(Light) tetraquarks in a Dyson-Schwinger, Bethe-Salpeter approach - PowerPoint PPT Presentation

(Light) tetraquarks in a Dyson-Schwinger, Bethe-Salpeter approach 1 P. C.WallboA, G. Eichmann, C. S. Fischer, W. Heupel 02.06.17 P.C. WallboA, FAIRNESS 1

Contents • Physics: The scalar mesons • CalculaRons: How the method works • Outlook 02.06.17 P.C. WallboA, FAIRNESS 2

Contents • Physics: The scalar mesons • CalculaRons: How the method works • Outlook 02.06.17 P.C. WallboA, FAIRNESS 3

Light mesons: MulRplet order u-, d-, s-quarks J P C PDG 02.06.17 P.C. WallboA, FAIRNESS 4

MulRplet order ( − 1) L +1 Quark models PDG 02.06.17 P.C. WallboA, FAIRNESS 5

MulRplet order � � � � PDG 02.06.17 P.C. WallboA, FAIRNESS 6

Masses ... M [GeV] 1 1 0 0 0 2 1 1 02.06.17 P.C. WallboA, FAIRNESS 7

... and widths M [GeV] ??? S-quarks OZI? 02.06.17 P.C. WallboA, FAIRNESS 8

Are they tetraquarks? M [GeV] � � � S-quarks Jaffe, RJ: Physical Review D, 15(1):267, 1977 02.06.17 P.C. WallboA, FAIRNESS 9

Results in BSE/DSE Eichmann, Fischer, Heupel Phys. LeF. B753:282-287, 2016 02.06.17 P.C. WallboA, FAIRNESS 10

CalculaRon roadmap • Quark propagator (DSE) • Bound states (BSE) for mesons, baryons, tetraquarks… 02.06.17 P.C. WallboA, FAIRNESS 11

Quark DSE k p p q p Full propagator Non interacRng Self energy Z S − 1 ( p ) = S − 1 0 ( p ) + D µ ν ( k ) γ µ S ( q ) Γ ν ( p, q ) q 02.06.17 P.C. WallboA, FAIRNESS 12

Quark DSE ?? ◆ Z ( k 2 ) ?? Γ µ ( q, k ) ✓ δ µ ν − k µ k ν D µ ν = k 2 k 2 ?? ?? ?? S − 1 ( p ) = − ip µ γ µ A ( p 2 ) + B ( p 2 ) S ( q ) 0 ( p ) = − ip µ γ µ + m S − 1 Z S − 1 ( p ) = S − 1 0 ( p ) + D µ ν ( k ) γ µ S ( q ) Γ ν ( p, q ) q 02.06.17 P.C. WallboA, FAIRNESS 13

Quark DSE � ◆ Z ( k 2 ) ∝ γ µ α eff ( k 2 ) Γ µ ( q, k ) ✓ δ µ ν − k µ k ν D µ ν = k 2 k 2 ?? ?? ?? S − 1 ( p ) = − ip µ γ µ A ( p 2 ) + B ( p 2 ) S ( q ) 0 ( p ) = − ip µ γ µ + m S − 1 In RL + MT only A,B unknown � Rainbow-Ladder -> solve for A,B + Maris-Tandy -> quark propagator 02.06.17 P.C. WallboA, FAIRNESS 14

Quark DSE, results: [GeV] 10 M = B A 1 b c s u/d chiral p 2 [GeV] 1 1000 02.06.17 P.C. WallboA, FAIRNESS 15

Meson BSE setup Self energy -> scaAering kernel cut Quark propagators from DSE Z Γ ab ( p, P ) = K ad,cb ( p, q, P ) [ S ( q + ) Γ ( q, P ) S ( − q − ] cd q Γ = K · Γ 02.06.17 P.C. WallboA, FAIRNESS 16

Meson BSE solve it Z Γ ab ( p, P ) = K ad,cb ( p, q, P ) [ S ( q + ) Γ ( q, P ) S ( − q − ] cd q 4 X Γ = f i ( Ω ) τ i ⊗ color ⊗ flavor i =1 Ω ( p 2 , p · P ) λ ( M ) Γ = K · Γ 02.06.17 P.C. WallboA, FAIRNESS 17

Tetraquark BSE(s) A. Khvedelidze, A. Kvinikhidze, Theor. Math. Phys. 90, 62 (1992) 2-body full equaRon approximaRon Eichmann, Fischer, Heupel Phys. LeF. B753:282-287, 2016 Heupel, Eichmann Fischer WallboF, tetraquarks in a DSE, BSE approach Phys. LeF. B718:545-549, 2012 02.06.17 P.C. WallboA, FAIRNESS 18

Tetraquark BSE, setup Quark propagators from DSE cut + perm. λ ( M ) Γ = K · Γ 02.06.17 P.C. WallboA, FAIRNESS 19

Tetraquark BSE, setup Quark propagators from DSE cut + perm. S-waves only! S4 Ω ( p 2 , q 2 , k 2 , p · q, ... ) → Ω ( S 0 , D, T 1 , T 2 ) 02.06.17 P.C. WallboA, FAIRNESS 20

Importance of mulRplets := set to constant value D important, T not! 02.06.17 P.C. WallboA, FAIRNESS 21

Why is D important? p 2 + q 2 − 2 k 2 √ 3 q 2 − p 2 Phase space restricted to triangle! 02.06.17 P.C. WallboA, FAIRNESS 22

Poles! √ 3 q 2 − p 2 , p 2 + q 2 − 2 k 2 ) = f 1 ( D ) f 1 ( 4 X Γ = f i ( Ω ) τ i ⊗ color ⊗ flavor i =1 τ 1 = γ 5 ⊗ γ 5 02.06.17 P.C. WallboA, FAIRNESS 23

Poles! √ 3 q 2 − p 2 , p 2 + q 2 − 2 k 2 ) = f 1 ( D ) f 1 ( 1 1 f 1 = π + ( p 1 + p 3) 2 · m 2 m 2 π + ( p 2 + p 4) 2 Exhibits poles! σ π π ?? Moving poles! 02.06.17 P.C. WallboA, FAIRNESS 24

Summary of results • Light scalars, because dynamically generated meson poles dominate • Tetraquark is resonance above two pion threshold 02.06.17 P.C. WallboA, FAIRNESS 25

Outlook • Technical improvements – Analysis of higher parRal waves – More systemaRc studies of results – Rigorous calculaRon of decay properRes σ → ππ • Establish method for heavy-light systems 02.06.17 P.C. WallboA, FAIRNESS 26

Outlook 02.06.17 P.C. WallboA, FAIRNESS 27

Outlook • Establish method for heavy-light systems • And other quantum numbers Esposito et al., I Journal Mod Phys A 30, 2014 02.06.17 P.C. WallboA, FAIRNESS 28

Outlook (approach) Hard calculaRon, limited to (almost) equal quark masses 02.06.17 P.C. WallboA, FAIRNESS 29

Outlook (approach) “Physical construcRon” + poles 4 X Γ = f i ( Ω ) τ i ⊗ color ⊗ flavor i =1 Γ q ¯ q = Γ π ⊗ Γ π + Γ ρ ⊗ Γ ρ + ... qq ¯ PW, Tetraquarks in a DSE/BSE approach 1 − ⊗ 1 − = 0 + Now back to s-wave truncated amplitude 02.06.17 P.C. WallboA, FAIRNESS 30

Summary • Strength: – Once truncaRon is set, no further input necessary – System chooses configuraRon dynamically (π-π) – Growing computaRon power -> full soluRon possible • Challenges: – heavy-light systems – Decays (extrapolaRon) – Mixing – Redo lots of coding 02.06.17 P.C. WallboA, FAIRNESS 31

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Also interesRng 02.06.17 P.C. WallboA, FAIRNESS 33

Why D? Poles! 2 02.06.17 P.C. WallboA, FAIRNESS 34

Tetraquarks in a DSE BSE approach WallboF, tetraquarks in a BSE/DSE approach 02.06.17 P.C. WallboA, FAIRNESS 35

Tetraquarks in a DSE BSE approach • sRll strong doublet D dependence of results • Problem: Symmetries! WallboF, tetraquarks in a BSE/DSE approach 02.06.17 P.C. WallboA, FAIRNESS 36

BSE eigenvalue/ extrapolaRon 02.06.17 P.C. WallboA, FAIRNESS 37

BSE eigenvalue/ extrapolaRon 02.06.17 P.C. WallboA, FAIRNESS 38

BSE eigenvalue/ extrapolaRon Treshold !! 02.06.17 P.C. WallboA, FAIRNESS 39