1. Free Quarks versus Hadronic Matter Xiao-Ming Xu

2. picture below the critical temperature T c

3. CHALLENGE new form of matter below T c : free quarks, free antiquarks and hadrons X.-M. Xu, R. Peng, arXiv:0708.3804; Chin. Phys. C33, 748 (2009)

4. F. Karsch, et al., Nucl. Phys. B605, 579 (2001) T=0.58T c T=0.66T c T=0.74T c T=0.84T c T=0.9T c T=0.94T c T=0.97T c T=1.06T c T=1.15T c

5. 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.

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

7. 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!

8. Cross Section meson-meson reaction a new mechanism for quark deconfinement

9. quark-quark potential Transition amplitude M fi is derived from quark-antiquark wave functions and the quark-quark potential b(T)=0.35[1-(T/T c ) 2 ]  (T c -T)  (T)=0.28  (T c -T) T c =0.175 GeV, d=0.897 GeV m u =m d =0.334 GeV, m s =0.575 GeV C.-Y. Wong, Phys. Rev. C65, 034902 (2002)

10. unpolarized cross section (1) L A =L B =0 (2) L A =0, L B  0, S A =0 (3) L A =0, L B =1, S A =1, S B =1

11. 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*

12. Cross sections for  + ,  +K,  +K* producing free quarks and antiquarks 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)

13. 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

14. master rate equation for free u and d quarks

15. master rate equation for free s quarks

16. master rate equations for , , K and K*

17. ratios of number densities number density of hadronic matter n H  n  +n  +n K +n K*  number density of free quarks n=n q +n s T (GeV) n/n H 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

18. 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)

19. 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)

20. n K in the left panel, n K* 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)

21. 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 T c : free quarks, free antiquarks and hadrons.