Medium effects in dense, excited hadron-quark matter

D.VoskresenskyMEPhI -GSI- JINR

Phase DiagramsWater and Nuclear Matter

Low density,low T: HIC liquid-gas; excited nuclei; high density, low T: NS;SNNN pairing, π,K,ρ condensates, CSC phases; high T: chiral restoration, deconfinement

Crossover;

I order tr.

cond

various phases

SupernovaCSC fluct.

NICA,

RHIC?

Variety of phases: 12 crystalline,3 glass, liquid, vapor, CEP

Chapline et al. (2007)

-CEP

Mixedphase

• Condensed matter physics• Nuclei• Neutron stars • Heavy ion collisions

information comes from:

To see manifestation of in-medium effects in dense non-equilibrium and equilibrium nuclear

matter (including phase transitions)

to describe it thorough analysis is required

the same nuclear matter but at different conditions:

one should search for specific non-trivial effects on T-n plane:

Punch line: : new experiments

full pion propagator

dressed vertex

Poles yield zero-sound modes in scalar and spin channels

Low energy excitations in nuclear Fermi liquid (Landau-Migdal approach)

based on a separation of long and short scalesRe-summed NN interaction

Paremeters of short-range interaction are extracted from atomic nuclei

“Pion degrees of freedom in nuclear matter”, Migdal, Saperstein,Troitsky,D.V Phys.Rep.190 (1990).

known phenomena in Fermi liquid

Antikaon spectra in nuclear matter

spectral density of K- excitations in nuclear matter at saturation

Possibility of S and/or P wave antikaon condensation in dense NS interiors Kolomeitsev, D.V. NPA 588 (1995) 889; PRC68 (2003) 015803

vacuum spectrum

in-medium spectrum

K- production in Ni+Ni collisionwith energy 1.8 GeV per nucleon

white body radiation problemGeneral consideration: Knoll, D.V. Ann. Phys. 249 (1996)

Only for low T, quasiparticle approximation is valid (allows to cut diagrams over G )For soft radiation: quasiclassics (all graphs in first line are of the same order):LPM effect

Direct reactions from piece of matter (v in NS, e+e-, γ, K+ in HIC)

expansion in full G-+

-+

White-body radiation problem (at low T):direct reactions: Similar to di-lepton radiation problem in HIC

Masses of NS are different from 1.18+-0.02 Msun to >1.8-1.9 Msun

test of the density dependence of baryon interactions

Cooling of neutron stars

First 105 years a neutron star cools down by neutrino emission

intermediate cooling

rapid cooling

How to describe all groups within one cooling scenario?

slow cooling

3 groups:

Neutron star cooling data

>10^3 in emissivity

modified Urca

pair formation breaking

direct Urca

processes on meson condensate

information on in-medium NN interaction

information on pairing

most efficient reactions (needs >11-14% proton fraction)

information on symmetry energy

Neutrino emission reactions

[Blaschke, Grigorian, Voskresensky, AA 424 (2004)]Hadronic NS interior

Nuclear medium cooling scenario

Information about nuclear EoS

points-DU reaction thresholds –constraint on the symmetry energy

Information important for HIC:(i) strong density dependence of NN

interaction,(ii) models of EoS with low DU threshold

density (with a strong density dependence of the symmetry energy) have problems with description of NS cooling (two fast cooling),standard RMF models yield too low DU threshold.

EoS for a RMF-based model with scaled hadron masses and

couplings (SHMC)Kolomeitsev,D.V., Nucl.Phys.A759 (2005); Klahn, et al. Phys.Rev.C74 (2006),Khvorostukhin,Toneev,D.V. Nucl. Phys. A791 (2007), A813 (2008)

allows to resolve low DU threshold density problem and to fulfill several other constraints from NS data

Partial chiral symmetry restoration, BR scaling:effective masses of mesons drop with temperature and density,

mean field-nucleon couplings drop at approximately the same rate:

Idea: to include resonances and meson excitations and to apply SHMC model in hydro calculations of HIC reactions

decrease of hadron masses with n B and T

horizontal dotted lines mσ = 2mπ and mσ = mπ

N,ω,ρ σ

Dashed lines demonstrate the results of the perturbative treatment of boson excitation.

For QGP phase (T>Tcr) at zero baryon chemical potential we use lattice EoS

For T>Tcr it is not bad described by “heavy bag” model:

mu ~ md ~ 400 MeV; ms ~ 450 MeV, mg ~ 600 MeV,

B=(215 MeV)4

Ivanov, Skokov, Toneev, PRD71 (2005) 014005

Problem: Hadron pressure is too high or QGP pressure is too low; extra decrease of couplings is required for the H-QGP phase transition to occur

Dashed lines demonstrate the results of the perturbative treatment of boson excitation.

Curves labelled by 2/3 and 1/10 correspond to the case when all gσB couplings except for nucleons are suppressed by factors 2/3 and 1/10.

