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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
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Neutron Stars are born in Supernovae
SN in A.D.1054 was visible from Earth
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Neutron Stars are born in Supernovae
SN in A.D.1054 was visible from Earthwith naked eyes
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Neutron Stars are born in Supernovae
SN in A.D.1054 was visible from Earthwith naked eyes for 23 days
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Compact Stars are born in Supernova
SN in A.D.1054 was visible with naked eyes for 23 days
AT DAYLIGHT
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Neutron Stars are born in Supernova
SN in A.D.1054 was visible with naked eyes for 23 days
Records found in: China
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Neutron Stars are born in Supernova
SN in A.D.1054 was visible with naked eyes for 23 days
Records found in: China Middle East
?
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Neutron Stars are born in Supernova
SN in A.D.1054 was visible with naked eyes for 23 days
Records found in: China Middle East America
Europe ... probably missed itEast-West schism the very same year
?
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Hubble STSupernova remnant in Crab Nebula:
detectable frequencies:- optical
Courtesy of http://chandra.harvard.edu/photo/2009/crab
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Spitzer ST
Courtesy of http://chandra.harvard.edu/photo/2009/crab
Supernova remnant in Crab Nebula:
detectable frequencies:- optical- infrared
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Chandra ST
Courtesy of http://chandra.harvard.edu/photo/2009/crab
Supernova remnant in Crab Nebula:
detectable frequencies:- optical- infrared - x-ray
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Hubble ST
Spitzer ST
Chandra ST
Courtesy of http://chandra.harvard.edu/photo/2009/crab
Supernova remnant in Crab Nebula:
detectable frequencies:- optical- infrared - x-ray
obviously a complex &structuredsystem
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Hubble ST
Spitzer ST
Chandra ST
Courtesy of http://chandra.harvard.edu/photo/2009/crab
Supernova remnant in Crab Nebula:
detectable frequencies:- optical- infrared - x-ray
obviously a complex &structuredsystem
CRAB PULSAR
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Hubble ST
Spitzer ST
Chandra ST
Courtesy of http://chandra.harvard.edu/photo/2009/crab
Supernova remnant in Crab Nebula:
detectable frequencies:- optical- infrared - x-ray
obviously a complex &structuredsystem
CRAB PULSAR Age 958 yrs Rotatio
n29.6 /s
Mass ? Radius ?
Luminosity
? B-field ?
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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 ?
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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
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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
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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
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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
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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
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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
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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?
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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))
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Thom
as Klähn – S
eoulA
pril 2
01
2
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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
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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
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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
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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
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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
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
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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
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
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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)
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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
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Effectively an ideal (SC) gas with medium dependent masses and chemical potentials
NJL type models: brief reminder
2Nc
2Nc
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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
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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.
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DSE ↔ NJL NJL model can be understood as an approximate solution of Dyson-Schwinger
equations
quark
gluon
q-g-vertex
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DSE ↔ NJL NJL model can be understood as an approximate solution of Dyson-Schwinger
equations
quark
gluon
q-g-vertex
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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:
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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
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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
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NJL model within DS framework
Renormalization ofchem. pot. due tovector interaction
mass gap equation
This is a 1 to 1 reproduction of the (basic) NJL model
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NJL model within DS framework
Renormalization ofchem. pot. due tovector interaction
mass gap equation
This is a 1 to 1 reproduction of the (basic) NJL model
Steepest descent approximation
1 to 1 NJL (regularization issue ignored)
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NJL model within DS framework
Renormalization ofchem. pot. due tovector interaction
mass gap equation
This is a 1 to 1 reproduction of the (basic) NJL model
Steepest descent approximation
1 to 1 NJL (regularization issue ignored)
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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
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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 )
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NJL
*
*
Preliminary
const while μ*<B
No surprises
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Munczek/Nemirowsky -> NJL‘s complement
MN antithetic to NJLNJL: contact interaction in xMN: contact interaction in p
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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
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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)
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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
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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!