Locating QCD s critical end point

Transcription

1 Locating QCD s critical end point Christian S. Fischer Justus Liebig Universität Gießen 31st of Oct 2016 Eichmann, CF, Welzbacher, PRD93 (2016) [ ] Eichmann, Sanchis-Alepuz, Williams, Alkofer, CF, PPNP in press [ ] Christian S. Fischer (University of Gießen) Locating QCD s critical end point 1 / 26

2 Overview 1.Introduction 2.Gluons, quarks and the CEP 3.Baryon effects on the CEP dq dq NB N Christian S. Fischer (University of Gießen) Locating QCD s critical end point 2 / 26

3 QCD phase transitions Text text Text2 text Text3 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 3 / 26

4 QCD phase transitions Text text Text2 text Text3 chemical potential Is this happening?? Christian S. Fischer (University of Gießen) Locating QCD s critical end point 3 / 26

5 QCD phase transitions Text text Text2 text Text3 chemical potential Lattice-QCD present: extrapolation future: exact methods? DSE/FRG not exact, but allow for 10%-physics Is this happening?? Christian S. Fischer (University of Gießen) Locating QCD s critical end point 3 / 26

6 Search for the CEP Taylor expansion (Nf2): Datta, Gavai and Gupta, NPA (2013) 883c! Gavai, Gupta, PRD 71 (2005) Reweighting (Nf21): Fodor, Katz, JHEP 0404 (2004) 050 Analytic continuation (Nf3): de Forcrand, Philipsen, JHEP 0811 (2008) 012;! NPB 642 (2002) 290 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 4 / 26

7 Chiral transition line from analytic continuation μ 0 1 iµ Calc. boundary at imaginary μ Lattice method: and extrapolate to real μ Control systematics Calc. boundary at imaginary μ and extrapolate to real μ Control systematics Results: Larger curvature than previous results (but: different definitions and error budget) Bellwied, Borsanyi, Fodor, Günther, Katz, Ratti and Szabo, PLB B 751 (2015) 559 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 5 / 26

8 Overview 1.Introduction 2.Gluons, quarks and the CEP 3.Baryon effects on the CEP dq dq NB N Christian S. Fischer (University of Gießen) Locating QCD s critical end point 6 / 26

9 QCD order parameters from propagators Chiral order parameter: h i Z 2 N c Tr D 1 T X Z d 3 p S( p, ) (2 ) 3 Deconfinement: dressed Polyakov loop Z 2 0 d 2 e i h i Synatschke, Wipf, Wozar, PRD 75, (2007) Bilgici, Bruckmann, Gattringer, Hagen, PRD (2008) CF, PRL (2009) Polyakov loop potential L 1 N c Tre ig A 0 Braun, Gies, Pawlowski, PLB 684, 262 (2010) Braun, Haas, Marhauser, Pawlowski, PRL 106 (2011) Fister, Pawlowski, PRD (2013) CF, Fister, Luecker, Pawlowski, PLB 732 (2013) ( S) A Christian S. Fischer (University of Gießen) Locating QCD s critical end point 7 / 26

10 Nf21-QCD with DSEs quenched propagator from lattice up/down strange quenched: without quark-loop Nf2: Nf21: isospin symmetry solve coupled system of 233 equations Vertex: ansatz built along STI and known UV/IR behaviour Christian S. Fischer (University of Gießen) Locating QCD s critical end point 8 / 26

11 Glue at finite temperature (T 0) T-dependent gluon propagator from quenched lattice simulations: T0 T0.6 T c T0.99 T c T2.2 T c 2 T0 T0.6 T c T0.99 T c T2.2 T c Z T (p) 1 Z L (p 2 ) p 2 [Gev 2 ] p 2 [Gev 2 ] Crucial difference between magnetic and electric gluon Maximum of electric gluon near Tc Cucchieri, Maas, Mendes, PRD 75 (2007) CF, Maas, Mueller, EPJC 68 (2010) FRG: Fister, Pawlowski, arxiv: Cucchieri, Mendes, PoS FACESQCD 007 (2010) Aouane, Bornyakov, Ilgenfritz, Mitrjushkin, Muller-Preussker and Sternbeck, PRD 85 (2012) Silva, Oliveira, Bicudo, Cardoso, PRD 89 (2014) Christian S. Fischer (University of Gießen) Locating QCD s critical end point 9 / 26

