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the qcd phase diagram at nonzero temperature and baryon density has been the subject of numerous studies during the past few years @xcite . two regions of the phase diagram have been placed under special scrutiny . first , in the low temperature and high density domain , the ground state is believed to be a color superconductor @xcite . there are numerous types of color superconducting phases that emerge as the baryon chemical potential increases @xcite . second , in the high temperature and low baryon density domain , there is a transition from the hadronic phase to the quark gluon plasma phase @xcite . this latter domain is probed by heavy ion collision experiments .    in heavy ion collision experiments baryon number , isospin and strangeness are conserved . the time between the formation of the fireball and its freeze - out is so short that only the strong interactions play a significant role . in the past heavy ion collision experiments , the value of the strangeness chemical potential is @xmath0 of the value of the baryon chemical potential , whereas the value of the isospin chemical potential is @xmath1 of the value of the baryon chemical potential @xcite . thus the strangeness and isospin chemical potentials are small but not negligible . it is therefore worthwhile to study the qcd phase diagram in the high temperature region with nonzero baryon , isospin and strangeness chemical potentials .    at zero chemical potentials , numerical simulations on the lattice find that the temperature of the transition from the hadronic phase to the quark gluon plasma phase is given by @xmath2  mev . however , at nonzero baryon chemical potential lattice simulations suffer from the so - called sign problem : the fermion determinant is complex . as a consequence , traditional methods can not be used to study the qcd phase diagram at nonzero baryon chemical potential . however , recent advances have allowed studies of the high temperature and low baryon chemical potential region . the situation at zero baryon and strangeness chemical potentials and nonzero isospin chemical potential is simpler : there is no sign problem and traditional methods can be used @xcite ( as in qcd with two colors at nonzero baryon chemical potential @xcite ) . the results in this case are in complete agreement with effective theory studies @xcite . from these lattice studies it appears that the critical temperature s dependence on small baryon chemical potential at zero isospin and strangeness chemical potentials matches its dependence on small isospin chemical potential at vanishing baryon and strangeness chemical potentials . we will show that the hadron resonance gas model supports this conclusion . recently , the study of the qcd phase diagram at nonzero temperature , baryon and isospin chemical potentials has attracted attention @xcite . using different models , it was found that an arbitrarily small isospin chemical potential could greatly alter the qcd phase diagram at high temperature and small baryon chemical potential and have important consequences for heavy ion collision experiments . there are two phase transitions at high temperature . there are phases where the @xmath3 and @xmath4 quark sectors are decoupled @xcite . these results need to be confirmed by other methods , in particular on the lattice . we study the qcd phase diagram at high temperature and nonzero baryon , isospin and strangeness chemical potentials using the hadron resonance gas model . it has been shown both experimentally and on the lattice that the hadronic phase is very well described by a weakly interacting hadron resonance gas @xcite . we use two different methods to determine the location of the transition . first , it has been found on the lattice that the phase transition that separates the hadronic phase from the quark gluon plasma phase corresponds to a surface of constant energy density : @xmath5  gev/@xmath6 @xcite . second , the quark - antiquark condensate for the @xmath3 and @xmath4 quarks