experimental evidence for hadronic deconfinement in p-p collisions at 1.8 tev *
DESCRIPTION
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 fm 3 , - PowerPoint PPT PresentationTRANSCRIPT
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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)
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.
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EXPERIMENTAL SET UP E-735 2
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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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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
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Fig.2
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Hanbury Brown , Twiss Pion Correlation Measurements
Evidence for expansion
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Dependence of Rg & t on dN
c / dh
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Dependence of the Gaussian radius RG
on (dN /d )h . The gluon diagram
indicates that two gluons are required to form two pions.C
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Fig.3
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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 =
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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
10
np =
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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
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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
-
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
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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