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Hadron Spectroscopy in the Diquark Model

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Hadron Spectroscopy in the Diquark Model Hadron Spectroscopy in the Diquark Model Jacopo Ferretti University of Jyväskylä Diquark Correlations in Hadron Physics: Origin, Impact and Evidence September 23-27 2019, ECT*, Trento, Italy Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 1 / 38 Summary Quark Model (QM) formalism Exotic hadrons and their interpretations Fully-heavy and heavy-light tetraquarks in the diquark model The problem of baryon missing resonances Strange and nonstrange baryons in the diquark model Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 2 / 38 Constituent Quark Models Complicated quark-gluon dynamics of QCD 1. Effective degree of freedom of Constituent Quark is introduced: same quantum numbers as valence quarks mass ≈ 1=3 mass of the proton 3. Baryons ! bound states of 3 constituent quarks 4. Mesons ! bound states of a constituent quark-antiquark pair 5. Constituent quark dynamics ! phenomenological (QCD-inspired) interaction Phenomenological models q X 2 2 X αs H = p + m + − + βrij + V (Si ; Sj ; Lij ; rij ) i i r i i<j ij Coulomb-like + linear confining potentials + spin forces Several versions: Relativized Quark Model for baryons and mesons (Capstick and Isgur, Godfrey and Isgur); U(7) Model (Bijker, Iachello and Leviatan); Graz Model (Glozman and Riska); Hypercentral QM (Giannini and Santopinto), ... Reproduce reasonably well many hadron observables: baryon magnetic moments, lower part of baryon and meson spectrum, hadron strong decays, nucleon e.m. form factors ... Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 3 / 38 Relativized Quark Model for Baryons/Mesons S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985) S. Capstick and N. Isgur, Phys. Rev. D 34, 2809 (1986) Relativized QM Hamiltonian q X 2 2 X H = pi + mi + Vconf (rij ) + Vhyp(rij ) + Vso(rij ) i i<j Confining potential 3 3 αs(rij ) Vconf (rij )= − c + βrij − Fi · Fj 4 4 rij Hyperfine interaction αs(rij ) 8π 3 1 3 Si ·rij Sj ·rij Vhyp(rij )= − m m 3 Si · Sj δ (rij ) + 3 r 2 − Si · Sj Fi · Fj i j rij Spin-orbit interaction αs(rij ) 1 1 Si Sj Vso(rij )= − 3 m + m m + m · LFi · Fj rij i j i j Relativistic effects Inserted in the Hamiltonian by means of phenomenological parameterization Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 4 / 38 Charmonium spectrum in the relativized QM S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985) Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 5 / 38 Exotic Hadrons: Possible Interpretations See e.g. Y. R. Liu et al., Prog. Part. Nucl. Phys. 107, 237 (2019) X (3872) [now χc1(3872)]. Discovered by Belle in 2003 in B± ! K ±X (X ! J= π+π−). First observed exotic state. Its properties are not completely compatible with those of a cc¯ state Exotics: Meson and baryon states whose properties and/or quantum numbers cannot be described by considering qq¯ or qqq degrees of freedom only Multiquark states: 1. baryons made up of more than 3 valence quarks qqqqq¯ ! pentaquarks qqqqqq ! exa-quarks or dibaryons 2. mesons made up of more than a qq¯ pair qqq¯q¯ ! tetraquarks Hybrid mesons/baryons: hadrons made up of qqq or qq¯ valence quarks plus gluonic degrees of freedom Glueballs: particles consisting of gluonic degrees of freedom only, without valence quarks Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 6 / 38 Tetraquarks Tetraquarks: bound states of four valence quarks/antiquarks (qqq¯q¯) R.L. Jaffe, Phys. Rev. D 15, 267 & 281 (1977) Combine 4 quarks in terms of qq/q¯q¯ or qq¯ substructures: 1. Compact Tetraquark model: [qq]¯ [¯qq¯]3 3c c 1c 2. Meson-meson molecular mode: [[qq¯] [qq¯] ] 1c 1c 1c 3. Hadro-charmonium model: [qq¯] [QQ¯] 1c 1c 1c q q q q charmonium diquark q c c q q q q light meson q antidiquark compact tetraquark molecule hadro-charmonium Possible mixing between qq¯ and qqq¯ q¯ components Unquenched Quark Model (UQM) Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 7 / 38 Exotic Meson Candidates. Hidden-charm sector PC State J Mexp (MeV) Γ (MeV) Observing Process Experiment X (3872) 1++ 3871:69 ± 0:17 < 1:7 B± ! K ±π+π−J= Belle +− + − + − Zc (3900) 1 3886:6 ± 2:4 28:1 ± 2:6 e e ! π π J= BESIII −− + − + − Y (4008) 1 4008 ± 40 226 ± 44 e e ! γISRπ π J= Belle ± +− + − + − Zc (4020) 1 4024:1 ± 1:9 13 ± 5 e e ! π π hc BESIII ++ +8 X (4140) 1 4146:8 ± 2:5 19−7 γγ ! φJ= CDF ± − +45 +108 0 + − Zc (4240) 0 4239 ± 18−10 220 ± 47−74 B ! K π (2S) LHCb −− + − + − Y (4260) 1 4230 ± 8 55 ± 19 e e ! γISRπ π J= BaBar ++ +19 +14 + + X (4274) 1 4273−9 56−16 B ! J= φK CDF, LHCb −− + − + − Y (4360) 1 4341 ± 8 102 ± 9 e e ! γISRπ π (2S) Belle ± + +15 ± Zc (4430) 1 4478−18 181 ± 31 B ! Kπ (2S) Belle ++ +16 + + X (4500) 0 4506−19 92 ± 29 B ! J= φK LHCb −− +8 +40 + − + − Y (4630) 1 4634−7 92−24 e e ! Λc Λc Belle −− + − + − Y (4660) 1 4643 ± 9 72 ± 11 e e ! γISRπ π (2S) Belle ++ +17 + + X (4700) 0 4704−26 120 ± 50 B ! J= φK LHCb Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 8 / 38 Exotic Mesons. The well-known case of the X (3872) X (3872): JPC = 1++ quantum numbers, narrow width (< 1:2 MeV) Mass Problem: Experimental mass: 3871:69 ± 0:17 MeV [PDG] Incompatible with QM predictions. For example, Relativized QM ! 