12 Approximation for Quark-Gluon interaction T,μ,m-dependent vertex: Abelian WTI (q, k, p) Z e C(k) C(p) d 1 d 2 q 2 q2 2 q 2 A(k) A(p) j j 2 0 (µ)ln[q 2 / 2 2! 1] 4 perturbation theory Infrared ansatz: d2 fixed to match gluon input d1 fixed via quark condensate (see later) correct UV (quant.) and IR-behavior (qual.) explicit solutions at T0: Mitter, Pawlowski and Strodthoff, PRD 91 (2015) Williams, CF, Heupel, PRD PRD 93 (2016) Christian S. Fischer (University of Gießen) Locating QCD s critical end point 10 / 26

13 Critical line/surface for heavy quarks Polyakov Loop: Φ m 320 MeV m 363 MeV m 400 MeV Mean-field scaling (T-T c )/T c T [MeV] Deconfinement transition in agreement with lattice QCD Correct tricritical scaling Fromm, Langelage, Lottini, Philipsen, JHEP 1201 (2012) 042 CF, Luecker, Pawlowski, PRD 91 (2015) 1 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 11 / 26

14 Critical line/surface for heavy quarks Polyakov Loop: Φ m 320 MeV m 363 MeV m 400 MeV Mean-field scaling (T-T c )/T c T [MeV] Deconfinement transition in agreement with lattice QCD Correct tricritical scaling Fromm, Langelage, Lottini, Philipsen, JHEP 1201 (2012) 042 CF, Luecker, Pawlowski, PRD 91 (2015) 1 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 11 / 26

15 Nf21, μ0, physical point 1 0,8 zero chemical potential Lattice QCD Quark Condensate dressed Polyakov Loop l,s (T)/ l,s (0) 0,6 0,4 0, T [MeV] Lattice: Borsanyi et al. [Wuppertal-Budapest], JHEP 1009(2010) 073 DSE: CF, Luecker, PLB 718 (2013) 1036, CF, Luecker, Welzbacher, PRD 90 (2014) Christian S. Fischer (University of Gießen) Locating QCD s critical end point 12 / 26

16 Nf21, μ0, physical point zero chemical potential Lattice QCD Quark Condensate dressed Polyakov Loop l,s (T)/ l,s (0) T [MeV] Lattice: Borsanyi et al. [Wuppertal-Budapest], JHEP 1009(2010) 073 DSE: CF, Luecker, PLB 718 (2013) 1036, CF, Luecker, Welzbacher, PRD 90 (2014) Christian S. Fischer (University of Gießen) Locating QCD s critical end point 12 / 26

17 Nf21, μ0, physical point l,s (T)/ l,s (0) zero chemical potential Lattice QCD Quark Condensate dressed Polyakov Loop Z L T 187 MeV Quenched T 215 MeV Quenched T 235 MeV Quenched T 187 MeV Lattice T 215 MeV Lattice T 235 MeV Lattice T 187 MeV DSE T 215 MeV DSE T 235 MeV DSE T [MeV] p [GeV] Lattice: Borsanyi et al. [Wuppertal-Budapest], JHEP 1009(2010) 073 DSE: CF, Luecker, PLB 718 (2013) 1036, CF, Luecker, Welzbacher, PRD 90 (2014) Lattice: Aouane, et al.prd D87 (2013), [arxiv: ] DSE: CF, Luecker, PLB 718 (2013) 1036, [arxiv: ] quantitative agreement: DSE prediction verified by lattice Christian S. Fischer (University of Gießen) Locating QCD s critical end point 12 / 26

18 Nf21: Condensate and dressed Polyakov Loop Quark condensate Polyakov-Loop L 1 N c tr e ig R A 0 CF, Fister, Luecker, Pawlowski, PLB 732 (2014) 273 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 13 / 26

19 Nf21: phase diagram T [MeV] DSE: chiral crossover DSE: critical end point DSE: chiral first order DSE: deconfinement crossover µ q [MeV] Christian S. Fischer (University of Gießen) Locating QCD s critical end point 14 / 26

20 Nf21: phase diagram µ B /T2 µ B /T3 T [MeV] DSE: chiral crossover DSE: critical end point DSE: chiral first order DSE: deconfinement crossover µ q [MeV] CEP at large μ CF, Luecker, PLB 718 (2013) 1036, CF, Fister, Luecker, Pawlowski, PLB 732 (2014) 273 CF, Luecker, Welzbacher, PRD 90 (2014) combined evidence of FRG and DSE: no CEP at μb/t<2 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 14 / 26

