Free Quarks versus Hadronic Matter

Xiao-Ming Xu

picture below the critical temperature Tc

CHALLENGE new form of matter below Tc:

free quarks, free antiquarks and hadrons

X.-M. Xu, R. Peng, arXiv:0708.3804; Chin. Phys. C33, 748 (2009)

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

T=0.58Tc

T=0.66Tc

T=0.74Tc

T=0.84Tc

T=0.9Tc

T=0.94Tc

T=0.97Tc

T=1.06Tc

T=1.15Tc

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.

Possibility for Creating Free Quarks and Antiquarks

plateau energy at T=0.16 GeV: 0.42 GeV

quark-antiquark relative-motion energy: 0.056 GeV, 0.436 GeV, K 0.113 GeV, K* 0.358 GeV

average kinetic energy: 0.366 GeV, 0.291 GeV, K 0.309 GeV, K* 0.285 GeV

A meson-meson collision to a full stop leads to

relative-motion energy + average kinetic energy:0.422 GeV for +, 0.727 GeV for +, 0.422 GeV for K+K,

0.643 GeV for K*+K*, larger than the plateau energy.

Quark and antiquark are in a scattering state, become free!

Cross Section

meson-meson reaction

a new mechanism for quark deconfinement

,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

We calculate

unpolarized cross sections for the production of free quarks and antiquarks in collisions

+, +, +K, +K*,

+, +K, +K*,

K+K, K+K*,

K*+K*

Cross sections for +, +K, +K* producing free quarks and antiquarksT=0.174 GeV (solid, chiral limit),

0.174 GeV (dashed, constituent quark mass), 0.16 GeV (dotted), 0.15 GeV (dot-dashed), 0.14 GeV (long dashed)

recombination of quark and antiquark

A free quark and a free antiquark combine into a meson M by radiating a gluon

Cross sections for the E1 transition are calculated via

C.-Y. Wong, J. Phys. G28 (2002) 2349

gMqq

master rate equation for free u and d quarks

nnnndt

dnq unpol

freerelunpol

freerel v2v

nnnnnn KKKK unpol

freerel*unpol

free*relunpol

freerel vv2

3v

2

3

KKKKKKKK nnnnnn unpol

freerel*unpol

free*relunpol

freerel v2

1v

2

3v

2

3

qqgqqKKKKKKKK nnnnnn unpol

rel**unpol

free**rel*unpol

free*rel vv2

1v

sqgKsqsqKgsqqqgqq nnnnnn unpol

*relunpol

relunpol

rel vvv

master rate equation for free s quarks

*unpol

free*relunpol

freerel v2

1v

2

1KKKK

s nnnndt

dn

KKKKKKKK nnnnnn unpol

freerel*unpol

free*relunpol

freerel v2

1v

2

1v

2

1

**unpol

free**rel*unpol

free*rel v2

1v KKKKKKKK nnnn

qsgKqsqsKgqs nnnn unpol

*relunpol

rel vv

master rate equations for , , K and K*

sqgsqjKKKj

KjK nnnn

dt

dn

unpol

Krel*,,,

unpolfreerel vv

sqgsqjKKKj

jKK nnnn

dt

dn

unpol

*Krel**,,,

unpolfree*rel

* vv

qqgqqjKKj

j nnnndt

dn

unpol

rel*,,,

unpolfreerel vv

qqgqqjKKj

j nnnndt

dn

unpol

rel*,,,

unpolfreerel vv

qsKgqs nn unpol

relv

qsgKqs nn unpol

*relv

ratios of number densities

number density of hadronic matter

nH n+n+nK+nK*

number density of free quarks

n=nq+ns

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

0.174 0.22 in the chiral limit

0.174 0.076 with the constituent quark mass

0.16 0.025

0.15 0.01

0.14 0.0038

Number density of free quarks T=0.174 GeV (solid, chiral limit),

0.174 GeV (dashed, constituent quark mass), 0.16 GeV (dotted), 0.15 GeV (dot-dashed), 0.14 GeV (long dashed)

n in the left panel, n in the right panel T=0.174 GeV (solid, chiral limit),

0.174 GeV (dashed, constituent quark mass), 0.16 GeV (dotted), 0.15 GeV (dot-dashed), 0.14 GeV (long dashed)

nK in the left panel, nK* in the right panel T=0.174 GeV (solid, chiral limit),

0.174 GeV (dashed, constituent quark mass), 0.16 GeV (dotted), 0.15 GeV (dot-dashed), 0.14 GeV (long dashed)

SUMMARY

a. an appreciable amount of free quarks and antiquarks produced by meson-meson reactions

b. a new mechanism for quark deconfinement at high temperature.

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

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