3.95 GeV X(3872) very close to D0D¯∗0 threshold ) Importance of threshold effects? Peculiar decay modes: Main decay modes are into D0D¯0π0 (Br > 0.4) and D0D¯∗0 (Br > 0.3) J= ρ (isospin violating, Br > 0.032) and J= ! (Br > 0.023) decay modes Decay properties not compatible with those of a cc¯ state Several interpretations: DD¯∗ meson-meson molecule Compact tetraquark (diquark-antidiquark) state cc¯ core + meson-meson pair loops (Unquenched Quark Model interpretation) Hadro-charmonium Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 9 / 38 Meson-meson molecular model See e.g. N. A. Törnqvist, Z. Phys. C 61, 525 (1994) Meson-meson molecules: bound states of two mesons Binding energy is relatively small Emergence of molecular states only close to meson-meson thresholds Binding: one-meson exchange forces and/or contact interactions One-pion-exchange (OPE) potential 2 g (σ1·q)(σ2·q) Vπ(q) = − 2 (τ1 · τ2) 2 2 fπ q +mπ σi and τi (i = 1; 2) ! spin and isospin matrices acting on light quarks i fπ ≈ 132 MeV ! pion decay constant mπ ! pion mass g ! dimensionless coupling constant Molecule wave function Obtained by combining the wave functions of the two meson Consider also relative orbital angular momentum between two mesons Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 10 / 38 Hadro-charmonium (hadro-quarkonium) model S. Dubynskiy and M. B. Voloshin, Phys. Lett. B 666, 344 (2008) J. Ferretti, Phys. Lett. B 782, 702 (2018) Heavy QQ¯ state embodied in a light qq¯ one (Q = c or b; q = u; d or s) Binding provided by multiple gluon-exchange forces QCD analog of van der Waals-type interactions Parametrization of the heavy quarkonium-light meson interaction: ( 2πα M − QQ¯ M for r < R 3R3 M Vhq(r) = M 0 for r > RM RM = light meson radius, MM = light meson mass αQQ¯ = quarkonium diagonal chromo-electric polarizability Hamiltonian: Hhq = MQQ¯ + MM + Vhq(r) + Thq k2 Thq = 2µ , k = relative momentum, µ = reduced mass of the system Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 11 / 38 Unquenched quark model (UQM) K. Heikkila, S. Ono and N. A. Törnqvist, Phys. Rev. D 29, 110 (1984) J. Ferretti, G. Galatà and E. Santopinto, Phys. Rev. C 88, 015207 (2013) Bare meson jAi develops a meson-meson continuum component jBCi " Z # X hBCkj Hqq¯ jAi j Ai = NA jAi + dk jBCki MA − EB − EC BC ¯ ¯ jAi = QQ ; jBCi = qQ − Qq¯ ; Hqq¯ = pair-creation operator UQM Hamiltonian HUQM = HA + HBC + Hqq¯ HA(HB;C) ! QQ¯ (qQ¯) bare meson Hamiltonian of A (B and C) ! REL QM Hqq¯ ! couples A to BC meson-meson components by creating a light qq¯ pair Physical Mass of a meson A: MA = EA +Σ( MA)= bare mass + self-energy correction Self-energy corrections Z 1 2 X jhBCkj Hqq¯ jAij Σ(MA) = dk MA − EB − EC BC 0 Sum over a complete set of intermediate states jBCi Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 12 / 38 Compact tetraquark (diquark-antidiquark) model (I) Compact tetraquarks: diquark-antidiquark bound states 4 body problem ! 2 body one ρ D q3 q4 q3 q4 λ r ≈ r q1 q2 q1 q2 σ D Diquark: Effective bosonic degree of freedom 2 strongly correlated quarks with no internal spatial excitation Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 13 / 38 Compact tetraquark (diquark-antidiquark) model (II) Possible diquark color configurations: color antitriplet (3¯c, attractive interaction) color sextet (6c, repulsive interaction) ) 3¯c is favored Diquark WF: ΨD = ΨspaceΨcolorΨspin−flavor is antisymmetric (Pauli principle) ) Ψspin−flavor is symmetric Diquark spin-flavor wave function: decomposed in terms of S = 0, 3¯f (scalar diquark) S = 1, 6f (axial-vector diquark) OGE calculations ) scalar configuration is energetically favored Jacopo Ferretti (University of Jyväskylä) hadron spectroscopy (diquark model) Sept 23-27 2019, ECT* 14 / 38 Compact tetraquark (diquark-antidiquark) model (III) Different approaches to study tetraquark properties: Potential models Algebraic models QCD calculations Mass inequality relations and so on Diquark models for tetraquarks: Several versions L.
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