Hadron spectra and QCD phase diagram from DSEs

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Hadron spectra and QCD phase diagram from DSEs Christian S.

Gernot Eichmann, Helios Sanchis-Alepuz, Richard Williams,

Williams, Alkofer, CF, PPNP 91, 1-100 [1606.

1 Hadron spectra and QCD phase diagram from DSEs Christian S. Fischer Justus Liebig Universität Gießen ECT* 017 with Gernot Eichmann, Helios Sanchis-Alepuz, Richard Williams, Christian Welzbacher Review: Eichmann, Sanchis-Alepuz, Williams, Alkofer, CF, PPNP 91, [ ] Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 1 / 43

Take home messages Light baryon spectrum: Eichmann, CF, Sanchis-Alepuz, PRD 94 (016) [1607.05748] M [GeV].0 1.8 1.6 1.

2 Take home messages Light baryon spectrum: Eichmann, CF, Sanchis-Alepuz, PRD 94 (016) [ ] M [GeV] N(1880) N(1710) N(1440) N(1895) N(1650) N(1535) N(1900) N(170) N(1875) N(1700) N(150) (190) (1600) (1940) (1700) (1910) (1900) (160) 1. (13) 1.0 N(940) Critical end point of QCD: CF, Luecker, PLB 718 (013) 1036, CF, Luecker, Welzbacher, PRD 90 (014) 0340 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram / 43

3 Overview 1.Baryon spectrum - light and strange.gluons, quarks and the CEP 3.Hadronic effects on quark and glue dq dq NB N Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 3 / 43

4 Light baryon spectrum - quark model Text text Text text Text3 Loring, Metsch, Petry, EPJA 10 (001) 395 missing resonances - three-body vs. quark-diquark level ordering: N 1 ± vs. ± 1 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 4 / 43

5 Strange baryon spectrum quark model light, strange and heavy spectrum probe QCD physics at different scales need flavor dependent QCD forces to explain spectrum models: parametrization via exchange of Goldstone-bosons Ronniger, Metsch, EPJA 47 (011) 16 see also Glozmann, Riska, Plessars et al. flavor dependent forces should be determined from QCD Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 5 / 43

6 Baryon spectroscopy from QCD Underlying QCD forces two-body vs. three-body confinement spin structure meson cloud effects heavy/heavy-light systems Missing resonances Δ vs Y - configuration Regge trajectories?! (Hyper)-Fine structure GB-exchange vs QCD Flavor dependence 3-quark vs. quark-diquark Coupled-channel effects Strategies to deal with this situation: Nonperturbative QCD: Lattice, Functional methods Effective theories with hadronic dof Klemt, Richard, Rev.Mod.Phys. 8 (010) 1095 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 6 / 43

7 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) Hadron spectra and QCD phase diagram 7 / 43

8 Diquark-Quark approximation BSE for baryons (derived from equation of motion for G) Faddeev equation (no three-body forces) Diquark-quark Input in both cases: quark propagator and interaction Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 8 / 43

9 Diquark-Quark approximation BSE for baryons (derived from equation of motion for G) Faddeev equation (no three-body forces) Diquark-quark Input in both cases: quark propagator and interaction Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 8 / 43

10 Diquark-Quark approximation BSE for baryons (derived from equation of motion for G) Faddeev equation (no three-body forces) Diquark-quark Input in both cases: quark propagator and interaction Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 8 / 43

Diquark-Quark approximation BSE for baryons (derived from equation of motion for G) Faddeev equation (no three-body forces) Diquark-quark -1-1

11 Diquark-Quark approximation BSE for baryons (derived from equation of motion for G) Faddeev equation (no three-body forces) Diquark-quark Input in both cases: quark propagator and interaction Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 8 / 43

12 The DSE for the quark propagator Approximations: I) NJL/contact model: II) Quark-diquark model: Ansatz for quark prop (and diquark wave function) III) Rainbow-ladder: IV) Beyond rainbow-ladder: Sanchis-Alepuz, Williams, PLB 749 (015) 59 Williams, CF, Heupel, PRD93 (016) 03406, and refs. therein Binosi, Chang, Papavassiliou, Qin, Roberts PRD95 (017) and refs. therein solve DSEs for quarks, gluons and quark-gluon vertex Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 9 / 43

13 DSE/Faddeev landscape I) II) III) III) IV) IV) Roberts et al Oettel, Alkofer Roberts, Bloch Segovia et al. Eichmann, Alkofer Nicmorus, Krassnigg Eichmann, Alkofer Sanchis-Alepuz, CF Sanchis-Alepuz, CF Williams Sanchis-Alepuz, Williams Eichmann, N*-Workshop, Trento 015 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 10 / 43

