Hadronic interactions Hadronic interactions are strongly modifiedare strongly modified near the QCD critical near the QCD critical pointpoint

Edward ShuryakEdward ShuryakDepartment of Physics and AstronomyDepartment of Physics and Astronomy

State University of New YorkState University of New York

Stony Brook NY 11794 USAStony Brook NY 11794 USA

Overview

• sQGP

• New hydro phenomenon => Conical flow

• many mesons survive at T>Tc

• plus hundreds of exotic colored binary states.

• Lattice data hint towardLattice data hint toward lighter sigmalighter sigma•If sigma mass movesIf sigma mass moves Walecka cancellation is Walecka cancellation is violated and much violated and much stronger NN and rhoN stronger NN and rhoN potentialspotentials•When m(sigma) crosses When m(sigma) crosses 2m(pion)=>resonance 2m(pion)=>resonance ReV(pions) gets repulsiveReV(pions) gets repulsive•Should affect N and pi flows in opposite directions•Is it what is happeningat 40 GeV?

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

hydro describes both radial and elliptic flows (from Phenix)

proton pion

Hydro models:Teaney(w/ & w/oRQMD)

Hirano(3d)

Kolb

Huovinen(w/& w/oQGP)

nucl-ex/0410003

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

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

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

<p_t(\phi)> at

180 degr., with

a value

Consistent with background

Well-known facts Well-known facts about the critical pointabout the critical point

If mq is nonzero,2-nd order line =>CrossoverOnly one critical pointOnly sigma gets massless

A general pictureA general picture

Pion mass is nearly Pion mass is nearly unchangedunchanged

In shaded areaIn shaded area sigma sigma gets stablegets stable

Inside dashed line pion Inside dashed line pion av.pot.av.pot. gets repulsive gets repulsive

The corr. length is time The corr. length is time limitedlimited

mm 2

Em 2

Signals suggested Signals suggested beforebefore

Stephanov,ES,Rajagopal:Stephanov,ES,Rajagopal: e-by-e fluctuations should be e-by-e fluctuations should be

enhancedenhanced ``focusing” of adiabatic paths, which ``focusing” of adiabatic paths, which

tend to end near the critical pointtend to end near the critical point

(see nice work by Nonaka+Asakawa)(see nice work by Nonaka+Asakawa)

But both are very subtle! But both are very subtle!

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)

• 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 peakThe r.h.s.=>Baryon melting!

2)^/1( m

300/1)/exp( TMN

But But chiral susceptibility chiral susceptibility still still seem to show hints towardseem to show hints toward massless sigma ? => one has massless sigma ? => one has to reduce quark mass!to reduce quark mass!=> larger computers needed=> larger computers needed

The condensatechanges little

But much higher peak in the chiral Succeptibility:Ligter sigma

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

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

The average N The average N potentialpotential

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

A reminder:Effective pion-pion potential

and resonances

sigmaM is forward scattering amplitude, e.g.

M changes sign when sqrt(s)>m(sigma)!

Pion-pion interaction

Em 2

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

mm 2

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)

•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

Estimated effect on Estimated effect on the flows:the flows: RepulsiveRepulsive interaction interaction adds adds to to

radial and elliptic flows of radial and elliptic flows of pions!pions!

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

Now we go to 40 GeVA, NA49 Is the

collapse of the N flow (already

seen) our

signal? b

Summary

• New hydro phenomenon => Conical flow

• sQGP= many mesons survive at T>Tc

• plus hundreds of exotic colored binary states.

• Lattice data hint towardLattice data hint toward lighter sigmalighter sigma•When sigma mass When sigma mass smaller than 2m(pion)smaller than 2m(pion)V(pions) gets repulsiveV(pions) gets repulsive•If sigma mass movesIf sigma mass moves Walecka cancellation is Walecka cancellation is violated and much violated and much stronger NN and rhoN stronger NN and rhoN potentialspotentials•Should affect N and pion flows in opposite direction•Is it what is happeningat 40 GeV?

Additional slidesAdditional slides

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

Distribution of radial velocity v_r (left) and modulus v (right).

(note tsunami-like features, a positive and negative parts of the wave)

Calculation of the ionization rateES+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/Tc for a gluon 15,10,5 GeV. Red-elastic, black -ionization

How strong is strong?For a screened Coulomb potential, Schr.eqn.=>a simple

condition for a bound state

• (4/3)s (M/MDebye) > 1.68

• M(charm) is large, MDebye is not, about 2T

• If (Md) indeed runs and is about ½-1, it is large enough to bind charmonium till about T=3Tc

• Since q and g quasiparticles are heavy,

M about 3T, they are bound as well !

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).

Here is the binding and |psi(0)|^2 is indeed bound till nearly 3 Tc

E/2MVs T/Tc

/J

Solving for binary bound statesES+I.Zahed, hep-ph/0403127

• In QGP there is no confinement =>

• Hundreds of colored channels may have bound states as well!

The pressure puzzle is resolved!Masses, potentials and EoS from lattice are

mutually consistentM/Tc vc T/Tc and p/pSB vs T/Tc

``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

Can we verify existence of bound states at T>Tc experimentally?

Dileptons from sQGP: