Glueballs, Tetraquarks and Excited Baryons from Dyson-Schwinger Equations Christian S
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Glueballs, tetraquarks and excited baryons from Dyson-Schwinger equations Christian S. Fischer Justus Liebig Universität Gießen with Gernot Eichmann, Walter Heupel, Helios Sanchis-Alepuz and Richard Williams Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 1 / 38 Overview 1.Introduction 2.Gluons and glueballs 1 1 − = − 3.Quarks and mesons − 4.Tetraquarks 5.Excited baryons Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 2 / 38 Glueballs Lattice: States in the light and heavy quark energy regions Most calculations quenched Preliminary unquenched results: larger masses Gregory et al., JHEP 1210 (2012) 170 DSE: structural information Morningstar and Peardon, PRD 60 (1999) 034509 Y.~Chen et al., PRD 73 (2006) 014516 Meyers, Swanson, PRD 87 (2013) 3, 036009 Sanchis-Alepuz, CF, Kellermann and von Smekal, PRD 92 (2015) 3, 034001 Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 3 / 38 Tetraquarks in the light meson sector f (980) ⇡⇡,KK¯ 0 ! a (980) ⇡⌘,KK¯ 0 ! Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 4 / 38 Tetraquarks in the light meson sector Light meson sector: Scalars! f (980) ⇡⇡,KK¯ 0 ! a (980) ⇡⌘,KK¯ 0 ! Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 4 / 38 Tetraquarks in the light meson sector Light meson sector: Scalars! f (980) ⇡⇡,KK¯ 0 ! a (980) ⇡⌘,KK¯ 0 ! Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 4 / 38 Tetraquark candidates in charmonium region Internal structure ?? Wolfgang Gradl, BESIII, St Goar 2015 Related to details of underlying QCD forces between quarks Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 5 / 38 Baryons: quark model Text text Text2 text Text3 Loring, Metsch, Petry, EPJA 10 (2001) 395 ‘missing resonances’ ?! parity doubling ?! 1 ± 1 ± level ordering: N vs. Λ 2 2 Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 6 / 38 Explaining the Roper Quark model: p(2S), but generically too large mass e.g. Loring, Metsch, Petry, EPJA 10 (2001) 395 and many others… Hybrid ? Evidence from lattice to the contrary Dudek, Edwards, PRD 85 (2012) 054016 Dynamically generated by coupled channels (no ‘bare’ state) Krehl, Hanhart, Krewald and Speth, PRC C 62 (2000) 025207 Doring, Hanhart, Huang, Krewald and Meissner, NPA 829 (2009) 170 Dynamically modified by coupled channels Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama and Sato, PRL 104 (2010) 042302 ‘bare’ state via DSE/Faddeev (NJL, QCD inspired model) Wilson, Cloet, Chang and Roberts, PRC 85 (2012) 025205, Segovia, El-Bennich, Rojas, Cloet, Roberts, Xu and Zong, PRL 115 (2015) 17 Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 7 / 38 Lattice QCD and the Roper different actions volume effects interpolators large discrepancies ! m2 m ⇡ ⇠ q (Gell-Mann-Oakes-Renner) Liu, Chen, Gong, Sufian, Sun and Li, PoS LATTICE 2013 (2014) 507 Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 8 / 38 Lattice QCD and the Roper different actions volume effects interpolators large discrepancies ! m2 m ⇡ ⇠ q (Gell-Mann-Oakes-Renner) Liu, Chen, Gong, Sufian, Sun and Li, PoS LATTICE 2013 (2014) 507 Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 8 / 38 Bound states and resonances from DSEs, BSEs, FEs Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 9 / 38 Overview 1.Introduction 2.Gluons and glueballs 1 1 − = − 3.Quarks and mesons − 4.Tetraquarks 5.Excited baryons Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 10 / 38 QCD in covariant gauge Quarks, gluons and ghosts 1 = [ , A, c]exp d4x ¯ (iD/ m) (F a )2 ZQCD D − − − 4 µ⌫ Z ( Z ✓ +gauge term + c¯( @D)c) − ) Landau gauge propagators in momentum space, p p Z(p2) DGluon(p) = δ µ ν µν µν − p2 p2 ✓ ◆ Quark 2 2 1 S (p) = Z (p )[ ip/ + M(p )]− f − The Goal: gauge invariant information in a gauge fixed approach. Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 11 / 38 Landau gauge gluon propagator 1 1 2 − = − 1 pµp⌫ Z(p ) − 2 D (p)= δ µ⌫ µ⌫ − p2 p2 ✓ ◆ 1 1 − 2 − 6 + 1 − 2 Sternbeck et. al. (2006) 1 1 1.5 DSE − = − − ) 2 1 Z(p spacelike momenta: good agreement with lattice 0.5 fully dressed gluon is not massless ! 0 0 1 2 3 4 5 recent improvement: 3g-vertex p [GeV] Eichmann, Williams, Alkofer, Vujinovic PRD 89, (2014) 10 CF, Maas, Pawlowski, Annals Phys. 324 (2009) 2408. Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 12 / 38 Landau gauge gluon propagator spectral spectral function: positivity function violations Cornwall, Papavassiliou,... Gluon cannot appear in detector! Strauss, CF, Kellermann, Phys. Rev. Lett. 109, (2012) 252001 Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 13 / 38 Glueballs from DSE/BSEs Mixing of two-gluon amplitudes with ghost-antighost Probes analytical structure of gluons and ghosts Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 14 / 38 Glueballs from DSE/BSEs Mixing of two-gluon amplitudes with ghost-antighost Probes analytical structure of gluons and ghosts Results: M(0++)=1.64 GeV + M(0− )=4.53 GeV ghosts do not contribute ! Sanchis-Alepuz, CF, Kellermann and von Smekal, PRD 92 (2015) 3, 034001 (see also Meyers, Swanson, PRD 87 (2013) 3, 036009) Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 14 / 38 Overview 1.Introduction 2.Gluons and glueballs 1 1 − = − 3.Quarks and mesons − 4.Tetraquarks 5.Excited baryons Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 15 / 38 DSEs and Bethe-Salpeter equation Kernel K uniquely related to quark-DSE via axWTI π, ρ,... →Pion is bound state and Goldstone boson Maris, Roberts, Tandy, PLB 420 (1998) 267 Two strategies: I. use rainbow-ladder model for quark-gluon interaction →ok for many phenomenological applications II. calculate gluon and vertex from their DSEs Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 16 / 38 Strategie I: Model for quark-gluon interaction 2 2 k2 2 7 k η 2 2 α(k )=⇤⇥ e− Λ + αUV (k ) Maris, Roberts,Tandy, PRC 56 (1997), PRC 60 (1999) Λ2 ⇣ ⌘ ✓ ◆ fix ⇤ from fπ; small dependence of many results on ⌘ masses mu=md, m s, m c, from π, Κ, J/ψ Renormalizable and momentum dependent ! Qualitatively similar to results from explicit calculation CF, Maas, Pawlowski, Annals Phys. 324 (2009) 2408. Williams, EPJA 51 (2015) 5, 57. Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 17 / 38 Quark mass: flavor dependence 1 Typical solution: 10 0 ) [GeV] 2 10 -1 10 -2 10 Bottom quark Charm quark -3 10 Strange quark Up/Down quark 1 2 2 Chiral limit [S(p)]− =[ ip/ + M(p )]/Zf (p ) -4 Quark Mass Function: M(p 10 − -2 -1 0 1 2 3 10 10 10 10 10 10 2 2 p [GeV ] 0.4 Lattice: quenched Lattice: unquenched (Nf=2+1) 2 DSE: quenched M(p ): momentum dependent! 0.3 DSE: unquenched (Nf=2) 0.2 Dynamical mass: Mstrong≈350 MeV M(p) [GeV] 0.1 Flavour dependence because of mweak 0.0 0.0 1.0 2.0 3.0 4.0 ¯ 3 p [GeV] Chiral condensate: ΨΨ (250 MeV) CF, Nickel, Williams, EPJ C 60 (2009) 47 h i⇡ Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 18 / 38 Quark mass: flavor dependence 1 Typical solution: 10 0 ) [GeV] 2 10 -1 10 -2 10 Bottom quark NotCharm directly quark measurable ! -3 10 Strange quark Up/Down quark 1 2 2 Chiral limit [S(p)]− =[ ip/ + M(p )]/Zf (p ) -4 Quark Mass Function: M(p 10 − -2 -1 0 1 2 3 10 10 10 10 10 10 2 2 p [GeV ] 0.4 Lattice: quenched Lattice: unquenched (Nf=2+1) 2 DSE: quenched M(p ): momentum dependent! 0.3 DSE: unquenched (Nf=2) 0.2 Dynamical mass: Mstrong≈350 MeV M(p) [GeV] 0.1 Flavour dependence because of mweak 0.0 0.0 1.0 2.0 3.0 4.0 ¯ 3 p [GeV] Chiral condensate: ΨΨ (250 MeV) CF, Nickel, Williams, EPJ C 60 (2009) 47 h i⇡ Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 18 / 38 Rainbow-ladder: heavy meson spectrum DSE/BSE CF, Kubrak, Williams, EPJA 51 (2015) Hilger et al. PRD 91 (2015) good channels: 1--,2++, 3 —,…: prediction for tensor state acceptable channels : 0-+,1++,... deficiencies in other channels: ’imbalance’ of spin-structure Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 19 / 38 Rainbow-ladder: heavy meson spectrum DSE/BSE CF, Kubrak, Williams, EPJA 51 (2015) Hilger et al. PRD 91 (2015) good channels: 1--,2++, 3 —,…: prediction for tensor state acceptable channels : 0-+,1++,... deficiencies in other channels: ’imbalance’ of spin-structure Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 19 / 38 Rainbow-ladder: heavy meson spectrum DSE/BSE CF, Kubrak, Williams, EPJA 51 (2015) Hilger et al. PRD 91 (2015) good channels: 1--,2++, 3 —,…: prediction for tensor state acceptable channels : 0-+,1++,... deficiencies in other channels: ’imbalance’ of spin-structure Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 19 / 38 Overview 1.Introduction 2.Gluons and glueballs 1 1 − = − 3.Quarks and mesons − 4.Tetraquarks 5.Excited baryons Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 20 / 38 Tetraquarks from the four-body interaction Exact equation: + perm. Two-body interactions Three- and four-body interactions Kvinikhidze & Khvedelidze, Theor.