14 DSE/Faddeev landscape I) II) III) III) IV) IV) Roberts et al Oettel, Alkofer Roberts, Bloch Segovia et al. Eichmann, Alkofer Nicmorus, Krassnigg Eichmann, Alkofer Sanchis-Alepuz, CF Sanchis-Alepuz, CF Williams Sanchis-Alepuz, Williams Eichmann, N*-Workshop, Trento 015 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 10 / 43

15 Rainbow-ladder model for quark-gluon interaction Combine gluon with quark-gluon vertex: effective coupling (k ) 7 k e k UV (k ) Maris, Roberts,Tandy, PRC 56 (1997), PRC 60 (1999) scale from f π, masses mumd, ms from m π, mk UV from perturbation theory parameter : band of results Binosi, Chang, Papavassiliou and Roberts, PLB 74 (015) 183 Eichmann, Sanchis-Alepuz, Williams, Alkofer, CF, PPNP 91, [ ] Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 11 / 43

16 Rainbow-ladder model for quark-gluon interaction Combine gluon with quark-gluon vertex: effective coupling (k ) 7 k e k UV (k ) Maris, Roberts,Tandy, PRC 56 (1997), PRC 60 (1999) scale from f π, masses mumd, ms from m π, mk UV from perturbation theory parameter : band of results Binosi, Chang, Papavassiliou and Roberts, PLB 74 (015) 183 Eichmann, Sanchis-Alepuz, Williams, Alkofer, CF, PPNP 91, [ ] Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 11 / 43

Rainbow-ladder model for quark-gluon interaction Combine gluon with quark-gluon vertex: effective coupling (k ) 7 k e k UV (k ) Maris, Roberts,Tandy, PRC 56 (1997), PRC 60 (1999) scale from f π,

17 Rainbow-ladder model for quark-gluon interaction Combine gluon with quark-gluon vertex: effective coupling (k ) 7 k e k UV (k ) Maris, Roberts,Tandy, PRC 56 (1997), PRC 60 (1999) scale from f π, masses mumd, ms from m π, mk UV from perturbation theory parameter : band of results Binosi, Chang, Papavassiliou and Roberts, PLB 74 (015) 183 Eichmann, Sanchis-Alepuz, Williams, Alkofer, CF, PPNP 91, [ ] Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 11 / 43

18 Quark mass: flavor dependence Typical solution: [S(p)] 1 [ ip/ M(p )]/Z f (p ) Quark Mass Function: M(p ) [GeV] Bottom quark Charm quark Strange quark Up/Down quark Chiral limit p [GeV ] M(p) [GeV] Lattice: quenched Lattice: unquenched (N f 1) DSE: quenched DSE: unquenched (N f ) M(p ): momentum dependent! Dynamical mass: Mstrong 350 MeV Flavour dependence because of mweak p [GeV] CF, Nickel, Williams, EPJ C 60 (009) 47 Chiral condensate: h i (50 MeV) 3 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 1 / 43

19 Quark mass: flavor dependence Typical solution: [S(p)] 1 [ ip/ M(p )]/Z f (p ) Quark Mass Function: M(p ) [GeV] Bottom quark Charm quark Strange quark Up/Down quark Chiral limit Not directly measurable! p [GeV ] M(p) [GeV] Lattice: quenched Lattice: unquenched (N f 1) DSE: quenched DSE: unquenched (N f ) M(p ): momentum dependent! Dynamical mass: Mstrong 350 MeV Flavour dependence because of mweak p [GeV] CF, Nickel, Williams, EPJ C 60 (009) 47 Chiral condensate: h i (50 MeV) 3 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 1 / 43

20 Quantum numbers: non-exotic vs exotic non-relativistic qq-coupling S :1/ 1/! 0 1 P :( 1) L1 C :( 1) LS J PC S L J PC or S1 L J 1 P 1 3 P0 3 P1 3 P relativistic qq-coupling (P, p) 5 [F 1 (P, p) F (P, p)ip/ F 3 (P, p)pp ip/ F 4 (P, p)[p/, P/ ]] s-wave p-wave P :( 1) L1 conventional states more complicated exotic quantum numbers possible! 0, 0, 1,... Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 13 / 43

