Temperature-dependent Cross S ections for Meson-Meson Nonresonant R eactions in Hadronic Matter Xiao-Ming Xu Collaborators: Y.-P. Zhang, Hui-Jun Ge
Jan 06, 2016
Temperature-dependent Cross Sections for Meson-Meson Nonresonant Reactions
in Hadronic Matter
Xiao-Ming Xu
Collaborators: Y.-P. Zhang, Hui-Jun Ge
PHENIX results:
central Au-Au collisions, =200GeV, mid-rapidity
STAR results:
peripheral Au-Au collisions, =200GeV,mid-rapidity
NNs
984.0 933.0 KK
171.0 K 162.0 K
NNs
169.00
BRAHMS results: rapidity dependence in central collisions
constant near midrapidity
slowly decrease the other region
constant
,
K
KK
,
K
33 y
PHENIX results: pT and centrality dependences
constant
constant the whole centrality range
increase pT
increase centrality
cpT GeV/2 ,
K
K
,
K
K
,
KK
,
KK
Conclusion: , , K are dominant meson species in hadronic matter.
Role:(1) Meson-meson scatterings are crucial to chemical
equilibration, thermalization, hadron flows and hadron yields.
(2) Earlier decoupled mesons due to small cross sections can show relatively clear information on quark-gluon plasma.
Goal: meson-meson nonresonant reactions
I=2
I=1 KKKK*
I=1 KK*K*K
I=3/2 KK*
I=3/2 K*K*
I=3/2 KK*
I=3/2 K*K
Quark-interchange Mechanism
elastic scatterings:T. Barnes, E.S. Swanson, Phys. Rev. D46 (1992) 131
E.S. Swanson, Ann. Phys. 220 (1992) 73
J/ dissociation cross sections:K. Martins, D. Blaschke, E. Quack, Phys. Rev. C51 (1995) 2723
C.-Y. Wong, E.S. Swanson, T. Barnes, Phys. Rev. C65 (2001) 014903
T. Barnes, E.S. Swanson, C.-Y. Wong, X.-M. Xu, Phys. Rev. C68 (2003) 014903
X.-M. Xu, Nucl. Phys. A697 (2002) 825
Meson-meson nonresonant reactions:Y.-Q. Li, X.-M. Xu, Nucl. Phys. A 794 (2007) 210
Prior form: gluon propagation before quark interchange
Post form: gluon propagation after quark interchange
Phase shift
Cross section
)()( 1221 qqDqqC )()( 2211 qqBqqA
1
1
2
')'(2
dxxPTEE
EEPlfi
BA
BA
l
22222)2(
13
postfi
priorfi
DCBA
fi
MM
EEEET
2
0),(sin
'
32
1
tsMd
P
P
spriorfi
prior
2
postprior
S
SBA
unpol smSSSS
s ),,()12()12)(12(
1
postpostfiM
transition amplitude in the prior form
transition amplitude in the post form
3
3
3
3
)2()2(2222 1221
qqqq
DCBApriorfi
pdpdEEEEM
2211212121211221)( qqqqqqqqqqqqqqqq VVVV
2211111221
2111
3
3
3
3
)2()2(2222 qqqqqqqqqq
qqqqDCBA
postfi V
pdpdEEEEM
2211221221
1222
3
3
3
3
)2()2( qqqqqqqqqqqqqq V
pdpd
221121211221
1221 )()2()2( 3
3
3
3
qqqqqqqqqqqqqqqq VV
pdpd
in vacuum, Buchmuller-Tye potential
Linear confinement and the potential arising from one gluon exchange plus perturbative one- and two-loop corrections
r
rkrrV ba
ab
)(v
25
6
4
3
22)(
in vacuum, Potential in Momentum SpaceX.-M. Xu, Nucl. Phys. A697 (2002) 825
The first term is the Buchmuller-Tye potential.
The second term is the spin-spin interaction from the one-gluon exchange.
The third term is the spin-spin interaction from the one- and two- loop corrections to the one-gluon exchange.
)(16
22)( 2
2
2
QV baab
ba
baba
ba
baba
mm
ssQG
Qmm
ss
)(
25
16
2225
16
22
22
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.
Temperature-dependent potential in medium
critical temperature Tc=0.175 GeV.
)(exp
)(v
25
6)(tanh3.1
4
3
22)(
4
Err
rAr
T
TDrV
c
baab
the parametrization fit to the lattice data
meson masses from the schrodinger equation
in medium, Potential in Momentum Space
Calculate the transition amplitudes with the potential to obtain unpolarized cross sections
)(641)2(exp
)(sin8)()2(3.1
4
3
22)( 2
0
33
4
QEFAr
Qrrdr
T
TDQV
c
baab
ba
baba
ba
baba
mm
ssQG
Qmm
ss
)(
25
16
2225
16
22
22
I=2
I=1 KKKK*
Summary
We have obtained:
1. temperature-dependent potential fitted to the lattice data
2. temperature-dependent masses for , , K, K*
3. temperature-dependent cross sections for meson-meson nonresonant reactions