1. Hadronic interactions are strongly modified near the QCD critical point Edward Shuryak Department of Physics and Astronomy State University of New York Stony Brook NY 11794 USA

2. Overview sQGP New hydro phenomenon => Conical flow many mesons survive at T>Tc plus hundreds of exotic colored binary states. Lattice data hint toward lighter sigma Lattice data hint toward lighter sigma If sigma mass moves Walecka cancellation is violated and much stronger NN and rhoN potentialsIf sigma mass moves Walecka cancellation is violated and much stronger NN and rhoN potentials When m(sigma) crosses 2m(pion)=>resonance ReV(pions) gets repulsiveWhen m(sigma) crosses 2m(pion)=>resonance ReV(pions) gets repulsive Should affect N and pi flows in opposite directions Is it what is happening at 40 GeV?

3. Overview: sQGP: Very good liquid a Phase Diagram with ``zero binding lines” (ES+I.Zahed hep-ph/030726, PRC) it had one colored state, qq already but there are many more T The lines marked RHIC and SPS show the adiabatic cooling paths Chemical potential  B

4. hydro describes both radial and elliptic flows (from Phenix) protonpion Hydro models: Teaney (w/ & w/o RQMD) Hirano (3d) Kolb Huovinen (w/& w/o QGP) nucl-ex/0410003

5. Sonic boom from quenched jets Casalderrey,ES,Teaney, hep-ph/0411..; H.Stocker… the energy deposited by jets into liquid-like strongly coupled QGP must go into conical shock waves, similar to the well known sonic boom from supersonic planes. We solved relativistic hydrodynamics and got the flow picture If there are start and end points, there are two spheres and a cone tangent to both

6. Is such a sonic boom already observed? Mean Cs=.33 time average over 3 stages=> M.Miller, QM04 flow of matter normal to the Mach cone seems to be observed! See data from STAR,  +/- 1.23=1.91,4.37

7. PHENIX jet pair distribution (from B.Jacak) Note: it is only projection of a cone on phi Note 2: more recent data from STAR find also a minimum in at 180 degr., with a value Consistent with background

8. Well-known facts about the critical point If mq is nonzero, 2-nd order line => Crossover Only one critical point Only sigma gets massless

9. A general picture Pion mass is nearly unchanged Pion mass is nearly unchanged In shaded area sigma gets stable In shaded area sigma gets stable Inside dashed line pion av.pot. gets repulsive Inside dashed line pion av.pot. gets repulsive The corr. length is time limited The corr. length is time limited

10. Signals suggested before Stephanov,ES,Rajagopal: e-by-e fluctuations should be enhanced e-by-e fluctuations should be enhanced ``focusing” of adiabatic paths, which tend to end near the critical point ``focusing” of adiabatic paths, which tend to end near the critical point (see nice work by Nonaka+Asakawa) But both are very subtle!

11. Peaks get sharper! (in isoscalar but not isovector dens. Susceptibility): can it be a sign of a massless sigma? ( (mu/T)^6, Bielefeld+UK,hep-lat)

12. In vacuum and at mu=0, finite T sigma cannot show in vector correlators – C parity… => no peak But at nonzero it is in fact possible due to 2-loop diagram Unfortunately small due to 2 baryons (K.Redlich) while the usual resonance gas describes well the l.h.s. of the peak The r.h.s.=> Baryon melting!

13. But chiral susceptibility still seem to show hints toward massless sigma ? => one has to reduce quark mass! => larger computers needed The condensate changes little But much higher peak in the chiral Succeptibility: Ligter sigma

14. NN interactions The well known Walecka model => near exact cancellation between the two potentials If sigma mass ->0, huge attraction, if omega mass also - >0, huge repulsion

15. Examples of modified NN potential Black – the usual Red sigma mass=280 MeV and usual omega Blue (``realistic”) is sigma mass=280 MeV and omega mass=500 MeV

16. The average N potential

17. Rho,omega mass shifts Mesons don’t have omega-induced repulsion => no cancellations V(vectors)=(2/3)V(baryons) Tested at RHIC (STAR) where (according to G.Brown+ES) it contributed about 30 MeV to observed rho mass shift Reduction of m(sigma) by factor 2 leads to a factor 4 increase, to about 120 MeV, (and that was for near-freezeout T=120 MeV) This is additional to other reasons for mass shift, and produces no width NA60 also sees excess at M=400-500 MeV in a dilepton spectrum, although less than CERES

18. A reminder: Effective pion-pion potential and resonances M is forward scattering amplitude, e.g. M changes sign when sqrt(s)>m(sigma)!

