1. EXPERIMENTAL EVIDENCE FOR HADRONIC DECONFINEMENT In p-p Collisions at 1.8 TeV * L. Gutay - 1 * Phys. Lett. B528(2002)43-48 (FNAL, E-735 Collaboration Purdue, Duke, Iowa, Norte Dame, Wisconsin) AsssAsss We have measured deconfined volumes, 4.4 < V < 13.0 fm 3, produced by a one dimensional (1D) expansion. These volumes are directly proportional to the charged particle pseudorapidity densities 6.75 < dN c / d  < 20.2. The hadronization temperature is T= 179.5 G 5 (syst) MeV. Using Bjorken's 1D model, the hadronization energy density is  F = 1.10 G 0.26(stat) GeV/fm 3 corresponding to an excitation of 24.8 G 6.2(stat) quark-gluon degrees of freedom.

2. EXPERIMENTAL SET UP E-735 2

3. Experiment E-735 was located in the C  in the Interaction region of the Fermi National Accelerator Laboratory (FNAL). The p-p interaction was surrounded by a cylindrical drift chamber which in turn was covered by a single layer hodoscope including endcaps. Multiplicity range : 10  c   200 Pseudorapidity Range : -3.25  Momentum Range : 0.1  p t    GeV/c Spectrometer Coverage : -0.37  X 20 0  is the azimuthal angle around the beam direction. - 3

4. Multiple Parton Collision Cross Sections Comparison of the cross sections for single, double and triple encounter collisions. The multiplicity distribution is made up of three contributions corresponding to single, double, and triple parton-parton collisions. Due to low x gluons 4 Fig.2

5. Hanbury Brown, Twiss Pion Correlation Measurements Evidence for expansion 5

6. Dependence of R g &  on dN c / d  6

7. Dependence of the Gaussian radius R G on (dN /d . The gluon diagram indicates that two gluons are required to form two pions. C 7 Fig.3

8. Hadronization Volume HBT correlation measurements with pions. The Cylindrical volume of the pion source V=  (  l   ) 2. 2 l R h ( d N c /d   l   l R = 1.56, h= 0.073 ± 0.011 V= (0.645± 0.130) ( d N c /d  fm 3 4.4 ± 0.9 < V < 13.0 ± 2.6 fm 3 For 6.75 < d N c /d   We assume that for d N c /d  > 6.75 the system is initially above the deconfinement transition (Then expands to final volume V) 8

9. Entropy Density s( T ) at Hadronization (After Expansion ) Bjorken 1D boost invariant equation to estimate no. of pions/fm 3 (3/2) (dN C / d  A 2 T A is the Transverse Area and T is the Proper Time at freeze out The collision occurs at longitudinal coordinate z= 0 and time t= 0. s( T ) / s( T 0 ) = T 0 / T T = ( t 2 -z 2 ) ½ T 0 is the initial proper time when thermalization has occurred s ( T ) ] n  = 9

10. For a relativistic massless ideal gas above the phase transition the maximum expansion velocity, responsible for most of the longitudinal expansion, is likely to be the sound velocity v s 2 = 1/3 The expansion time t = z / v s = l R R G / v s T = ( 3z 2 - z 2 ) 1/2 = ˆ 2 z The proper time at hadronization T f = ‡  ‡ l R h dN c / d  Pions/fm 3 (3/2) (dN C / d   2 2 l R h dN c / d  = (3/2) (1/ ‡ 2 ) n  = 1.64 G 0.33(stat) pions / fm 3  2 2 l R h Independent of dN c / d  10 n =n =

11. Temperature Determination The negative particle p t spectrum is used to measure the temperature T he slope parameter (b -1 ) i.e. "Temperature" is obtained from a fit of the invariant cross-section d 2 N c / dy d 2 p t to the function A exp(-bp t ) for 0.15  p t  GeV/c. T slope value is constant to  1  for 6.75 < dN c /d   20.2 T slope = 179.5 ± 5 (syst) 11

12. Fig. 4. Relative meson and hyperon yields versus rest mass. For the mesons, the inverse slope parameter T m = 162±5 MeV, and for the hyperons T m = 173±12 MeV. Relative Particle Yields 12

13. Hadronization Energy Density,  f  f =  h F h ( m h )   1/ ˆ 2)  2 2 l R h ( m h )   m h + p t ) 22 ½ Average transverse mass of hadron h F h is a hadron abundance factor for , K,  p, n,  0,  etc.  = 0.95 fm, l R = 1.56, h = 0.073  f = 1.10 ± 0.26(stat) GeV/fm 3 13

14. Number of Degrees of Freedom (DOF ), G(T slope ) n c = V G(T slope ) 1.202 (kT slope ) 3  2 h 3 c 3 For a quark-gluon plasma : G(T slope ) = G g (T slope ) + G q (T slope ) + G q (T slope ) = 16+ (21/2) (f) where f are the number of quark flavors = 2 - We assume that pion emission from the source can be determined by the number of constituents in the source at hadronization, that one pion is a quark-antiquark pair and that two gluons are required to produce two pions n   n g + (n q +n q )/ 2 ( see Fig.3) - 14

15. n  .     G  g.  16.1 T slope (GeV) G  g are the effective number of gluon DOF G(T slope ) = n g + n q + n q = (1 + 21/16) G  g = 23.5  6 DOF - Again nearly 8 times the DOF = 3 of a pion gas G(T slope ) from  f and T slope After the isentropic expansion, the energy E in the volume V at a temperature T is also constant E= (3/4) S( T slope ).T slope E = V T slope G(T slope )  2 k 4 30 h 3 c 3 1 G(T slope ) = 24.8  6.2(stat) DOF 3 15 4

16. CONCLUSIONS * We have measured the deconfined hadronic volumes produced by a one dimensional isentropic expansion. * The freeze out no. of pions / fm 3 n  = 1.64 ± 0.33  * The hadronization temperature is T slope = 179  5 MeV. * The freeze out energy density is  f = 1.10  GeV/ fm 3. * The number of DOF in the source is 23.5±6, 24.8±6.2 In general agreement with those expected for QGP. * The measured constant n ,   f , T slope values characterize the quark-gluon to hadron thermal phase transition. 16

17. Comparison with Lattice Gauge Theory  / T 4 =  2 /  30 G(T slope ) = 8.15±2.0 (stat) In Fig.5 the Temperature T = T slope, T c is the critical temperature 17 Slope