QCD phase diagram in an extended effective Lagrangian approach J. - PowerPoint PPT Presentation

Outline Introduction and formalism Results Conclusions QCD phase diagram in an extended effective Lagrangian approach J. Moreira 1 , J. Morais 1 , B. Hiller 1 , A. H. Blin 1 ,A. A. Osipov 2 1 Centro de Física da Univ. Coimbra, Coimbra, Portugal 2 Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Moscow region, Russia SEWM 2018, 28/06/2018 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 1 / 23

Outline Introduction and formalism Results Conclusions Outline Introduction and formalism 1 Motivation Nambu–Jona-Lasinio Model Extended Nambu–Jona-Lasinio Model: multi-quark interactions Extended Nambu–Jona-Lasinio Model: explicit chiral symmetry breaking interactions Thermodynamic potential Polyakov potentials Results 2 Extended NJL Extended NJL with Log. Polyakov potential Extended NJL with Exp. K-Log. Polyakov potential Correlations in the uds base Conclusions 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 2 / 23

Outline Introduction and formalism Results Conclusions Introduction QCD : the Theory of Strong Interactions Very successfull pQCD at high energy Non-perturbative low energy regime requires the use of other tools for instance: lQCD AdS/QCD Dyson-Schwinger FRG Chiral pertubation theory Effective models Dynamical / Explicit Chiral Symmetry Breaking plays a big role in low energy phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 3 / 23

Temperature T Quark-Gluon Plasma sQGP Critical Point I n h o m o g e n Quarkyonic e Hadronic Phase o u s Matter S ? c uSC B 2SC dSC Liquid-Gas CFL Color Superconductors CFL- K , Crystalline CSC 0 Nuclear Superfluid Baryon Chemical Potential m B Meson supercurrent Gluonic phase, Mixed phase Outline Introduction and formalism Results Conclusions Phase diagram for strongly interacting matter A clear and present challenge 1 : 1 N. Cabbibo, G. Parisi Phys.Lett. 59B (1975) 67-69; Kenji Fukushima, Tetsuo . . . . . . . . . . . . . . . . . . . . Hatsuda Rept.Prog.Phys.74:014001,2011; http://nica.jinr.ru/physics.php . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 4 / 23

Outline Introduction and formalism Results Conclusions Phase diagram for strongly interacting matter A clear and present challenge 1 : Temperature T Quark-Gluon Plasma sQGP Critical Point I n h o m o g e n Quarkyonic e Hadronic Phase o u s Matter S ? c uSC B 2SC dSC Liquid-Gas CFL Color Superconductors 0 CFL- K , Crystalline CSC Nuclear Superfluid Baryon Chemical Potential m B Meson supercurrent Gluonic phase, Mixed phase 1 N. Cabbibo, G. Parisi Phys.Lett. 59B (1975) 67-69; Kenji Fukushima, Tetsuo . . . . . . . . . . . . . . . . . . . . Hatsuda Rept.Prog.Phys.74:014001,2011; http://nica.jinr.ru/physics.php . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 4 / 23

Outline Introduction and formalism Results Conclusions Phase diagram for strongly interacting matter A clear and present challenge 1 : Temperature T Quark-Gluon Plasma sQGP Critical Point I n h o m o g e n Quarkyonic e Hadronic Phase o u s Matter S ? c uSC B 2SC dSC Liquid-Gas CFL Color Superconductors 0 CFL- K , Crystalline CSC Nuclear Superfluid Baryon Chemical Potential m B Meson supercurrent Gluonic phase, Mixed phase 1 N. Cabbibo, G. Parisi Phys.Lett. 59B (1975) 67-69; Kenji Fukushima, Tetsuo . . . . . . . . . . . . . . . . . . . . Hatsuda Rept.Prog.Phys.74:014001,2011; http://nica.jinr.ru/physics.php . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 4 / 23

Outline Introduction and formalism Results Conclusions Nambu–Jona-Lasinio Model NJL : effective model for the non-perturbative low energy regime of QCD with Dynamical Chiral Symmetry Breaking ( D χ SB ) NJL shares the global symmetries with QCD Dynamical generation of the constituent mass Light pseudoscalar as (quasi) Nambu-Goldstone boson Quark condensates as order parameter No gluons (no confinement/deconfinement) Local and non renormalizable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 5 / 23

Outline Introduction and formalism Results Conclusions Multi-quark interations ( u , d and s ) 2 L eff = q ı/ ∂ q + L m 2 Σ = ( s a − ı p a ) 1 2 λ a , s a = ¯ q λ a q , p a = ¯ . . . . . . . . . . . . . . . . . . . . q λ a ıγ 5 q , and a = 0 , 1 , . . . , 8 . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23