should almost vanish at the transition temperature . in this article , we determine the critical temperature , @xmath7 , at nonzero baryon , isospin and strangeness chemical potentials by using both approaches . we compute the surfaces of constant energy density as well as the quark - antiquark condensate in a hadron resonance gas model at nonzero temperature , baryon , isospin and strangeness chemical potentials . we show that both methods agree qualitatively as well as quantitatively . we find that the critical surface has small curvature , and that the critical temperature slowly decreases when either the baryon , the isospin , or the strangeness chemical potentials are increased . we assume that the pressure in the hadronic phase is given by the contributions of all the hadron resonances up to @xmath8  gev treated as a free gas , as in @xcite . all the thermodynamic observables can be derived from the pressure since @xmath9 where @xmath10 is the grand canonical partition function in a finite volume @xmath11 , at nonzero temperature , @xmath12 , baryon chemical potential , @xmath13 , isospin chemical potential , @xmath14 , and strangeness chemical potential , @xmath15 . the energy density is given by @xmath16 for a quark @xmath17 with mass @xmath18 , the quark - antiquark condensate is given by @xmath19    at nonzero temperature , the contributions of massive states are exponentially suppressed @xmath20 . their interactions are also exponentially suppressed @xmath21 . therefore this approximation should be valid at low enough temperatures . however , since we are studying qcd at temperatures up to @xmath22  mev , the lightness of the pions could be a problem , since @xmath23  mev . the hadron resonance gas model should be a good approximation for the other hadrons since they have a mass larger than @xmath24 @xmath25  mev . the physics of pions at nonzero temperature has been extensively studied in chiral perturbation theory @xcite . the pions contributions to the pressure have been calculated up to three loops in chiral perturbation theory @xcite . it has been shown that the free gas approximation and chiral perturbation theory agree at the one loop level , and that , in chiral perturbation theory , the two - loop corrections to the pressure are below a few percents of the one - loop contributions for temperatures under @xmath26  mev @xcite . thus the hadron gas resonance model is a good approximation also for the pions . the hadron resonance gas model has already been used in the literature and has been shown to give a very good description of the hadronic phase and of the critical temperature @xcite .    in the free gas approximation , the contribution to the pressure due to a particle of mass @xmath27 , baryon charge @xmath28 , isospin @xmath29 , strangeness @xmath30 , and degeneracy @xmath31 is given by @xmath32 where @xmath33 for fermions and @xmath34 for bosons , and @xmath35 is the modified bessel function . this particle s contribution to the energy density is given by @xmath36,\end{aligned}\ ] ] and its contribution to the quark - antiquark condensate is given by @xmath37 in order to compute ( [ qq1 ] ) , we need to know @xmath38 as a function of @xmath39 or @xmath40 . we make two assumptions in order to compute ( [ qq1 ] ) . first , we assume that the gell - mann@xmath41oakes@xmath41renner relation is valid @xmath42 where @xmath43  mev is the pion decay constant , and @xmath44 is the quark - antiquark condensate at zero temperature and chemical potentials . second , based on lattice results , we assume that the pion mass dependence of the hadron masses is given by @xmath45 where @xmath46 @xcite . therefore , combining ( [ gor ] ) and ( [ mhmpi ] ) , we assume that @xmath47 notice that since the hadron spectrum is isospin symmetric , we have that @xmath48 in the hadron resonance model at any temperature , baryon , isospin and strangeness chemical potentials . therefore , the rich structure of the phase diagram found in @xcite can not be seen in this model . finally at fixed @xmath12 , it can