free quarks versus hadronic matter xiao-ming xu. picture below the critical temperature t c
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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)