21 DSEs and Bethe-Salpeter equation axwti,... Kernel K uniquely related to quark-dse via axialvector Ward-Takahashi-Identity (axwti): Z Z i (K 5 S KS 5 ) µs D µ 5 Z 5 µs D µ Pion is bound state and Goldstone boson Maris, Roberts, Tandy, PLB 40 (1998) 67 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 14 / 43

(axwti): Z Z i (K 5 S KS 5 ) µs D µ 5 Z 5 µs D µ Pion is bound state and Goldstone

22 DSEs and Bethe-Salpeter equation axwti,... Kernel K uniquely related to quark-dse via axialvector Ward-Takahashi-Identity (axwti): Z Z i (K 5 S KS 5 ) µs D µ 5 Z 5 µs D µ Pion is bound state and Goldstone boson Maris, Roberts, Tandy, PLB 40 (1998) 67 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 14 / 43

23 Charmonium spectrum good channels: 1 --,, 3 --,... acceptable channels: 0 - clear deficiencies in other channels: missing spin-structure excited states fine! (in good channels) DSE/BSE CF, Kubrak, Williams, EPJA 51 (015) Hilger et al. PRD 91 (015) Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 15 / 43

24 Charmonium spectrum good channels: 1 --,, 3 --,... acceptable channels: 0 - clear deficiencies in other channels: missing spin-structure excited states fine! (in good channels) DSE/BSE CF, Kubrak, Williams, EPJA 51 (015) Hilger et al. PRD 91 (015) Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 15 / 43

25 Light meson spectrum good channels (ground state): 0 -, 1 -- acceptable channels (ground state) :, 3 --,... clear deficiencies in other channels and excited states drastic improvement beyond rainbow-ladder! CF, Kubrak, Williams, EPJA 50 (014) 16 Williams, CF, Heupel, PRD93 (016) Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 16 / 43

26 Light meson spectrum good channels (ground state): 0 -, 1 -- acceptable channels (ground state) :, 3 --,... clear deficiencies in other channels and excited states drastic improvement beyond rainbow-ladder! CF, Kubrak, Williams, EPJA 50 (014) 16 Williams, CF, Heupel, PRD93 (016) Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 16 / 43

27 Light meson spectrum [] (1600) 1.5 (1300) (1450) (1450) (135) (160) (1400) 1.0 PDG 0.5 3PI-3L PI-3L CF, Kubrak, Williams, EPJA 50 (014) 16 Williams, CF, Heupel, PRD93 (016) good channels (ground state): 0 -, 1 -- acceptable channels (ground state) :, 3 --,... clear deficiencies in other channels and excited states drastic improvement beyond rainbow-ladder! Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 16 / 43

28 Faddeev - equation relativistic bound state: 64 tensor structures for octett: s, p, d - waves 18 tensor structures for decuplett: s, p, d, f - waves (P, p, q) X l l F l (P, p, q) (flavour colour) Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 17 / 43

29 Light baryon spectrum: diquarks M [GeV] N(1880) N(1710) N(1440) N(1895) N(1650) N(1535) N(1900) N(170) N(1875) N(1700) N(150) (190) (1600) (1940) (1700) (1910) (1900) (160) 1. (13) 1.0 N(940) nucleon and delta - channels: good results but: severe problems in all other channels artifact of rainbow-ladder: ps and v too strongly bound! Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 18 / 43

30 Light baryon spectrum: diquarks M [GeV] N(1880) N(1710) N(1440) N(1895) N(1650) N(1535) N(1900) N(170) N(1875) N(1700) N(150) (190) (1600) (1940) (1700) (1910) (1900) (160) 1. (13) 1.0 N(940) scav psv all all nucleon and delta - channels: good results but: severe problems in all other channels artifact of rainbow-ladder: ps and v too strongly bound! Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 18 / 43

31 Light baryon spectrum: diquarks M [GeV] N(1880) N(1710) N(1440) N(1895) N(1650) N(1535) N(1900) N(170) N(1875) N(1700) N(150) (190) (1600) (1940) (1700) (1910) (1900) (160) 1. (13) 1.0 N(940) scav psv all all nucleon and delta - channels: good results but: severe problems in all other channels artifact of rainbow-ladder: ps and v too strongly bound! Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 18 / 43

32 Light baryon spectrum: diquarks M [GeV] N(1880) N(1710) N(1440) N(1895) N(1650) N(1535) N(1900) N(170) N(1875) N(1700) N(150) (190) (1600) (1940) (1700) (1910) (1900) (160) 1. (13) 1.0 N(940) scav psv all all nucleon and delta - channels: good results but: severe problems in all other channels artifact of rainbow-ladder: ps and v too strongly bound! reduce binding in ps and v diquark channels, adjust to ρ-a1-splitting Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 18 / 43

