beiglböck  (Springer. Berlin, 1985). 'OJ. Cleymans. R. V. Gavai. and E. Suhonen; Phys. Rep. 130, 217 (1986). IlP. Subramanian, H. Stoecker, and W. Greiner, Phys. Lett. 173B, 468 (1986). I2u.  Heinz, P. R. Subramanian, H. Stoecker, and  W. Grei- ner, J. Phys. G 12. 1237 (1986). "H.  Stoecker and W. Greiner, Phys. Rep. 137, 277 (1986). I%.  Stoecker, G. Graebner, J. A. Maruhn, and  W. Greiner. Phys. Lett. 95B, 192 (1980). 155.  D. Bjorken, Phys. Rev. D 27, 140 (1983). 16~.  K.  Kerman  md M, S. Weis, Phys.  Rev.  C  8,  408 (1973): H. Liu and G. L. Shaw, Phys. Rev. D 30, I137 (1984). 

Separation of strangeness from antistrangeness in the phase transition from quark to hadron matter: Possible formation of strange quark matter in heavy-ion collisions

Separation of strangeness from antistrangeness in the phase transition from quark to hadron matter: Possible formation of strange quark matter in heavy-ion collisions

Abstract

Similar works

Full text

Available Versions

Hochschulschriftenserver - Universität Frankfurt am Main