be readily seen from ( [ en1 ] ) and ( [ qq1 ] ) that an increase in either @xmath13 , or @xmath14 , or @xmath15 will increase @xmath49 and decrease @xmath50 . thus using either @xmath49 or @xmath50 as a criterion to determine the critical temperature , we find that an increase in either @xmath13 , or @xmath14 , or @xmath15 decreases @xmath7 , and that at fixed @xmath13 an increase in @xmath14 or @xmath15 results in a decrease of @xmath7 as well . lattice simulations have shown that the transition from the hadronic phase to the quark gluon plasma phase takes place at a constant energy density @xmath51  gev/@xmath6 @xcite . we use this criterion to determine the critical temperature as a function of baryon , isospin and strangeness chemical potentials . our results for the critical temperature as a function of @xmath13 at fixed @xmath14 and @xmath15 are shown in figure  [ fig1 ] . +    we find that this criterion constrains the critical temperature in a band of @xmath52  mev . at zero chemical potentials , we find that @xmath53  mev , which is in good agreement with lattice simulations . the temperature decreases as @xmath13 increases , as expected , but the decrease is slow . at the accuracy we can achieve using this method , an increase in @xmath14 does indeed decrease the critical temperature at fixed @xmath13 , but this effect is small at best . the decrease of the critical temperature is more important when @xmath15 is increased .    in figure  [ fig2 ] , we compare the critical temperature as a function of @xmath13 at @xmath54 with the critical temperature as a function of @xmath14 at @xmath55 . notice that we limit ourselves to @xmath56 and @xmath57 in order to avoid the pion and kaon superfluid phases @xcite . we find that the critical temperature curves are almost identical in both cases . this is in agreement with results from the lattice . we can fit our result for the critical temperature as a function of @xmath13 , @xmath14 and @xmath15 . by construction , since the pressure is an even function of @xmath14 in the hadron resonance model , the critical temperature is also even in @xmath14 . we find @xmath58 where @xmath59 is the critical temperature at zero chemical potentials . the fit is excellent , with a linear regression coefficient @xmath60 . the critical temperature can also be computed from the quark - antiquark condensate . indeed @xmath50 is of the order of the light quark masses at the phase transition and therefore almost vanishes . we determine the critical temperature by finding the point where @xmath61 in the hadron resonance gas model . we obtain a range of critical temperatures , since in the relation ( [ mhmq ] ) the constant @xmath62 is not precisely known @xcite . our results for the critical temperature as a function of @xmath13 at fixed @xmath14 and @xmath15 using @xmath50 are shown in figure  [ fig3 ] . +    we find that this criterion constrains the critical temperature to a band of @xmath63  mev . at zero chemical potentials , we find that @xmath64  mev , which is in good agreement both with the result obtained above using the @xmath49-criterion , as well as with lattice simulations . as expected , the critical temperature decreases as @xmath13 increases . as in the previous method , we find that an increase in the isospin chemical potential might reduce the critical temperature , but not in a significant way . the strangeness chemical potential has a stronger effect on the critical temperature . in figure  [ fig4 ] , we compare the critical temperature as a function of @xmath13 at @xmath54 with the critical temperature as a function of @xmath14 at @xmath55 . we find that the critical temperature curves are almost identical in both cases . we can fit our result for the critical temperature as a function of @xmath13 , @xmath14 and @xmath15 . we find @xmath65 where @xmath59 is the critical temperature at zero chemical potentials . the fit is excellent , with a linear regression coefficient @xmath66 . finally we can compare the critical temperatures obtained using these