33 Light baryon spectrum: diquarks M [GeV] N(1880) N(1710) N(1440) N(1895) N(1650) N(1535) N(1900) N(170) N(1875) N(1700) N(150) (190) (1600) (1940) (1700) (1910) (1900) (160) 1. (13) 1.0 N(940) scav psv Eichmann, CF, Sanchis-Alepuz, PRD 94 (016) [ ] spectrum in one to one agreement with experiment correct level ordering (without coupled channel effects!) three-body agrees with diquark-quark where applicable Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 19 / 43

34 Light baryon spectrum: diquarks M [GeV] N(1880) N(1710) N(1440) N(1895) N(1650) N(1535) N(1900) N(170) N(1875) N(1700) N(150) (190) (1600) (1940) (1700) (1910) (1900) (160) 1. (13) qqq 1.0 N(940) scav psv Eichmann, CF, Sanchis-Alepuz, PRD 94 (016) [ ] spectrum in one to one agreement with experiment correct level ordering (without coupled channel effects!) three-body agrees with diquark-quark where applicable Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 19 / 43

35 Properties of the Roper Leading amplitude Several q-values (relative momentum) angular mom. decomposition ( arb. norm. ) p ( GeV ) Eichmann, CF, Sanchis-Alepuz, PRD 94 (016) zero crossing of wave function: s-state every state is mixture of several partial waves! different internal structure of radial excitations tension with simpler calculations ( contact interaction, QCD based model ): Wilson, Cloet, Chang and Roberts, PRC 85 (01) 0505, Segovia, El-Bennich, Rojas, Cloet, Roberts, Xu and Zong, PRL 115 (015) 17 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 0 / 43

36 Excited spectrum: Omega M [GeV].8.6 Ω(470)?.4. Ω(380)? Ω(50)? Ω(167) Eichmann, CF, in preparation same level ordering as quark model, but larger masses exp. quantum numbers? Ronniger, Metsch, EPJA 47 (011) 16 assignment according to: Gamermann, Garcia-Recio, Nieves and Salcedo, PRD 84 (011) Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 1 / 43

37 Overview 1.Baryon spectrum - light and strange.gluons, quarks and the CEP 3.Hadronic effects on quark and glue dq dq NB N Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram / 43

38 QCD phase diagram Interesting open questions: Existence and location of critical point Details of phase transitions Properties of Quarks and Gluons in QGP Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 3 / 43

39 QCD phase diagram Quarks de-confined and (almost) massless Quarks confined and massive Interesting open questions: Existence and location of critical point Details of phase transitions Properties of Quarks and Gluons in QGP Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 3 / 43

40 QCD phase transitions Text text Text text Text3 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 4 / 43

41 QCD phase transitions Text text Text text Text3 chemical potential Is this happening?? Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 4 / 43

42 QCD phase transitions Text text Text 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) Hadron spectra and QCD phase diagram 4 / 43

43 Search for the CEP Taylor expansion (Nf): Gavai, Gupta, PRD 71 (005) ! Datta, Gavai and Gupta, NPA (013) 883c! Bazavov et al., PRD 95 (017) C. Schmidt, plenary Reweighting (Nf1): Fodor, Katz, JHEP 0404 (004) 050 Analytic continuation (Nf3): de Forcrand, Philipsen, JHEP 0811 (008) 01;! NPB 64 (00) 90 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 5 / 43

44 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 (015) 559 J. Günther, plenary Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 6 / 43

45 QCD order parameters from propagators Chiral order parameter: h i Z N c Tr D 1 T X Z d 3 p S( p, ) ( ) 3 Deconfinement: Polyakov loop potential L 1 N c Tre ig A 0 ( S) A Braun, Gies, Pawlowski, PLB 684, 6 (010) Braun, Haas, Marhauser, Pawlowski, PRL 106 (011) Fister, Pawlowski, PRD (013) CF, Fister, Luecker, Pawlowski, PLB 73 (013) Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 7 / 43

46 The DSE for the quark propagator Two strategies: I. use model for gluon! Qin, Chang, Chen, Liu and Roberts, PRL 106 (011) Gutierrez, Ahmad, Ayala, Bashir and Raya, JPG 41 (014) 07500! ok for first insights not good enough for systematic study II. treat Yang-Mills sector explicitly Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 8 / 43

