July 22, 2004R. Soltz, Hot Quarks, Taos, NM1 Future Directions in HBT This title has been used before These predictions are seldom right Title

July 22, 2004R. Soltz, Hot Quarks, Taos, NM2 HBT-Puzzle For Dummies Some very smart people have contributed to our understanding of HBT They just don’t care to be associated with it anymore Possible copyright infringement suit! Title #2 and by one, but not of…

July 22, 2004R. Soltz, Hot Quarks, Taos, NM3 Solving the HBT Puzzle: Noble quest or trivial pursuit I will try to convince you of the former But, some will remain unconvinced … For those of you in this category - watch for embedded trivia questions - answer all correctly and collect your beer(s) Final Title

July 22, 2004R. Soltz, Hot Quarks, Taos, NM4 Volumes & Lifetimes 2 nd Law Thermodynamics Ideal Gas Relativistic Fermi/Bose Gas  =0 Pions (3) vs. QGP (37)

July 22, 2004R. Soltz, Hot Quarks, Taos, NM5 HBT (GGLP) Basics In the simplest approximation, the technique has not changed since before most of you were born Goldhaber, Goldhaber, Lee, and Pais, PR 120:300 (1960) For identical bosons/fermions But this (plane wave) approximation neglects many effects P(p 1,p 2 ;r 1,r 2 ) = P(p 1,p 2 )/P(p 1 )P(p 2 ) = 1 + |  (p 1 - p 2 ) | 2 ~ Gaussian source in x i yields Gaussian correlation in conjugate variable q i =p 1i- p 2i Who made first use of this pedagogic picture?

July 22, 2004R. Soltz, Hot Quarks, Taos, NM6 HBT Complexities We have neglected –Final state interactions Coulomb interaction Strong interaction Weak decays –Position-momentum correlations –Things more subtle, such as special relativity State of the art analysis incorporates most of these, but not all 1/R side Who performed first “correction” for Coulomb? Where is the first mention of Lorentz effects in HBT?

July 22, 2004R. Soltz, Hot Quarks, Taos, NM7 HBT - current state of the art Bowler/Sinyukov factorization –Assumes |  C +  C * | 2 = F C |  +  * | 2 –Still an approximation to 2-3% for kaons ~50 ways to handle Coulomb/Weak decays All subsequent data shown use the first technique Direct Fit –Symmetrized Coulomb waves –See M.Heffner QM04 P. Chung et al, PRL 91: (2003) Source Imaging, D. Brown –No factorization –No Gaussian assumption

July 22, 2004R. Soltz, Hot Quarks, Taos, NM8 HBT Radius Definitions (b=0) R long ~  F R side  k T ~ R geo R out || k T

July 22, 2004R. Soltz, Hot Quarks, Taos, NM9 HBT Radius Dynamics Transverse Expansion profile Transverse Freeze-out profile Positive x-p correlations reduce all R Hydrodynamic :  ~ x ; R~1/√m T Heisenberg :  ~ 1/x ; R~1/m T Positive x-t correlations=>reduce R out R 2 out =  x 2  t) 2  x  t “inside-outside” cascade

July 22, 2004R. Soltz, Hot Quarks, Taos, NM10 HBT Experimental Results Excellent agreement (phobos too) Systematics well under control A Precision Tool !

July 22, 2004R. Soltz, Hot Quarks, Taos, NM11 More Experimental Systematics STAR PRL 93:12301 (2004) PHENIX nucl-ex/ Don’t tell me HBT radii don’t relate to a physical size b≠0

July 22, 2004R. Soltz, Hot Quarks, Taos, NM12 Model Comparison (the puzzle) No model correct Does R out /R side of unity imply no long-lived mixed phase? the puzzle

July 22, 2004R. Soltz, Hot Quarks, Taos, NM13 Model Calculation Systematics Each theory paper has explored systematic changes in at least one important variable – T f = Freeze-out Temp/profile – T c = Critical Temp. –  el = parton scattering cross-section –  E = Latent Heat/transition order – T ch = chem. Freeze-out temp – n = viscoscity (-20% R out, -60% R long ) D. Teany, nucl-th/ Instead of looking for correct answer, explore systematics

July 22, 2004R. Soltz, Hot Quarks, Taos, NM14 HBT radii vs. S(x,p) and x-t corr. Using x-rms incorrect (at least for low k T pions) 1.Extract radii or check for equivalence 2.Freeze-out matters x-t term comparable to  x and  t Z. Lin et al, PRL 89: (2002) What was the first reference to explore x-t correlations in a cascade model?

July 22, 2004R. Soltz, Hot Quarks, Taos, NM15 Partonic cross-sections Variation in radii for reasonable  el /opacity less than sys. errors AMPT shows little sensitivity for  el =3,6,10,16 mb D. Molnar and M. Gyulassy, PRL 92: (2004) significantly reduced opacity

July 22, 2004R. Soltz, Hot Quarks, Taos, NM16 T c in hybrid model Results for kaons Lower T C 160 vs. 200 MeV –shortens hadronic phase –  E ~ 1.5 vs. 2.9 GeV –slight drop R out –~20% drop in R out /R side S. Soff, et al., PRL 88: (2002) R out /R side sensitive to T C & latent heat RORO RSRS RLRL

July 22, 2004R. Soltz, Hot Quarks, Taos, NM17 T f & latent heat in chiral model --- T F = 130 MeV, --- T F = 80 MeV Predictions for R side and R out only Significant drop in R out /R side for 2 nd order transition D. Zschiesche, PRC 65: (2002) R out /R side sensitive to T F and transition order  E=0 GeV  E=1.7 GeV

July 22, 2004R. Soltz, Hot Quarks, Taos, NM18 3D w/ T ch with hybrid approach R long nailed ! Sudden freeze- out may be too sudden but 2D Hybrid has larger R long,side

July 22, 2004R. Soltz, Hot Quarks, Taos, NM19 Review of Models R out /R side is particularly sensitive to freeze-out dynamics, perhaps uniquely so –could be used to “tune” freeze-out profile –better to calculate with re-scattering model Radii sensitive to  E and T C and T F No evidence yet for strong dependence on partonic phase, except perhaps at higher p T In a physical model, all these things are coupled trivial pursuit noble quest

July 22, 2004R. Soltz, Hot Quarks, Taos, NM20 Solving the Puzzle First –abandon sudden freeze-out Second –run 3D hydro with small  E, low T C, and short hadronic re-scattering phase to define freeze-out Ultimate Goal –run hydro hybrid to map out complete  2 complete parameter space for realistic EOS and init. cond. comparing to full set of observables How much person and computing power would this require?

July 22, 2004R. Soltz, Hot Quarks, Taos, NM21 A job for parameterizations? Can parameterizations be used to speed up mapping of the  2 space? –Maybe –Worth investigating First benchmark parameterizations to full calculations

July 22, 2004R. Soltz, Hot Quarks, Taos, NM22 And for the experiments… Extend asHBT to higher k T >0.5 GeV –more complete test of spatial evolution Extend pion radii to higher k T > 1 GeV –more sensitive to pre-hadronic phase Extend to kaons, protons –investigate meson/baryon dynamics HBT with 2-photons –probe early dynamics

July 22, 2004R. Soltz, Hot Quarks, Taos, NM23 The proton-proton “conundrum” Evidence for same expansion dynamics in p-p collisions Are we seeing a universal property of particle production? Maybe - this is not (yet) a precision test 4 bins is not enough to study differences in dynamics R out / R out (pp) R side / R side (pp) R long / R long (pp) T. Gutierrez, nucl-ex/ (2004)

July 22, 2004R. Soltz, Hot Quarks, Taos, NM24 Solving the Puzzle First –abandon sudden freeze-out Second –run 3D hydro with small  E, low T C, and short hadronic re-scattering phase to define freeze-out Ultimate Goal –run hydro hybrid to map out complete  2 complete parameter space for realistic EOS and init. cond. comparing to full set of observables How much person and computing power would this require?

July 22, 2004R. Soltz, Hot Quarks, Taos, NM25 Size & Lifetime Bose-Einstein Correlations