Outline Introduction and formalism Results Conclusions Multi-quark interations ( u , d and s ) 2 L eff = q ı/ ∂ q + L m Explicit Chiral symmetry breaking L m = q ˆ mq 2 Σ = ( s a − ı p a ) 1 2 λ a , s a = ¯ q λ a q , p a = ¯ . . . . . . . . . . . . . . . . . . . . q λ a ıγ 5 q , and a = 0 , 1 , . . . , 8 . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23

Outline Introduction and formalism Results Conclusions Multi-quark interations ( u , d and s ) 2 L eff = q ı/ ∂ q + L m + L NJL L m = q ˆ mq Nambu–Jona-Lasinio (4 q) Σ † Σ [ ] L NJL = G tr 2 Σ = ( s a − ı p a ) 1 2 λ a , s a = ¯ q λ a q , p a = ¯ . . . . . . . . . . . . . . . . . . . . q λ a ıγ 5 q , and a = 0 , 1 , . . . , 8 . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23

Outline Introduction and formalism Results Conclusions Multi-quark interations ( u , d and s ) 2 L eff = q ı/ ∂ q + L m + L NJL + L H L m = q ˆ mq [ Σ † Σ ] L NJL = G tr ’t Hooft determinant (6 q) Σ † ]) ( [ L H = κ det [Σ] + det 2 Σ = ( s a − ı p a ) 1 2 λ a , s a = ¯ q λ a q , p a = ¯ . . . . . . . . . . . . . . . . . . . . q λ a ıγ 5 q , and a = 0 , 1 , . . . , 8 . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23

Outline Introduction and formalism Results Conclusions Multi-quark interations ( u , d and s ) 2 L eff = q ı/ ∂ q + L m + L NJL + L H + L 8 q L m = q ˆ mq [ Σ † Σ ] L NJL = G tr ( [ Σ † ]) L H = κ det [Σ] + det Eight quark interaction term ]) 2 , L 8 q = L ( 1 ) 8 q + L ( 2 ) L ( 1 ) L ( 2 ) Σ † Σ Σ † ΣΣ † Σ ( [ [ ] 8 q , 8 q = g 1 tr 8 q = g 2 tr 2 Σ = ( s a − ı p a ) 1 2 λ a , s a = ¯ q λ a q , p a = ¯ . . . . . . . . . . . . . . . . . . . . q λ a ıγ 5 q , and a = 0 , 1 , . . . , 8 . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23

Outline Introduction and formalism Results Conclusions Multi-quark interations ( u , d and s ) 2 L eff = q ı/ ∂ q + L m + L NJL + L H + L 8 q L m = q ˆ mq [ Σ † Σ ] L NJL = G tr ( [ Σ † ]) L H = κ det [Σ] + det ]) 2 , L 8 q = L ( 1 ) 8 q + L ( 2 ) L ( 1 ) L ( 2 ) ( [ Σ † Σ [ Σ † ΣΣ † Σ ] 8 q , 8 q = g 1 8 q = g 2 tr tr OZI violation in L H and L ( 1 ) 8 q . 2 Σ = ( s a − ı p a ) 1 2 λ a , s a = ¯ q λ a q , p a = ¯ . . . . . . . . . . . . . . . . . . . . q λ a ıγ 5 q , and a = 0 , 1 , . . . , 8 . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23

Outline Introduction and formalism Results Conclusions Multi-quark interations ( u , d and s ) 2 L eff = q ı/ ∂ q + L m + L NJL + L H + L 8 q + L χ L m = q ˆ mq Extended Explicit Chiral symmetry breaking L χ [ Σ † Σ ] L NJL = G tr ( [ Σ † ]) L H = κ det [Σ] + det ]) 2 , L 8 q = L ( 1 ) 8 q + L ( 2 ) L ( 1 ) L ( 2 ) ( [ Σ † Σ [ Σ † ΣΣ † Σ ] 8 q , 8 q = g 1 8 q = g 2 tr tr Non canonical explicit chiral symmetry breaking terms 2 Σ = ( s a − ı p a ) 1 2 λ a , s a = ¯ q λ a q , p a = ¯ . . . . . . . . . . . . . . . . . . . . q λ a ıγ 5 q , and a = 0 , 1 , . . . , 8 . . . . . . . . . . . . . . . . . . . . J. Moreira (CFisUC,BLTP) QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23