two different approaches : constant energy density and disappearance of the quark - antiquark condensate . we present our results in figure  [ fig5 ] at nonzero @xmath13 with @xmath54 , nonzero @xmath14 with @xmath55 , and nonzero @xmath67 with @xmath68 , respectively . +    we find that the critical temperature at zero chemical potentials , @xmath59 , is lower when we use the @xmath49-criterion than when we use the @xmath50-criterion . if the critical curve is normalized with respect to @xmath59 , we find that the two methods are in very good agreement . if we compare the fits ( [ crittenfit ] ) and ( [ crittsigmafit ] ) , we find that the @xmath13 and @xmath15 coefficients are very close in both cases , whereas the @xmath14 coefficients almost differ by a factor of three . however , this large difference in the coefficients leads to critical temperatures that only differ by a few percents in the region of interest . we therefore conclude that both methods yield critical temperatures that are in very good agreement . we have used the hadron resonance gas model to determine the temperature of the transition from the hadronic phase to the quark gluon plasma phase as a function of baryon , isospin and strangeness chemical potentials . this is of interest for heavy ion collision experiments , since baryon , isospin and strangeness chemical potentials are nonzero in this case . we have used two different methods to determine the critical temperature . the first one relies on the observation on the lattice that the quark gluon plasma phase emerges at a constant energy density @xcite . the second method is based on the fact that the quark - antiquark condensate for the light quarks should almost disappear at the transition between the hadronic phase and the quark gluon plasma phase . we find that the critical temperatures found in both methods are in very good agreement .    in the hadron resonance gas model , the critical temperature decreases as the baryon , isospin , or strangeness chemical potentials increase , albeit slowly . in agreement with recent lattice simulations and several models @xcite , we find that the critical temperature as a function of the quark chemical potential at zero isospin chemical potential is almost identical to the critical temperature as a function of isospin chemical potential at zero quark chemical potential . we also find that the critical temperature decreases slightly when the isospin chemical potential is increased at fixed baryon chemical potential . this might be important for heavy ion collision experiments : a choice of different isotopes should reduce the critical temperature that separates the hadronic phase from the quark gluon plasma phase .        for a review see , k.  rajagopal and f.  wilczek , arxiv : hep - ph/0011333 ; for a review see , s.  muroya , a.  nakamura , c.  nonaka and t.  takaishi , prog . phys .   * 110 * , 615 ( 2003 ) . for a review see , p.  braun - munzinger , k.  redlich and j.  stachel , arxiv : nucl - th/0304013 . d.  bailin and a.  love , phys . rept .   * 107 * , 325 ( 1984 ) ; m.  g.  alford , k.  rajagopal and f.  wilczek , phys . b * 422 * , 247 ( 1998 ) ; r.  rapp , t.  schafer , e.  v.  shuryak and m.  velkovsky , phys . lett .   * 81 * , 53 ( 1998 ) . for a review see , m.  g.  alford , ann . nucl .  part . sci .   * 51 * , 131 ( 2001 ) ; f.  karsch , e.  laermann and a.  peikert , nucl . b * 605 * , 579 ( 2001 ) . a.  ali khan _ et al . _ [ cp - pacs collaboration ] , phys . d * 63 * , 034502 ( 2001 ) . z.  fodor and s.  d.  katz , jhep * 0404 * , 050 ( 2004 ) . c.  bernard _ et al . _ [ milc collaboration ] , arxiv : hep - lat/0405029 . z.  fodor and s.  d.  katz , phys . b * 534 * , 87 ( 2002 ) ; jhep * 0203 * , 014 ( 2002 ) ; jhep * 0404 * , 050 ( 2004 ) ; c.  r.  allton _ et al . _ , phys . d * 66 * , 074507 ( 2002 ) ; phys . d * 68 * , 014507 ( 2003 ) ; f.  karsch _ et al . _ , nucl .  phys .  