21 Nf21: phase diagram T [MeV] 200 µ B /T2 µ B /T Lattice: DSE: chiral curvature crossover range κ DSE: chiral critical crossover end point DSE: critical chiral first end order point DSE: chiral deconfinement first ordercrossover DSE: deconfinement crossover µ q [MeV] Extrapolated curvature from lattice Kaczmarek at al. PRD 83 (2011) , Endrodi, Fodor, Katz, Szabo, JHEP 1104 (2011) 001 Cea, Cosmai, Papa, PRD 89 (2014), PRD 93 (2016) Bonati et al., PRD 92 (2015) Bellwied et al. PLB 751 (2015) 559 CEP at large μ CF, Luecker, PLB 718 (2013) 1036, CF, Fister, Luecker, Pawlowski, PLB 732 (2014) 273 CF, Luecker, Welzbacher, PRD 90 (2014) combined evidence of FRG and DSE: no CEP at μb/t<2 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 14 / 26

22 Nf211: effects of charm up/down strange charm Physical up/down, strange and charm quark masses Transition controlled by chiral dynamics no lattice or model results available yet Christian S. Fischer (University of Gießen) Locating QCD s critical end point 15 / 26

23 Nf211: effects of charm up/down strange 1.2 charm 1 Physical up/down, strange and charm quark masses Transition controlled by chiral dynamics no lattice or model results available yet T/T c (µ0) N f 21 N f 211 Effects very small! µ u/d [MeV] CF, Luecker, Welzbacher, PRD 90 (2014) Christian S. Fischer (University of Gießen) Locating QCD s critical end point 15 / 26

24 Location of CEP in freece-out landscape Figure taken from talk of T. Galatyuk, Erice 2016 Caveats: inhomogeneous phases effects of baryons? Müller, Buballa and Wambach, PLB 727 (2013) 240 Nc2: Brauner, Fukushima and Hidaka, PRD 80 (2009) Strodthoff, Schaefer and Smekal, PRD 85 (2012) Christian S. Fischer (University of Gießen) Locating QCD s critical end point 16 / 26

25 Overview 1.Introduction 2.Gluons, quarks and the CEP 3.Baryon effects on the CEP dq dq NB N Christian S. Fischer (University of Gießen) Locating QCD s critical end point 17 / 26

26 QCD phase transitions I Fukushima, Hatsuda, Rept. Prog. Phys. 74 (2011) Text Low temperatures, large chemical potential: baryons are important degrees of freedom How do baryons affect the quark condensate?? Christian S. Fischer (University of Gießen) Locating QCD s critical end point 18 / 26

27 Baryons: Quark model Text text Text2 text Text3 Loring, Metsch, Petry, EPJA 10 (2001) 395 missing resonances - three-body vs. quark-diquark level ordering: N 1 2 ± vs. ± 1 2 > Eichmann, A2 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 19 / 26

28 Extracting spectra from correlators DSE/BSE Lattice BSE for baryons (derived from equation of motion for G) exact equation for baryon wave function Christian S. Fischer (University of Gießen) Locating QCD s critical end point 20 / 26

29 Baryon effects onto quark Off-shell baryon in vertex NB B dq dq NB N Dependence on T and μ via -propagators -wave functions Exploratory calculation: use wave functions from Tμ0 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 21 / 26

30 Vacuum: Baryons from BSEs BSE for baryons (derived from equation of motion for G) Faddeev equation (no three-body forces) Diquark-quark Christian S. Fischer (University of Gießen) Locating QCD s critical end point 22 / 26

31 Vacuum: Baryons from BSEs BSE for baryons (derived from equation of motion for G) Faddeev equation (no three-body forces) Diquark-quark Christian S. Fischer (University of Gießen) Locating QCD s critical end point 22 / 26

32 Vacuum: Baryons from BSEs BSE for baryons (derived from equation of motion for G) Faddeev equation (no three-body forces) Diquark-quark Input: Non-perturbative quark, quark-gluon interaction (RL) (k 2 ) 7 k 2 2 e 2 k 2 2 UV (k 2 ) Christian S. Fischer (University of Gießen) Locating QCD s critical end point 22 / 26

33 Vacuum: DSE/Faddeev landscape Roberts et al Oettel, Alkofer Roberts, Bloch Segovia et al. Eichmann, Alkofer Nicmorus, Krassnigg Eichmann, Alkofer Sanchis-Alepuz, CF Sanchis-Alepuz, CF Williams Eichmann, N*-Workshop, Trento 2015 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 23 / 26

34 Vacuum: DSE/Faddeev landscape Roberts et al Oettel, Alkofer Roberts, Bloch Segovia et al. Eichmann, Alkofer Nicmorus, Krassnigg Eichmann, Alkofer Sanchis-Alepuz, CF Sanchis-Alepuz, CF Williams Eichmann, N*-Workshop, Trento 2015 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 23 / 26

