EXPERIMENTAL EVIDENCE FOR HADRONIC DECONFINEMENT In p-p Collisions at 1.8 TeV *

1. 1 EXPERIMENTAL EVIDENCE FOR HADRONIC DECONFINEMENT In p-p Collisions at 1.8 TeV * - L. Gutay (FNAL, E-735 Collaboration Purdue, Duke, Iowa, Norte Dame, Wisconsin) We have measured deconfined volumes, 4.4 < V < 13.0 fm3 , produced by a one dimensional (1D) expansion. These volumes are directly proportional to the charged particle pseudorapidity densities 6.75 < dNc / dh < 20.2 . The hadronization temperature is T= 179.5 G5 (syst) MeV. Using Bjorken's 1D model, the hadronization energy density is eF = 1.10 G0.26(stat) GeV/fm3corresponding to an excitation of 24.8G6.2(stat) quark-gluon degrees of freedom. Asss * Phys. Lett. B528(2002)43-48

2. 2 EXPERIMENTAL SET UP E-735

3. 3 Experiment E-735 was located in the Cf 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 < N c < 200 Pseudorapidity Range : -3.25 < h < 3.25 Momentum Range : 0.1 < pt< 1.5 GeV/c Spectrometer Coverage : -0.37 < h < 1.00 , Dj X 200 Dj is the azimuthal angle around the beam direction. -

4. 4 Multiple Parton Collision Cross Sections Due to low x gluons 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. Fig.2

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

6. 6 Dependence of Rg & t on dNc / dh

7. 7 Fig.3 Dependence of the Gaussian radius RG on (dN/dh). The gluon diagram indicates that two gluons are required to form two pions. C

8. 8 Hadronization Volume HBT correlation measurements with pions. The Cylindrical volume of the pion source V= p (lt t)2 . 2 lRh (dNc /dh) lt = 1, lR = 1.56 , h= 0.073 ± 0.011 V= (0.645± 0.130) (dNc /dh) fm 3 4.4 ± 0.9 < V < 13.0 ± 2.6fm 3 For6.75 < dNc /dh < 20.2 We assume that fordNc /dh > 6.75 the system is initially above the deconfinement transition (Then expands to final volume V)

9. 9 Entropy Density s(T) at Hadronization (After Expansion ) Bjorken 1D boost invariant equation to estimate no. of pions/fm 3 (3/2) (dNC / dh) s (T) ] np= 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(T0) = T0 / T T = ( t 2 -z 2) T0 is the initial proper time when thermalization has occurred ½

10. 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 vs2 = 1/3 The expansion time t = z / vs = lRRG / vs T = ( 3z 2 - z 2 ) 1/2 = ˆ2 z Tf =‡ ‡lRhdNc/dh The proper time at hadronization (3/2) (dNC / dh) (3/2) (1/‡2 ) np= Pions/fm3 = pt22 lRhdNc/dh pt22 lRh np = 1.64 G 0.33(stat) pions / fm3 Independent of dNc/dh

11. 11 Temperature Determination The negative particle ptspectrum is used to measure the temperature The slope parameter (b-1) i.e. "Temperature" is obtained from a fit of the invariant cross-section d2 Nc/ dy d2pt to the function A exp(-bpt) for 0.15 £ pt £ 0.45 GeV/c. Tslope value is constant to ± 1% for 6.75 < dNc /dh< 20.2 Tslope = 179.5 ± 5 (syst)

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

13. 13 Hadronization Energy Density, ef åh Fh ( mh )^ ( 1/ˆ2) Fh is a hadron abundance factorfor p, K, j, p, n, L0, X etc. ef = pt22 lRh ½ 2 2 ( mh )^ = ( mh + pt) Average transverse mass of hadron h t = 0.95 fm , lR = 1.56 , h = 0.073 ef= 1.10 ± 0.26(stat) GeV/fm3

14. 14 Number of Degrees of Freedom (DOF ), G(Tslope) nc = V G(Tslope) 1.202 (kTslope)3 p2 h3 c3 For a quark-gluon plasma : G(Tslope) = Gg(Tslope) + Gq(Tslope) + Gq(Tslope) = 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 np = ng + (nq +nq)/2 ( see Fig.3) -

15. np = (1 + 2 .21/64) Gg.16.1 Tslope(GeV) Gg are the effective number of gluon DOF 3 15 G(Tslope) = ng + nq + nq = (1 + 21/16) Gg = 23.5 ± 6 DOF - G(Tslope) from ef and Tslope After the isentropic expansion, the energy E in the volume V at a temperature T is also constant E= (3/4) S( Tslope ) .Tslope G(Tslope) p2 k4 4 E = V Tslope 1 G(Tslope) = 24.8± 6.2(stat) DOF 30h3 c3 Again nearly 8 times the DOF = 3 of a pion gas

16. 16 CONCLUSIONS * We have measured the deconfined hadronic volumes produced by a one dimensional isentropic expansion. * The freeze out no. of pions / fm3 np = 1.64 ± 0.33 . * The hadronization temperature is Tslope = 179 ± 5 MeV. * The freeze out energy density is ef =1.10 ± 0.26 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 np ,ef, Tslope values characterize the quark-gluon to hadron thermal phase transition.

17. Comparison with Lattice Gauge Theory 17 e / T 4 =p 2 /30 G(Tslope) = 8.15±2.0 (stat) Slope In Fig.5 the Temperature T = Tslope , Tc is the critical temperature