proc . * 129 * , 614 ( 2004 ) ; p.  de forcrand and o.  philipsen , nucl . b * 642 * , 290 ( 2002 ) ; nucl . * 129 * , 521 ( 2004 ) ; m.  delia and m.  p.  lombardo , phys . d * 67 * , 014505 ( 2003 ) . r.  v.  gavai and s.  gupta , phys . d * 68 * , 034506 ( 2003 ) ; r.  gavai , s.  gupta and r.  roy , prog . suppl .   * 153 * , 270 ( 2004 ) . v. azcoiti , talk presented at lattice 2004 , fermilab ( 2004 ) . j.  b.  kogut and d.  k.  sinclair , phys . d * 66 * , 034505 ( 2002 ) ; nucl .  phys . * 119 * , 556 ( 2003 ) ; nucl . suppl .   * 129 * , 542 ( 2004 ) ; d.  k.  sinclair , j.  b.  kogut and d.  toublan , prog . suppl .   * 153 * , 40 ( 2004 ) . s.  hands , j.  b.  kogut , m.  p.  lombardo and s.  e.  morrison , nucl . b * 558 * , 327 ( 1999 ) ; s.  muroya , a.  nakamura and c.  nonaka , nucl . * 94 * , 469 ( 2001 ) ; j.  b.  kogut , d.  toublan and d.  k.  sinclair , phys . b * 514 * , 77 ( 2001 ) ; s.  hands , i.  montvay , l.  scorzato and j.  skullerud , eur . j.  c * 22 * , 451 ( 2001 ) j.  b.  kogut , d.  toublan and d.  k.  sinclair , nucl .  phys . b * 642 * , 181 ( 2002 ) ; nucl .  phys . suppl .   * 119 * , 559 ( 2003 ) ; phys . d * 68 * , 054507 ( 2003 ) ; p.  giudice and a.  papa , phys . d * 69 * , 094509 ( 2004 ) . j.  b.  kogut , m.  a.  stephanov and d.  toublan , phys . b * 464 * , 183 ( 1999 ) ; j.  b.  kogut _ et al . _ , nucl . b * 582 * , 477 ( 2000 ) ; d.  t.  son and m.  a.  stephanov , phys . lett .   * 86 * , 592 ( 2001 ) ; k.  splittorff , d.  t.  son and m.  a.  stephanov , phys . d * 64 * , 016003 ( 2001 ) ; j.  b.  kogut and d.  toublan , phys . d * 64 * , 034007 ( 2001 ) ; k.  splittorff , d.  toublan and j.  j.  m.  verbaarschot , nucl . b * 620 * , 290 ( 2002 ) ; nucl . b * 639 * , 524 ( 2002 ) ;    b.  klein , d.  toublan and j.  j.  m.  verbaarschot , phys . d * 68 * , 014009 ( 2003 ) ; d.  toublan and j.  b.  kogut , phys . b * 564 * , 212 ( 2003 ) ; m.  frank , m.  buballa and m.  oertel , phys . b * 562 * , 221 ( 2003 ) ; a.  barducci , r.  casalbuoni , g.  pettini and l.  ravagli , phys . d * 69 * , 096004 ( 2004 ) ; d.  n.  walters and s.  hands , arxiv : hep - lat/0407034 . a.  barducci , g.  pettini , l.  ravagli and r.  casalbuoni , phys .  lett . b * 564 * , 217 ( 2003 ) . j.  cleymans and k.  redlich , phys . lett .   * 81 * , 5284 ( 1998 ) . f.  karsch , k.  redlich and a.  tawfik , eur . j.  c * 29 * , 549 ( 2003 ) ; phys . b * 571 * , 67 ( 2003 ) ; f.  karsch , prog . * 153 * , 106 ( 2004 ) ; m.  delia and m.  p.  lombardo , arxiv : hep - lat/0406012 . p.  gerber and h.  leutwyler , nucl . b * 321 * , 387 ( 1989 ) . j.  gasser and h.  leutwyler , phys . b * 188 * , 477 ( 1987 ) ; a.  schenk , nucl . b * 363 * , 97 ( 1991 ) ; a.  schenk , phys . d * 47 * , 5138 ( 1993 ) ; d.  toublan , phys .  rev . d * 56 * , 5629 ( 1997 ) . j.  b.  kogut and d.  toublan , phys .  rev . d * 64 * , 034007 ( 2001 ) ; v.  a.  miransky and i.  a.  shovkovy , phys . lett .   * 88 * , 111601 ( 2002 ) ; t.  schafer , d.  t.  son , m.  a.  stephanov , d.  toublan and j.  j.  m.  verbaarschot , phys . b * 522 * , 67 ( 2001 ) .
we use a hadron resonance gas model to study the qcd phase diagram at nonzero temperature , baryon , isospin and strangeness chemical potentials . 
 we determine the temperature of the transition from the hadronic phase to the quark gluon plasma phase using two different methods . 
 we find that the critical temperatures derived in both methods are in very good agreement . 
 we find that the critical surface has a small curvature . 
 we also find that the critical temperature s dependence on the baryon chemical potential at zero isospin chemical potential is almost identical to its dependence on the isospin chemical potential at vanishing baryon chemical potential . 
 this result , which holds when the chemical potentials are small , supports recent lattice simulation studies . 
 finally , we find that at a given baryon chemical potential , the critical temperature is lowered as either the isospin or the strangeness chemical potential are increased . 
 therefore , in order to lower the critical temperature , it might be useful to use different isotopes in heavy ion collision experiments .