35 Vacuum: Light baryon spectrum Christian S. Fischer (University of Gießen) Locating QCD s critical end point 24 / 26

36 Vacuum: Light baryon spectrum [] qqq q-dq PDG ** PDG *** PDG **** Three-body and diquark-quark approach agree qualitatively Spectrum in one-to-one agreement with experiment Correct level ordering (wo. coupled channel effects)! Eichmann, CF, Sanchis-Alepuz, Eichmann, Sanchis-Alepuz, Williams, Alkofer, CF, PPNP in press [ ] Christian S. Fischer (University of Gießen) Locating QCD s critical end point 24 / 26

37 Baryon effects on the CEP - results (Nf2) dq dq NB N T/T c No Baryons Baryons included Zero chemical potential: no effects after rescaling CEP: almost no effects µ q [MeV] Eichmann, CF, Welzbacher, PRD93 (2016) [ ] Christian S. Fischer (University of Gießen) Locating QCD s critical end point 25 / 26

38 Baryon effects on the CEP - results (Nf2) dq dq NB N T/T c No Baryons Baryons included Baryons included with µ-dep. prefactor Zero chemical potential: no effects after rescaling CEP: almost no effects µ q [MeV] But: strong μ-dependence of baryon wave function may change situation Eichmann, CF, Welzbacher, PRD93 (2016) [ ] Christian S. Fischer (University of Gießen) Locating QCD s critical end point 25 / 26

39 Summary QCD with finite chemical potential: back-reaction of quarks onto gluons important Nf21 and Nf211: CEP at μc/tc > 3 charm quark does not influence CEP Baryon effects may or may not be significant for CEP Work in progress: - mesons and baryons at finite T and μ - volume effects of CEP from DSEs Christian S. Fischer (University of Gießen) Locating QCD s critical end point 26 / 26

40 Backup Christian S. Fischer (University of Gießen) Locating QCD s critical end point 27 / 26

41 Critical scaling from DSEs 0-1 ~ ln(t) ln B(p0,ω p πt) ln <ΨΨ> -2-3 YM π, σ ln(t T c ) Need to take meson part of vertex explicitly into account T0: meson cloud corrections of order of % 78 (2008) TTc: meson corrections are dominant! Critical scaling: h i(t) B(t) t /2 CF, Williams, CF and Mueller, PRD 84 (2011) f 2 s t (t (T c T )/T c ) π,s Christian S. Fischer (University of Gießen) Locating QCD s critical end point 28 / 26

42 Approximation for Quark-Gluon interaction T,μ,m-dependent vertex: Abelian WTI (q, k, p) Z e C(k) C(p) d 1 d 2 q 2 q2 2 q 2 A(k) A(p) j j 2 0 (µ)ln[q 2 / 2 2! 1] 4 perturbation theory Infrared ansatz: d2 fixed to match gluon input d1 fixed via quark condensate (see later) correct UV (quant.) and IR-behavior (qual.) CF, Pawlowski, PRD 80 (2009) Mitter, Pawlowski and Strodthoff, PRD 91 (2015) Williams, Fischer, Heupel, PRD 93 (2016) Christian S. Fischer (University of Gießen) Locating QCD s critical end point 29 / 26

43 DSE/Faddeev landscape (Tμ0) Roberts et al Oettel, Alkofer Roberts, Bloch Segovia et al. Eichmann, Alkofer Nicmorus, Krassnigg Eichmann, Alkofer Sanchis-Alepuz, CF Sanchis-Alepuz, CF Williams Eichmann, N*-Workshop, Trento 2015 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 30 / 26

44 DSE/Faddeev landscape (Tμ0) Roberts et al Oettel, Alkofer Roberts, Bloch Segovia et al. Eichmann, Alkofer Nicmorus, Krassnigg Eichmann, Alkofer Sanchis-Alepuz, CF Sanchis-Alepuz, CF Williams Eichmann, N*-Workshop, Trento 2015 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 30 / 26

45 DSE/Faddeev landscape (Tμ0) Roberts et al Oettel, Alkofer Roberts, Bloch Segovia et al. Eichmann, Alkofer Nicmorus, Krassnigg Eichmann, Alkofer Sanchis-Alepuz, CF Sanchis-Alepuz, CF Williams Eichmann, N*-Workshop, Trento 2015 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 30 / 26

46 DSE/Faddeev landscape (Tμ0) Roberts et al Oettel, Alkofer Roberts, Bloch Segovia et al. Eichmann, Alkofer Nicmorus, Krassnigg Eichmann, Alkofer Sanchis-Alepuz, CF Sanchis-Alepuz, CF Williams Eichmann, N*-Workshop, Trento 2015 Christian S. Fischer (University of Gießen) Locating QCD s critical end point 30 / 26