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

L. Gutay

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1

* Phys. Lett. B528(2002)43-48

(FNAL, E-735 Collaboration Purdue, Duke, Iowa, Norte Dame, Wisconsin)

Asss

We have measured deconfined volumes, 4.4 < V < 13.0 fm3 ,produced by a one dimensional (1D) expansion. These volumes aredirectly proportional to the charged particle pseudorapiditydensities 6.75 < dN

c / dh < 20.2 . The hadronization temperature is

T= 179.5 5 (syst) MeV. Using Bjorken's 1D model, the hadronization

energy density is eF

= 1.10 0.26(stat) GeV/fm3 corresponding to an

excitation of 24.86.2(stat) quark-gluon degrees of freedom.

EXPERIMENTAL SET UP E-735 2

Experiment E-735 was located in the C f 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 < Nc < 200

Pseudorapidity Range : -3.25 < < 3.25hMomentum Range : 0.1 < p

t < 1.5 GeV/c

Spectrometer Coverage : -0.37 < < 1.00 , h Dj 200

Dj is the azimuthal angle around the beam direction.

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3

Multiple Parton Collision Cross Sections

Comparison of the crosssections for single, double and triple encounter collisions.

The multiplicity distribution ismade up of three contributions corresponding to single, double, and triple parton-parton collisions.

Due to low x gluons

4

Fig.2

Hanbury Brown , Twiss Pion Correlation Measurements

Evidence for expansion

5

Dependence of Rg & t on dN

c / dh

6

Dependence of the Gaussian radius RG

on (dN /d )h . The gluon diagram

indicates that two gluons are required to form two pions.C

7

Fig.3

Hadronization Volume HBT correlation measurements with pions.

The Cylindrical volume of the pion source

V= p ( l t t )2 . 2 l

R h (dN

c /d )h

l t = 1, lR

= 1.56 , h= 0.073 ± 0.011

V= (0.645± 0.130) (dNc /d ) h fm 3

4.4 ± 0.9 < V < 13.0 ± 2.6 fm 3

For 6.75 < dNc /d < h 20.2

We assume that for dNc /d h > 6.75 the system

is initially above the deconfinement transition (Then expands to final volume V)

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Entropy Density s(T) at Hadronization (After Expansion )

Bjorken 1D boost invariant equation to estimate no. of pions/fm 3

(3/2) (dNC

/ d )h

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)½

T0 is the initial proper time

when thermalization has occurred

s (T) np =

9

For a relativistic massless ideal gas above the phase transitionthe maximum expansion velocity, responsible for most of the longitudinal expansion, is likely to be the sound velocity v

s2 = 1/3

The expansion time t = z / vs = l

RR

G / v

s

T = ( 3z 2 - z 2 ) 1/2 = 2 z

The proper time at hadronization T

f =� l

R h dN

c/dh

Pions/fm3(3/2) (dN

C / dh)

pt2 2 lR h dN

c/dh

= (3/2) (1/2 )

np = 1.64 0.33(stat) pions / fm3

pt2 2 lR h

Independent of dNc/dh

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np =

Temperature Determination

The negative particle pt spectrum is used to measure the temperature

The slope parameter (b-1) i.e. "Temperature" is obtained from a fitof the invariant cross-section d2 N

c/ dy d2 p

t to the function

A exp(-bpt ) for 0.15 £ p

t 0.45 £ GeV/c.

Tslope

value is constant to 1% for 6.75 < dNc /dh < 20.2

Tslope

= 179.5 ± 5 (syst)

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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 Tm

= 173±12 MeV.

Relative Particle Yields12

Hadronization Energy Density, ef

e

f =

åh F

h ( m

h )^ ( 1/2)

pt2 2 lR h

( mh )^ = ( m

h + p

t )

2 2 ½Average transverse mass of hadron h

Fh is a hadron abundance

factor for p, K, , j p, n, L0, X

etc.

t = 0.95 fm , lR

= 1.56 , h = 0.073

e

f= 1.10 ± 0.26(stat) GeV/fm3

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Number of Degrees of Freedom (DOF ), G(Tslope

)

n

c = V

G(Tslope

) 1.202 (kTslope

)3

p2 h3 c3

For a quark-gluon plasma :

G(Tslope

) = Gg(T

slope) + G

q(T

slope) + G

q(T

slope) = 16+ (21/2) (f)

where f are the number of quark flavors = 2

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We assume that pion emission from the source can be determined by the number of constituents in the source at hadronization, that one pion isa quark-antiquark pair and that two gluons are required to produce twopions n p = n

g + (n

q +n

q)/2 ( see Fig.3)-

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n p = (1 + 2 . 21/64 ) G g

. 16.1 T

slope (GeV)

G g are the effective number of gluon DOF

G(Tslope

) = ng + 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(Tslope

) from ef and T

slope

After the isentropic expansion, the energy E in the volume V at a temperature Tis also constant E= (3/4) S( T

slope ) .T

slope

E = V Tslope

G(T

slope) p2 k4

30 h3 c3 G(Tslope

) = 24.8 6.2(stat) DOF

315

4

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 T

slope = 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 n p , ef , Tslope values characterize the

quark-gluon to hadron thermal phase transition.

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Comparison with Lattice Gauge Theory

e / T 4 = p 2 / 30 G(Tslope

) = 8.15±2.0 (stat)

In Fig.5 the Temperature T = Tslope

, Tc

is the critical temperature

17Slope