medium effects in dense, excited hadron-quark...
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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 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