hadronic interactions are strongly modified near the qcd critical point edward shuryak department of...
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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: