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. 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) = µ µ µ 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)= 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 2 2 (k )=⇤⇥ e + UV (k ) Maris, Roberts,Tandy, PRC 56 (1997), PRC 60 (1999) 2 ⇣ ⌘ ✓ ◆

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: (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: (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. Math. Phys. 90 (1992) Heupel, Eichman, CF, PLB 718 (2012) 545-549 Eichman, CF, Heupel, 1508.07178 Basic idea: solve four-body equation without any assumption on internal clustering Key elements: quark propagator and interaction kernels

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 21 / 38 Solving the four-body equation

+ perm.

Input: Non-perturbative quark, quark-gluon interaction

2 2 k2 2 7 k 2 2 (k )=⇤⇥ e + UV (k ) 2 ⇣ ⌘ ✓ ◆

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 22 / 38 Structure of the amplitude

Scalar tetraquark:

p q k P

(P, p, q, k)= f (s ,...,s ) (P, p, q, k) color flavor i 1 9 ⇥ i ⇥ ⇥ i X 3 3¯, 6 6¯ or 9 Lorentz scalars 256 tensor ⌦ ⌦ structures 1 1, 8 8 (built from P,p,q,k) ⌦ ⌦ (scalar tetra)

good approximation: keep s-waves only; 16 tensor structures

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 23 / 38 Four-body equation: Organise Dirac-Lorentz-tensors into multiplets of S4

2 2 2 Singlet: S 0 =( p + q + k ) / 4 , carries overall scale Doublet: a = p3(q2 p2)/(4S ); s =(p2 + q2 2k2)/(4S ) 0 0 diquark pole

Eichman, CF, Heupel, arXiv: 1505.06336 Two triplets meson poles

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 24 / 38 Bound state masses

Different levels of approximations:

0 1500 MTetra [MeV]

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 25 / 38 Bound state masses

Different levels of approximations:

0 1500 MTetra [MeV]

Singlet only

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 25 / 38 Bound state masses

Different levels of approximations:

0 1500 MTetra [MeV]

Singlet only Singlet +Triplet I

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 25 / 38 Bound state masses

Different levels of approximations:

Singlet +Triplet II 0 1190 1500 MTetra [MeV]

Singlet only Singlet +Triplet I

Bound state of four massive quarks

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 25 / 38 Bound state masses

Different levels of approximations:

Singlet +Triplet II 0 350 1190 1500 MTetra [MeV]

Singlet + Doublet Singlet only Singlet +Triplet I

4m2 M 2 ⇡ 0 Bound state of S four massive quarks Two-pion resonance

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 25 / 38 Mass evolution of tetraquark

[] strange charm 1.5 6 MTetra 5 [GeV]

1.0 / 4

3 4-body BSE 0.5 2 2-body BSE 2 1 2 Eichman, CF, Heupel, 1508.07178 0.0 0 2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 [] []

Resonance becomes bound state for large mq Dynamical decision: meson clusters, not diquarks Results: m 350 MeV ⇠ m 750 MeV msss¯s¯ 1.5 GeV  ⇠ ⇠ m 1080 MeV mccc¯c¯ 5.7 GeV a0,f0 ⇠ ⇠ qualitatively similar to two-body framework Heupel, Eichman, CF, PLB 718 (2012) 545-549 Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 26 / 38 Outlook: heavy-light systems Dynamical situation in S4-doublet:

heavy-light diquarks cq c¯q¯

meson-molecules hadro-charmonium cq¯ cq¯ cc¯ qq¯

Dynamical decision of most important clustering!

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 27 / 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 28 / 38 DSE/Faddeev landscape

Roberts et al Oettel, Alkofer Eichmann, Alkofer Eichmann, Alkofer Sanchis-Alepuz, CF Roberts, Bloch Nicmorus, Krassnigg Sanchis-Alepuz, CF Williams Segovia et al.

Eichmann, N*-Workshop, Trento 2015

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 29 / 38 DSE/Faddeev landscape

Roberts et al Oettel, Alkofer Eichmann, Alkofer Eichmann, Alkofer Sanchis-Alepuz, CF Roberts, Bloch Nicmorus, Krassnigg Sanchis-Alepuz, CF Williams Segovia et al.

Eichmann, N*-Workshop, Trento 2015

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 29 / 38 DSE/Faddeev landscape

Roberts et al Oettel, Alkofer Eichmann, Alkofer Eichmann, Alkofer Sanchis-Alepuz, CF Roberts, Bloch Nicmorus, Krassnigg Sanchis-Alepuz, CF Williams Segovia et al.

Eichmann, N*-Workshop, Trento 2015

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 29 / 38 DSE/Faddeev landscape

Roberts et al Oettel, Alkofer Eichmann, Alkofer Eichmann, Alkofer Sanchis-Alepuz, CF Roberts, Bloch Nicmorus, Krassnigg Sanchis-Alepuz, CF Williams Segovia et al.

Eichmann, N*-Workshop, Trento 2015

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 29 / 38 Faddeev - equation

= + + +

relativistic bound state: 64 tensor structures for nucleon: s, p, d - wave 128 tensor structures for Delta: s, p, d, f - wave

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 30 / 38 Faddeev - equation

= + + +

irreducible three-body forces Sanchis-Alepuz, Williams, work in progress… two-body interactions: non-perturbative gluon exchange Eichmann, Alkofer, Krassnigg, Nicmorus, PRL 104 (2010)

meson exchange Sanchis-Alepuz, CF, Kubrak, PLB 733 (2014) two-body forces beyond one-particle exchange

Sanchis-Alepuz, Williams, PLB 749 (2015) 592 numerically expensive but manageable !

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 31 / 38 Faddeev - equation

= + + +

irreducible three-body forces Sanchis-Alepuz, Williams, work in progress… two-body interactions: non-perturbative gluon exchange Eichmann, Alkofer, Krassnigg, Nicmorus, PRL 104 (2010)

meson exchange Sanchis-Alepuz, CF, Kubrak, PLB 733 (2014) two-body forces beyond one-particle exchange

Sanchis-Alepuz, Williams, PLB 749 (2015) 592 numerically expensive but manageable !

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 31 / 38 Faddeev - equation

= + + +

irreducible three-body forces Sanchis-Alepuz, Williams, work in progress… two-body interactions: non-perturbative gluon exchange Eichmann, Alkofer, Krassnigg, Nicmorus, PRL 104 (2010)

meson exchange Sanchis-Alepuz, CF, Kubrak, PLB 733 (2014) two-body forces beyond one-particle exchange

Sanchis-Alepuz, Williams, PLB 749 (2015) 592 numerically expensive but manageable !

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 31 / 38 Baryon masses - gluon exchange only

1.9

1.8 [] Delta: 1.7 Sanchis-Alepuz et al., first covariant three-body PRD 84 (2011) 1.6 calculations ! 1.5 Nucleon: grosso modo: consistent Eichmann et al., 1.4 PRL 104 (2010), description of mesons and PRD 84 (2011) baryons 1.3 1.2 wave functions contain 1.1 –meson: sizable p-wave Maris & Tandy, 1.0 PRC 60 (1999) contributions 0.9

0.8

Eichmann, Alkofer, Krassnigg, Nicmorus, PRL 104 (2010) 0.7 Eichmann, PRD 84 (2011) 0.0 0.1 0.2 0.3 0.4 0.5 Sanchis-Alepuz ,Eichmann, Villalba-Chavez, Alkofer, PRD (2012) ![]

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 32 / 38 Mass of the Roper

= λ P P 2=m2

Operator Wave Eigenvalue Wave function function

ground state: largest eigenvalue λ=1 fake excited state at m =1.26 GeV cf. talk at PANDA meeting need full flavor wave function (MS+MA) to eliminate fake huge numerical effort extraction of wave function very expensive

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 33 / 38 Properties of the Roper

1

0.8 M =1.45 GeV Leading amplitude N ⇤ 0.6 Several q-values (relative momentum)

0.4

0.2

Nucleon Roper 0

( arb. norm. ) norm. ( arb. -0.2

s-wave 66% 15% -0.4

-0.6 p-wave 33% 61% 0 0.5 1 1.5 2 p ( GeV )

d-wave 1% 24% Sanchis-Alepuz, CF in preparation

different internal structure than nucleon zero crossing of wave function: 2s-state

tension with simple models: 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 34 / 38 Mass evolution

&"# !15/.'()*+6, !"#$%"&'()*++, 7$8939'()*+), -./0$1"%23'()*+4, & -./0$1"%23'()*+4,

%"#

%

$"# ())*)+,-).

$

!"# ! !"!# !"$ !"$# !"% !"%# !"& !"&# !"' /)))*)+,-)).%% Sanchis-Alepuz, CF in preparation

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 35 / 38 Mass evolution

3.5 Engel (2013) Edwards (2011) Mahbub (2012) Alexandrou (2014) 3 Alexandrou (2014) Liu (2014)

2.5

2

1.5 M ( GeV ) M ( GeV

1

0.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 m ( GeV22 ) Sanchis-Alepuz, CF in preparation

Mass evolution in agreement with Liu (2014)

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 35 / 38 EM form factor

Very preliminary… Low accuracy…

small differences at larger Q2 rp =0.75 fm rR =0.65 fm

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 36 / 38 N-Roper transition form factor

0.2

0.15

0.1

0.05

0.20 Very preliminary… 0.1 2 2 0 Q ( GeV ) Low accuracy… -0.1 -0.2 -0.3 -0.4 -0.5 0 0.5 1 1.5 2 2.5 Q2 ( GeV2 )

Numerical problems below 0.5 GeV2 and above 2.5 GeV2 F2: zero crossing seen !

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 37 / 38 Summary and outlook

Summary Mass gap in YM-theory: scalar glueball mass Tetraquarks dominated by internal meson-meson configurations Dynamical description of σ as π-π resonance First results for Roper in three-body framework

Outlook Improve numerical framework: precision, systematics Unquench complex gluon propagator Tetraquarks: explore heavy-light systems Baryons: transition form factors

Christian Fischer (University of Gießen) Glueballs, tetraquarks and excited baryons from DSEs 38 / 38