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Cold, dense quark matter NJL 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 Neutron Stars are born in Supernovae SN in A.D.1054 was visible from Earth with naked eyes Neutron Stars are born in Supernovae SN in A.D.1054 was visible from Earth with 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 SN in A.D.1054 was visible with naked eyes for 23 days Records found in: China 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 ? 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 it East-West schism the very same year Supernova remnant in Crab Nebula: Hubble ST detectable frequencies: - optical Courtesy of http://chandra.harvard.edu/photo/2009/crab Supernova remnant in Crab Nebula: detectable frequencies: - optical - infrared Spitzer ST Courtesy of http://chandra.harvard.edu/photo/2009/crab Supernova remnant in Crab Nebula: detectable frequencies: - optical - infrared - x-ray 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 & structured system Hubble ST Spitzer ST Chandra ST Courtesy of http://chandra.harvard.edu/photo/2009/crab Supernova remnant in Crab Nebula: Hubble ST detectable frequencies: - optical - infrared - x-ray Spitzer ST obviously a complex & structured system Chandra ST CRAB PULSAR Courtesy of http://chandra.harvard.edu/photo/2009/crab Supernova remnant in Crab Nebula: Hubble ST detectable frequencies: - optical - infrared - x-ray Spitzer ST obviously a complex & structured system Chandra ST CRAB PULSAR Age 958 yrs Rotation 29.6 /s Mass ? Radius ? Luminosity ? B-field ? Courtesy of http://chandra.harvard.edu/photo/2009/crab CRAB PULSAR Age 958 yrs Rotation 29.6 /s Mass ? Radius ? Luminosity ? B-field ? Courtesy of http://www.ast.cam.ac.uk/~optics/Lucky_Web_site 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 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 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 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 QCD Phase Diagram dense hadronic matter pQCD? 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 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)) 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 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 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 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 NS masses and the (QM) Equation of State NS mass is sensitive hadrons mainly to the sym. EoS Dense Nuclear Matter in terms of Quark DoF is barely understood Problem is attacked in vacuum Faddeev Equations (In particular true for heavy NS) Folcloric: QM is soft, hence no NS with QM core QCD Bethe Salpeter Equations Fact: QM is softer, but able to support QM core in NS Problem: (transition from NM to) QM is barely understood Baryons as composites of confined quarks and diquarks quarks NS masses and the (QM) Equation of State (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 confinement mainly to the sym. EoS hadrons QCD NS mass is sensitive dynamical breaking of chiral symmetry quarks 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 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 reminder Partition 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 NJL type models: brief reminder Effectively an ideal (SC) gas with medium dependent masses and chemical potentials 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 B Conclusion: 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 DSE ↔ NJL NJL model can be understood as an approximate solution of Dyson-Schwinger equations quark gluon q-g-vertex single particle: quark self energy Inverse (Single-)Quark Propagator: S ( p ; ) 1 Z 2 ( i p i 4 ( p 4 i ) m bm ) ( p ; ) i p revokes Poincaré covariance Renormalised Self Energy: ( p ; ) Z 1 g ( ) D ( p q ; ) 2 q a 2 S ( q ; ) ( q , p ; ) a Loss of Poincaré covariance increases complexity → technically and numerically more challenging → no surprise, though General Solution: Vacuum: 0 S ( p 2 ) 1 i p A ( p 2 ) B ( p 2 ) Medium: 0 S ( p 2 , p 4 ; ) 1 i p A ( p 2 , p 4 , ) i 4 ( p 4 i ) C ( p 2 , p 4 , ) B ( p 2 , p 4 , ) Similar structured equations in vacuum and medium, but in medium: 1. one more gap 2. gaps are complex valued 3. gaps depend on (4-)momentum, energy and chemical potential Effective gluon propagator S ( p ; ) 1 Z 2 ( i p i 4 ( p 4 i ) m bm ) ( p ; ) ( p ; ) Z 1 g ( ) D ( p q ; ) 2 q a 2 S ( q ; ) ( q , p ; ) a 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)) 2nd term NJL model: delta function in momentum space → Klähn et al. (2010) → Chen et al.(2008,2011) delta function in configuration space = const. In mom. space NJL model within DS framework gap solutions are momentum independent. Simple: A=1 Renormalization of chem. pot. due to vector interaction mass gap equation This is a 1 to 1 reproduction of the (basic) NJL model NJL model within DS framework Renormalization of chem. pot. due to vector interaction mass gap equation This is a 1 to 1 reproduction of the (basic) NJL model NJL model within DS framework Steepest descent approximation 1 to 1 NJL (regularization issue ignored) Renormalization of chem. pot. due to vector interaction mass gap equation This is a 1 to 1 reproduction of the (basic) NJL model NJL model within DS framework Steepest descent approximation 1 to 1 NJL (regularization issue ignored) Renormalization of chem. pot. due to vector interaction mass gap equation This is a 1 to 1 reproduction of the (basic) NJL model 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 * const while μ*<B No surprises * Preliminary Munczek/Nemirowsky -> NJL‘s complement MN antithetic to NJL NJL:contact interaction in x MN:contact interaction in p Munczek/Nemirowsky P ( ) P0 d n ( ) P0 const 0 2 2 2 p 2 Wigner Phase ~μ4 ~μ 5 .2 .4 2 GeV 2 p 2 2 2 to obtain 2 f1 ( p 0) 1 model is scale invariant regarding μ/η P ( ) well satisfied up to / 1 5 ( 1 . 09 GeV) ‚small‘ chem. Potential: 2 f 1 ( p 0, ) ← n ( ) T. Klahn, C.D. Roberts, L. Chang, H. Chen, Y.-X. Liu PRC 82, 035801 (2010) 2N cN 2 2 f d 3 p f1 ( p ) 4 5 DSE – simple effective gluon coupling Wigner Phase Less extreme, but again, 1particle number density distribution different from free Fermi gas distribution Chen et al. (TK) PRD 78 (2008) Conclusions NJL 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 nature result in quasi particle picture → essentially an ideal gas, eff. m and μ momentum dependent gap solutions enrich model space significantly and provide ability to investigate confinement/deconfinement + DCSB Conclusions Thank you! QCD 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