Cold , dense quark matter NJL type models and the need to go beyond

Cold, dense quark matterNJL type models and the need to go beyond

THOMAS KLÄHN

Collaborators: D. Zablocki, J.Jankowski, C.D.Roberts, R.Lastowiecki, D.B.Blaschke

2013/09/B/ST2/01560

Neutron Stars are born in Supernovae

SN in A.D.1054 was visible from Earth


SN in A.D.1054 was visible from Earthwith naked eyes


SN in A.D.1054 was visible from Earthwith naked eyes for 23 days

Compact Stars are born in Supernova

SN in A.D.1054 was visible with naked eyes for 23 days

AT DAYLIGHT

Neutron Stars are born in Supernova


Records found in: China



Records found in: China Middle East

?



Records found in: China Middle East America

Europe ... probably missed itEast-West schism the very same year

?

Hubble STSupernova remnant in Crab Nebula:

detectable frequencies:- optical

Courtesy of http://chandra.harvard.edu/photo/2009/crab

Spitzer ST


Supernova remnant in Crab Nebula:

detectable frequencies:- optical- infrared

Chandra ST



detectable frequencies:- optical- infrared - x-ray

Hubble ST

Spitzer ST

Chandra ST




obviously a complex &structuredsystem

Hubble ST

Spitzer ST

Chandra ST





CRAB PULSAR

Hubble ST

Spitzer ST

Chandra ST





CRAB PULSAR Age 958 yrs Rotatio

n29.6 /s

Mass ? Radius ?

Luminosity

? B-field ?

Courtesy of http://www.ast.cam.ac.uk/~optics/Lucky_Web_site

CRAB PULSAR Age 958 yrs Rotatio

n29.6 /s

Mass ? Radius ?

Luminosity

? B-field ?

Neutron Stars Variety of scenarios regarding inner structure: with or without QM

Question whether/how QCD phase transition occurs is not settled

Most honest approach: take both (and more) scenarios into account and compare to available data

Neutron Stars = Quark Cores? Variety of scenarios regarding inner structure: with or without QM

Question whether/how QCD phase transition occurs is not settled

Most honest approach: take both (and more) scenarios into account and compare to available data

QCD Phase Diagram

dense hadronic matter

HIC in collider experiments

Won’t cover the whole diagram

Hot and ‘rather’ symmetric

NS as a 2nd accessible option

Cold and ‘rather’ asymmetric

Problem is more complex than

It looks at first gaze www.gsi.de

http://www.gsi.de/

QCD Phase Diagram

dense hadronic matter

HIC in collider experiments

Won’t cover the whole diagram

Hot and ‘rather’ symmetric

NS as a 2nd accessible option

Cold and ‘rather’ asymmetric

Problem is more complex than

It looks at first gaze www.gsi.de

pQCD?

http://www.gsi.de/

Neutron Star Data

Data situation in general terms is good (masses, temperatures, ages, frequencies)

Ability to explain the data with different models in general is good, too.

... sounds good, but becomes tiresome if everybody explains everything …

For our purpose only a few observables are of real interest

Most promising: High Massive NS with 2 solar masses (Demorest et al., Nature 467, 1081-1083 (2010))

Thom

as Klähn – S

eoulA

pril 2

01

2

NS masses and the (QM) Equation of State NS mass is sensitive

mainly to the sym. EoS

(In particular true for

heavy NS)

Folcloric:

QM is soft, hence no

NS with QM core

Fact:

QM is softer, but able

to support QM core in NS

Problem:

(transition from NM to)

QM is barely understood




heavy NS)

Folcloric:


NS with QM core

Fact:



Problem:



Dense Nuclear Matter in terms of Quark DoF is barely understood

Problem is attacked in vacuum Faddeev Equations

Baryons as composites of confined quarks and diquarks

Bethe Salpeter Equations

quarks

hadrons

QC

D




heavy NS)

Folcloric:


NS with QM core

Fact:



Problem:



Dense Nuclear Matter in terms of Quark DoF is barely understood

Problem is attacked in vacuum Faddeev Equations

Baryons as composites of confined quarks and diquarks

Bethe Salpeter Equations

quarks

hadrons

QC

D

confinem

ent

dynam

ical bre

aki

ng o

f ch

iral sy

mm

etr

y

QCD in dense matter LQCD fails in dense (like DENSE) matter (Fermion-sign problem)

Perturbative QCD fails in non-perturbative domain

DCSB is explicitly not covered by perturbative approach:

Solution: ‘some’ non-perturbative approach ‘as close as possible’ to QCD

some = solvable; as close as possible = if possible DCSB, if possible confinement

State of the art: Nambu-Jona-Lasinio model(s) (+t.d. bag models, +hybrids)

NJL type models: brief reminderPartition function in path integral representation

Current-current interaction

Hubbard Stratonovich transformation

mean field approximation w.r. to bosonic fields -> shifts in mass, chem. Pot., 1p-energy -> quasi particles

Effectively an ideal (SC) gas with medium dependent masses and chemical potentials

NJL type models: brief reminder

2Nc

2Nc

NJL type models S: DCSB

V: renormalizes μ

D: diquarks → 2SC, CFL

TD Potential minimized

in mean-field approximation

Effective model by its nature;

can be motivated (1g-exchange)

doesn’t have to though and can

be extended (KMT, PNJL)

possible to describe hadrons

NJL model study for NS (TK, R.Łastowiecki, D.Blaschke, PRD 88, 085001

(2013))

Set A Set BConclusion: NS may or may not support a significant QM core.additional interaction channels won’t change this if coupling strengths are not precisely known.