47 Nf1-QCD with DSEs quenched propagator from lattice up/down strange quenched: without quark-loop Nf: Nf1: isospin symmetry solve coupled system of 33 equations Vertex: ansatz built along STI and known UV/IR behavior T,μ,m-dependent Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 9 / 43

48 Glue at finite temperature (T 0) T-dependent gluon propagator from quenched lattice simulations:.5.5 T0 T0.6 T c T0.99 T c T. T c T0 T0.6 T c T0.99 T c T. T c Z T (p) 1 Z L (p ) p [Gev ] p [Gev ] Crucial difference between magnetic and electric gluon Maximum of electric gluon near Tc Cucchieri, Maas, Mendes, PRD 75 (007) CF, Maas, Mueller, EPJC 68 (010) FRG: Fister, Pawlowski, arxiv: Cucchieri, Mendes, PoS FACESQCD 007 (010) Aouane, Bornyakov, Ilgenfritz, Mitrjushkin, Muller-Preussker and Sternbeck, PRD 85 (01) Silva, Oliveira, Bicudo, Cardoso, PRD 89 (014) Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 30 / 43

49 Approximation for Quark-Gluon interaction T,μ,m-dependent vertex: Abelian WTI (q, k, p) Z e C(k) C(p) d 1 d q q q A(k) A(p) j j 0 (µ)ln[q /! 1] 4 perturbation theory Infrared ansatz: d 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 (015) Williams, CF, Heupel, PRD PRD 93 (016) Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 31 / 43

50 Critical line/surface for heavy quarks Polyakov Loop: Φ m 30 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 Roberge-Weiss-transition seen Lattice: Fromm, Langelage, Lottini, Philipsen, JHEP 101 (01) 04 CF, Luecker, Pawlowski, PRD 91 (015) 1 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 3 / 43

51 Critical line/surface for heavy quarks Polyakov Loop: Φ m 30 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 Roberge-Weiss-transition seen Lattice: Fromm, Langelage, Lottini, Philipsen, JHEP 101 (01) 04 CF, Luecker, Pawlowski, PRD 91 (015) 1 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 3 / 43

Critical line/surface for heavy quarks Nf: CF and Mueller, PRD 84 (011) 054013 Polyakov Loop: 1 0.8 m 30 MeV m 363 MeV m 400 MeV Mean-field scaling 0.6 0.6 Φ 0.4 0.4 0. 0. 0 0.015 0.

52 Critical line/surface for heavy quarks Nf: CF and Mueller, PRD 84 (011) Polyakov Loop: m 30 MeV m 363 MeV m 400 MeV Mean-field scaling Φ (T-T c )/T c T [MeV] Deconfinement transition in agreement with lattice QCD Correct tricritical scaling Roberge-Weiss-transition seen Lattice: Fromm, Langelage, Lottini, Philipsen, JHEP 101 (01) 04 CF, Luecker, Pawlowski, PRD 91 (015) 1 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 3 / 43

53 Nf1, 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(010) 073 DSE: CF, Luecker, PLB 718 (013) 1036, CF, Luecker, Welzbacher, PRD 90 (014) 0340 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 33 / 43

54 Nf1, 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(010) 073 DSE: CF, Luecker, PLB 718 (013) 1036, CF, Luecker, Welzbacher, PRD 90 (014) 0340 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 33 / 43

55 Nf1, μ0, physical point l,s (T)/ l,s (0) zero chemical potential Lattice QCD Quark Condensate dressed Polyakov Loop Z L 4 3 T 187 MeV Quenched T 15 MeV Quenched T 35 MeV Quenched T 187 MeV Lattice T 15 MeV Lattice T 35 MeV Lattice T 187 MeV DSE T 15 MeV DSE T 35 MeV DSE T [MeV] p [GeV] Lattice: Borsanyi et al. [Wuppertal-Budapest], JHEP 1009(010) 073 DSE: CF, Luecker, PLB 718 (013) 1036, CF, Luecker, Welzbacher, PRD 90 (014) 0340 Lattice: Aouane, et al.prd D87 (013), [arxiv:11.110] DSE: CF, Luecker, PLB 718 (013) 1036, [arxiv: ] quantitative agreement: DSE prediction verified by lattice Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 33 / 43

56 Nf1: Condensate and dressed Polyakov Loop Quark condensate Polyakov-Loop L 1 N c tr e ig R A 0 CF, Fister, Luecker, Pawlowski, PLB 73 (014) 73 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 34 / 43