Problem: P >P ,arose since (i) many degrees of freedom are involved in hadron

resonances (ii) q-g are very massive that results in a low pressure in QGP phase

Possible solutions:(i) Coupling constants for resonances are additionally

suppressed (?)(ii) Hadron masses are not decreased (?)

may be more serious changes are required (?)(i) Incorrect interpretation of resonances as independent

particles (a sum-rule is welcome to diminish number of hadron degrees of freedom at large T) (?)

(ii) Inapplicability of standard phase transition theory to H-QGP phase transition (Mott-like transition, percolation effects, something else) (?)

h QGP

new experiments are welcome

new form of matter (non-Fermi liquid):completely blurred fermions (no quasiparticles, no

resonances – blurs)

Assume couplings are not desreased :

Dyugaev, JETP Lett. 58 (1993) 886; D.V. Nucl. Phys. A744 (2004) 378

Consider hot hadron-quark system at small baryon chemical potential

Electron-phonon interation in doped semiconductors

Analogy: electrons – baryons; phonons –light bosons (e.g. pions)

In condensed matter physics similar to:

There: enhanced electron-hole production Urbach law replaces the Boltzmann law even at low T

Completely blurred baryons due to strong interaction with boson resonances

Significant increase ofantibaryon production

HBC (hot Bose condensation) possibility: boson sub-system at high Tbecomes more dense than hot

Ratio of the fermion density to the corresponding Boltzmann quantity for gs =10 and gs =7

The effective scalar boson mass as functions of the temperature in units of Tbl.fs.

Dynamics of the first order phase transition and CEP:

Van der Waals-like EoS:Liquid-gas and H-QGP phase transitions

Skokov, D.V. , arXiv 0811.3868, Pisma ZhETF 90 (2009) 245; Nucl. Phys. A828 (2009) 401

We solve the system of hydro equations describing non-trivial fluctuations (droplets/bubbles, aerosol) in d=2 numerically, and for arbitrary d in the vicinity of the critical point analytically.

Supercooled gas; overheated liquid; aerosol-like mixture in spinodal

The Landau free energy

pressure

at critical point

Dynamics of I order phase transition near CEP

In dimensionless variables

processes in the vicinity of the phase transition critical point prove to be very slow

Hydrodynamical equations give for

where ρr is the reference density close to ρcr

viscosities

η/s ~1/4π:

η/s does not appear in equations of motion

for H-QGP phase transition: β~0.02-0.2 , for

Effectively very viscous fluidity!

Dynamics is controlled by the parameter β, which enters together with the second derivative in time. This parameter can be expressed in terms of the surface tension and the viscosity as

The larger viscosity and the smaller surface tension, the more viscous is the fluidity of seeds.

β<<1 regime of effectively viscous fluid β >>1 regime of perfect fluid

surface tension

(Tcr –T)/Tcr =0.15; Tcr=162 MeV; L=5 fm; β =0.2

Hadron-QGP phase transition: droplet/bubble evolution in metastable phases

R<RcrR>Rcr

droplet

bubble

Hadron-QGP phase transition: spinodal instability: aerosol-like mixture (mixed phase)

see also Randrup, PRC79 (2009) 024601

Far from CEP time evolution is sufficiently rapid –effect of warm Champagne

growing modes oscillating modes

typical time of the heat transport

Fog stage of a phase transition

for H-QGP phase transition Rfog~0.1-1 fm

typical seed size at which tρ=tT

Thus Tcr calculated in thermal models might be significantly higher than thevalue which may manifest in fluctuations in HIC

Heat transport effects may play important role

Anomalies in thermal fluctuations near CEP may have not sufficient time to develop

The larger viscosity and the smaller surface tension the effectively more viscous is the fluidity

Effects of spinodal decomposition

Manifestation of CSC fluctuations above Tcsc in HIC (?)

In some models Tcsc~100 MeV. At T<Tcsc

I or/and II order CSC phase transitions are possible, Gi ~1, fluctuation region can be very broad: (0.5-1.5) Tcsc

coherence length ξ ~0.2 fm |(Tcr-T)/Tcr |-1/2 is short at T far from Tcsc, thus fluctuations with smaller T in ~ξ3

volume are probable leading to accumulation of CSC domains with |(Tcr-T)/Tcr << 1 evolving slowly in time,

, a kind of mixed phase

D.V. PRC69 (2004) 06529, see also Kitazawa et. al. PRD65 (2002) 091504

• Careful analysis of fluctuations is requiredto distinguish different medium effects

• Search for anomalies in flow (due to phase transition and shock wave phenomena)

• One may hope to observe non-monotoneousbehavior of different observables due to manifestation of in-medium (and non-trivial fluctuation) effects at monotonous increase of collision energies:

collision energy increase with a certain energy step will be possible at NICA

On menu at NICAExamples of mixed phasesBack to punch line:

medium (and even strong ☺ effects) are expected