DSE ↔ NJL NJL model can be understood as an approximate solution of Dyson-Schwinger

equations

quark

gluon

q-g-vertex

Vacuum:

single particle: quark self energyInverse (Single-)Quark Propagator:

Renormalised Self Energy:

Loss of Poincaré covariance increases complexity → technically and numerically more challenging → no surprise, though

General Solution:

Similar structured equations in vacuum and medium, but in medium:1. one more gap2. gaps are complex valued3. gaps depend on (4-)momentum, energy and chemical potential

);())(();(bm442

1 pmipipiZpS

pi

q

aa

pqqSqpDgZp );,();(2

);()();( 21

revokes Poincaré covariance

0 )()()( 2212 pBpApipS

0 ),,(),,()(),,();,(4

24

2444

214

2 ppBppCipippApippS Medium:

Effective gluon propagator);())(();(

bm4421 pmipipiZpS

q

aa

pqqSqpDgZp );,();(2

);()();( 21

Ansatz for self energy (rainbow approximation, effective gluon propagator(s))

Specify behaviour of

Infrared strength running coupling for large k (zero width + finite width contribution)

EoS (finite densities):1st term (Munczek/Nemirowsky (1983)) delta function in momentum space → Klähn et al. (2010)2nd term → Chen et al.(2008,2011)NJL model: delta function in configuration space = const. In mom. space

NJL model within DS framework

gap solutions aremomentum independent.Simple: A=1

Renormalization ofchem. pot. due tovector interaction

mass gap equation

This is a 1 to 1 reproduction of the (basic) NJL model



mass gap equation




mass gap equation


Steepest descent approximation

1 to 1 NJL (regularization issue ignored)

Regularization Regularization completely ignored so far. Two sources for infinities:- zero point energy (usually resolved by vacuum subtraction)- scalar density (quadratically divergent, no vacuum subtraction if mass is not const/medium dep.)

‘Standard’ NJL: Cutoff (hard, soft (e.g. Lorentz, Gauss), 4-momentum)- finite quark density for any T > 0 at any μ > 0 (an ideal gas is an ideal gas is an…)- Have no ‘strict’ definition of confinement, BUT- Intuitively confinement implies nq=0- problem for description of truly confined bound states in medium beyond a ‘chemical’ picture

Recently exploited to investigate meson properties (Gutierrez-Guerrero et al. 2010, …)proper time regularization scheme (Ebert et al. 1996)

UV: removes UV divergence +IR: removes poles in complex plane

Proper Time Regularization neat scheme in vacuum:

more complicated at finite chem. potential:

and then a bit more at finite chem. potential and temperature:

(leading term in θ4 =1 )

NJL

*

*

Preliminary

const while μ*<B

No surprises

Munczek/Nemirowsky -> NJL‘s complement

MN antithetic to NJLNJL: contact interaction in xMN: contact interaction in p

Wigner Phase

to obtain model is scale invariant regarding μ/η well satisfied up to

‚small‘ chem. Potential: ←

p

222 2 p

2

22 2

),0( 21 pf

1)0( 21 pf

41

32

)(2

2)(

pfpd

NNn fc

0

500 )()( constPndPP

5)( P 1/ GeV)09.1(

~μ5

~μ4

.2 .4 2 GeV

T. Klahn, C.D. Roberts, L. Chang, H. Chen, Y.-X. Liu PRC 82, 035801 (2010)

Munczek/Nemirowsky

Ideal gas

Wigner Phase Less extreme, but again, 1particle number density distribution different from free Fermi gas distribution

DSE – simple effective gluon coupling

Chen et al. (TK) PRD 78 (2008)

ConclusionsNJL model is a powerful tool to explore possible features of dense QCD

It possibly might be a too powerful tool

NJL mf approximation equals gluon mf in momentum space in DSE

NB: Momentum independent gap solutions in their very natureresult in quasi particle picture → essentially an ideal gas, eff. m and μ

momentum dependent gap solutions enrich model space significantlyand provide ability to investigate confinement/deconfinement + DCSB

ConclusionsQCD in medium (near critical line):

- Task is difficult- Not addressable by LQCD- Not addressable by pQCD- DSE are promising tool to tackle non-perturbative in-medium QCD- Qualitatively very different results depending on effective gluon coupling

Thank you!

Cold , dense quark matter NJL type models and the need to go beyond

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