Free Quarks and Antiquarks versus Hadronic Matter

Xiao-Ming Xu

Collaborator: Ru Peng

Picture below Tc

Critical temperature Tc:

transition between quark gluon plasma and hadronic matter

Hadronic matter below Tc:

scatterings and flow of hadrons π, ρ, K, K*,…

We propose new form of matter below Tc:

free quarks, free antiquarks and hadrons

F. Karsch, et al., Nucl. Phys. B605, 579 (2001)

Medium effect

Lattice QCD calculations give temperature-dependent quark-quark potential.

Medium screening leads to weak binding of quarks.

When temperature increases, the confinement potential gets weak and the bound state gets loose.

We expect

Meson-meson collisions in high-temperature hadronic matter produce free quarks and antiquarks easily.

Cross Section

meson-meson reaction

,1

,1

,1

,1

,2

33

228 ])(][)([)2(32

1

q

q

q

q

q

BABAE

pd

E

pdd

mmsmms

22112211 )()( qqqqqqBqqA

,2

,1

,1

,2

,2

,2

,2

)cos|||(|||

2

fi2

qqqBAqqq

q

EppPPpEp

Mp

quark-quark potential

Transition amplitude Mfi is derived from quark-antiquark wave functions and the quark-quark potential

b(T)=0.35[1-(T/Tc)2] (Tc-T)

(T)=0.28 (Tc-T)

Tc=0.175 GeV, d=0.897 GeV

mu=md=0.334 GeV, ms=0.575 GeV

C.-Y. Wong, Phys. Rev. C65, 034902 (2002)

)

4

Q(exp

3

8

)Q)((

)(6

Q)(

4

22)Q(

2

2

22222 dss

mmT

Tb

TV ji

ji

ssjiij

unpolarized cross section

(1) LA=LB=0

(2) LA=0, LB0, SA=0

(3) LA=0, LB=1, SA=1, SB=1

)12)(12)(12(

1)(unpol

free

BBAAB LSS

s

),,,,,()12( ,2

,2

,1

,1

sSSmSLSqqqqSBz

master rate equation

time evolution of number densities of , , K and K* in static hadronic matter

jiKKj

ijKKi

q nndt

dn

*,,,

unpolfreerel

*,,,

v

jKKj

j nndt

dn

*,,,

unpolfreerelv

jKKj

j nndt

dn

*,,,

unpolfreerelv

jKKKj

KjK nn

dt

dn

*,,,

unpolfreerelv

jKKKj

jKK nn

dt

dn*

*,,,

unpolfree*rel

* v

Ratios of number densities

number density of hadronic matter

nH n+n+nK+nK*

Critical temperature Tc=0.175 GeV

T (GeV) nq/nH at time t=0.5 fm/c

0.174 0.87 in the chiral limit

0.174 0.33 with the constituent quark mass

0.16 0.11

0.15 0.05

0.14 0.02

SUMMARY

We have found:a. an appreciable amount of free quarks and antiquarks

produced by meson-meson reactions

b. a new mechanism for deconfinement of quarks and antiquarks at high temperature.

c. new form of matter below Tc : free quarks, free antiquarks and hadrons.

arXiv:0708.3804

22112211 )()( qqqqqqBqqA