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

QQ

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

QQ

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