57 Nf1: 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) Hadron spectra and QCD phase diagram 35 / 43

58 Nf1: phase diagram µ B /T 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 (013) 1036, CF, Fister, Luecker, Pawlowski, PLB 73 (014) 73 CF, Luecker, Welzbacher, PRD 90 (014) 0340 combined evidence of FRG and DSE: no CEP at μb/t< Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 35 / 43

59 Nf1: phase diagram T [MeV] 00 µ B /T 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 (011) , Endrodi, Fodor, Katz, Szabo, JHEP 1104 (011) 001 Cea, Cosmai, Papa, PRD 89 (014), PRD 93 (016) Bonati et al., PRD 9 (015) Bellwied et al. PLB 751 (015) 559 CEP at large μ CF, Luecker, PLB 718 (013) 1036, CF, Fister, Luecker, Pawlowski, PLB 73 (014) 73 CF, Luecker, Welzbacher, PRD 90 (014) 0340 combined evidence of FRG and DSE: no CEP at μb/t< Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 35 / 43

60 Nf11: 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) Hadron spectra and QCD phase diagram 36 / 43

61 Nf11: effects of charm up/down strange 1. 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 1 N f 11 Effects very small! µ u/d [MeV] CF, Luecker, Welzbacher, PRD 90 (014) 0340 Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 36 / 43

62 Location of CEP in freece-out landscape Figure taken from talk of T. Galatyuk, Erice 016 Caveats: inhomogeneous phases effects of baryons? Müller, Buballa and Wambach, PLB 77 (013) 40 Nc: Brauner, Fukushima and Hidaka, PRD 80 (009) Strodthoff, Schaefer and Smekal, PRD 85 (01) Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 37 / 43

63 Overview 1.Baryon spectrum - light and strange.gluons, quarks and the CEP 3.Hadronic effects on quark and glue dq dq NB N Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 38 / 43

64 Hadron effects onto quarks Tails of hadron poles do affect space-like momenta and therefore quark condensate! Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 39 / 43

65 Critical scaling from DSEs (Nf, chiral) 0-1 ~ ln(t) ln B(p0,ω p πt) ln <ΨΨ> non-resonant YM π, σ ln(t T c ) Need to take meson part of vertex explicitly into account T0: meson cloud corrections of order of 10-0 % CF, Williams, PRD 78 (008) Sanchis-Alepuz, CF, Kubrak, PLB 733 (014) [ ] TTc: meson corrections are dominant! Critical scaling: h i(t) B(t) t / CF and Mueller, PRD 84 (011) f s t (t (T c T )/T c ) π,s Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 40 / 43

66 Baryon effects onto CEP (Nf) dq dq NB N Dependence on T and μ via -propagators -wave functions Exploratory calculation: use wave functions from Tμ0 Eichmann, CF, Welzbacher, PRD93 (016) [ ] Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 41 / 43

67 Baryon effects on the CEP - results (Nf) dq dq NB N T/T c No Baryons Baryons included 0. Zero chemical potential: no effects after rescaling CEP: almost no effects µ q /µ q,c Eichmann, CF, Welzbacher, PRD93 (016) [ ] Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 4 / 43

68 Baryon effects on the CEP - results (Nf) 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 /µ q,c But: strong μ-dependence of baryon wave function may change situation Eichmann, CF, Welzbacher, PRD93 (016) [ ] Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 4 / 43

69 Summary Vacuum hadron physics: Meson spectra: spin physics very important Light baryon spectrum in good agreement with experiment Tetraquarks Glueballs Eichman, CF, Heupel, PLB 753 (016) 8-87 Sanchis-Alepuz, CF, Kellermann and von Smekal, PRD 9 (015) 3, Review: Eichmann, Sanchis-Alepuz, Williams, Alkofer, CF, PPNP 91, [ ] QCD with finite chemical potential: Nf1 and Nf11: CEP at μc/tc > 3 Baryon effects may or may not be significant for CEP Quark spectral functions CF, Pawlowski, Rothkopf and Welzbacher, arxiv: [hep-ph] Mesons and Baryons at finite T and μ Gunkel and CF, work in progress Christian S. Fischer (University of Gießen) Hadron spectra and QCD phase diagram 43 / 43

Locating QCD s critical end point

Locating QCD s critical end point Christian S. Fischer Justus Liebig Universität Gießen 31st of Oct 2016 Eichmann, CF, Welzbacher, PRD93 (2016) [1509.02082] Eichmann, Sanchis-Alepuz, Williams, Alkofer,