19. Pion-pion interaction At the boundary of the the shaded region sigma acts as the Feshbach resonance for cold atoms, making pion gas a liquid! Inside the dashed line Pion-pion interaction gets repulsive

20. Pion potential induced by sigma Re(V_eff(p=0,m_sigma)) [GeV] vs the sigma mass [GeV] Change from attraction to repulsion! A singularity at 2m(pion)

21. Sigma as additional slow field (a la magnito-hydrodynamics) Dumitru et al Much stronger (more attractive) NN forces => reduction of Nucleon radial and elliptic (V2) flows Effect on N flows

22. Estimated effect on the flows: Repulsive interaction adds to radial and elliptic flows of pions! Repulsive interaction adds to radial and elliptic flows of pions!

23. Let us now loot at the data, e.g. This is 158 GeVA from NA49, left v2 for pions, right for N, 3 centrality bins It is the normal case, with maxima at midrapidity

24. Now we go to 40 GeVA, NA49 Is the collapse of the N flow (already seen) our signal? b

25. Summary New hydro phenomenon => Conical flow sQGP= many mesons survive at T>Tc plus hundreds of exotic colored binary states. Lattice data hint toward lighter sigma Lattice data hint toward lighter sigma When sigma mass smaller than 2m(pion)When sigma mass smaller than 2m(pion) V(pions) gets repulsive If sigma mass moves Walecka cancellation is violated and much stronger NN and rhoN potentialsIf sigma mass moves Walecka cancellation is violated and much stronger NN and rhoN potentials Should affect N and pion flows in opposite direction Is it what is happening at 40 GeV?

26. Additional slides

27. Evaluating the Mach cone Distance traveled by sound is reduced since it is 1/3^(1/2) in QGP, about 0 in the mixed phase and.2^(1.2) in a resonance gas Cs_av=\int dt c_s(t)/t_f =.33 (not Cs^2!) Theta=arcos(Cs_av/c)=71 degrees or 1.23 rad

28. Distribution of radial velocity v_r (left) and modulus v (right). (note tsunami-like features, a positive and negative parts of the wave)

29. Calculation of the ionization rate ES+Zahed, hep-ph/0406100 Smaller than radiative loss if L>.5-1 fm Is there mostly near the zero binding lines, Thus it is different from both radiative and elastic looses, which are simply proportional to density Relates to non-trivial energy dependence of jet quenching (smaller at 62 and near absent at SPS) dE/dx in GeV/fm vs T/T c for a gluon 15,10,5 GeV. Red-elastic, black -ionization

30. How strong is strong? For a screened Coulomb potential, Schr.eqn.=>a simple condition for a bound state (4/3)  s (M/M D ebye ) > 1.68 M(charm) is large, M Debye is not, about 2T If  (M d ) indeed runs and is about ½-1, it is large enough to bind charmonium till about T=3T c Since q and g quasiparticles are heavy, M about 3T, they are bound as well !

31. Digression : Relativistic Klein-Gordon eqn has a critical Coulomb coupling for falling onto the center (known since 1920’s) (4/3)  s =1/2 is too strong, a critical value for Klein-Gordon (and it is 1 for Dirac).

32. Here is the binding and |psi(0)|^2 is indeed bound till nearly 3 Tc E/2M Vs T/Tc

33. Solving for binary bound states ES+I.Zahed, hep-ph/0403127 In QGP there is no confinement => Hundreds of colored channels may have bound states as well!

34. The pressure puzzle is resolved! Masses, potentials and EoS from lattice are mutually consistent M/Tc vc T/Tc and p/p SB vs T/Tc

35. ``Polymerization of sQGP? Multibody bound states (Casalderrey and ES, in progress) Qbar - g - g - g -…- g - Q color convoluted inside naturally ``Polymeric chains” are better bound than pairs because instead of m(reduced)=m/2 in relative motion in binaries there is nearly the full mass for polymers

36. Can we verify existence of bound states at T>Tc experimentally? Dileptons from sQGP: