Microscopic Model of Charmonium Strong Decays J. Segovia , D.R. Entem - PowerPoint PPT Presentation

Introduction Modeling strong decays Constituent quark model Microscopic decay model Results within charmonium sector Summary Microscopic Model of Charmonium Strong Decays J. Segovia , D.R. Entem and F. Fern´ andez segonza@usal.es The XIV International Conference on Hadron Spectroscopy (Hadron 2011) M¨ unchen, 13-17th of June 2011 University of Salamanca Spain J. Segovia et al. segonza@usal.es Microscopic Model of Charmonium Strong Decays

Introduction Modeling strong decays Constituent quark model Microscopic decay model Results within charmonium sector Summary Contents Introduction 1 Modeling strong decays 2 Constituent quark model 3 Microscopic decay model 4 Results within charmonium sector 5 Summary 6 J. Segovia et al. segonza@usal.es Microscopic Model of Charmonium Strong Decays

Introduction Modeling strong decays Constituent quark model Microscopic decay model Results within charmonium sector Summary 1.- Introduction 1.1.- A rather poorly understood area in hadronic physics Renew interest of charmonium → discovery of XYZ mesons performed by B factories One open topic: strong decays of c ¯ c states Poorly understood area: Is difficult to solve problems within QCD non-perturbative regime → Much of our knowledge of strong interaction comes from strong decays Open-flavor strong decays are mediated by q ¯ q pair production. Several phenomenological models have been developed to deal with this topic The relation of the phenomenological models to QCD microscopic decay mechanism has not been established J. Segovia et al. segonza@usal.es Microscopic Model of Charmonium Strong Decays

Introduction Modeling strong decays Constituent quark model Microscopic decay model Results within charmonium sector Summary 2.- Modeling strong decays 2.1.- How to deal with it 3 P 0 MODEL q pair is created from the vacuum → J PC = 0 ++ The q ¯ The created q ¯ q pair together with the q ¯ q pair in the original meson regroups in the two outgoing mesons via a quark rearrangement process → OZI rule FLUX-TUBE MODEL Similar to 3 P 0 model Takes into account the dynamics of the flux-tubes by including the overlaps of the flux-tube of the initial meson with those of the two outgoing mesons. MICROSCOPIC MODEL The strong decays are driven by interquark Hamiltonian which determines the spectrum J. Segovia et al. segonza@usal.es Microscopic Model of Charmonium Strong Decays

Introduction Modeling strong decays Constituent quark model Microscopic decay model Results within charmonium sector Summary 2.- Modeling strong decays 2.2.- Reference works on microscopic decay model ———— Little previous work in this area ———— ’Charmonium: The model’ and ’Charmonium: Comparison with experiment’ E. Eichten, K. Gottfried, T. Kinoshita, K.D. Lane and T.-M. Yan Phys. Rev. D 17 3090 (1978); 21 203 (1980) → Main features: Assume q ¯ q pair production from the static vector linear confining interaction The c ¯ c wave functions are those coming from the model except for the open-charm meson wave functions which are approximated by gaussians → Comments about results: Very early theoretical study of c ¯ c states There is an update → Phys. Rev. D 73 014014 (2006) Predicted partial and total widths of ψ (3770), ψ (4040) and ψ (4160) J. Segovia et al. segonza@usal.es Microscopic Model of Charmonium Strong Decays

Introduction Modeling strong decays Constituent quark model Microscopic decay model Results within charmonium sector Summary 2.- Modeling strong decays 2.2.- Reference works on microscopic decay model (Continuation) ’On the mechanism of open-flavor strong decays’ E.S. Ackleh, T. Barnes and E.S. Swanson Phys. Rev. D 54 , 6811 (1996) → Main features: Assume q ¯ q pair production from the scalar linear confining interaction and One-Gluon Exchange (OGE) Meson wave functions as SHO wave functions → Analytical decay rates → Comments about results: Overall scale of the total decay amplitudes is too large 8 ( Choice of model parameters > NOT DUE > > > Wave function approximation > > < 8 The discrepancy may be Non-relativistic reduction of amplitudes > < > POSSIBLY DUE Assumption of scalar linear potential > > > > > > Disregard a possible constant : : ’It would be interesting to apply these microscopic decay calculations to charmonium because the transverse OGE should be much smaller’ J. Segovia et al. segonza@usal.es Microscopic Model of Charmonium Strong Decays

Introduction Modeling strong decays Constituent quark model Microscopic decay model Results within charmonium sector Summary 2.- Modeling strong decays 2.3.- Summary E.S. Ackleh et al. E. Eichten et al. J. Segovia et al. Framework Non-relativistic Non-relativistic Non-relativistic Kernel Scalar linear + OGE Static linear Vector-scalar × (screened + cte) + OGE W.F. SHO Exact + SHO Exact solutions Coupled No Yes No Phase-Space Relativistic Relativistic Relativistic Application Some light meson decays Open-charm decays of c ¯ c Open-charm decays of c ¯ c Very recent works Yu.A. Simonov arXiv:1103.4028v1 [hep-ph] 21 Mar 2011 Bao-Fei Li et al. arXiv:1105.1620v1 [hep-ph] 9 May 2011 J. Segovia et al. segonza@usal.es Microscopic Model of Charmonium Strong Decays

Introduction Modeling strong decays Constituent quark model Microscopic decay model Results within charmonium sector Summary 3.- Constituent quark model 3.1.- Main features Spontaneous chiral symmetry breaking (Goldstone-Bosons exchange): f π γ 5 λ a π a − π π a π a + ... L = ¯ U γ 5 = 1 + i 1 ψ ( i γ µ ∂ µ − MU γ 5 ) ψ → 2 f 2 i 1 / 2 h Λ 2 M ( q 2 ) = m q F q 2 ´ ` = m q Λ 2 + q 2 QCD perturbative effects (One-Gluon Exchange): √ 4 πα s ¯ ψγ µ G µ λ c ψ L = i Confinement: V CON = a s V scalar CON + (1 − a s ) V vector CON ⇒ Screened potential: r ij ) = ˆ − a c (1 − e − µ c r ij ) + ∆ ˜ ( � V C λ c i · � λ c CON ( � j ) r ij ) = ` − a c µ c r ij + ∆ ´ ( � 8 i · � V C λ c λ c CON ( � j ) r ij → 0 < r ij ) = ( − a c + ∆)( � i · � V C λ c λ c CON ( � j ) r ij → ∞ : J. Segovia et al. segonza@usal.es Microscopic Model of Charmonium Strong Decays

Introduction Modeling strong decays Constituent quark model Microscopic decay model Results within charmonium sector Summary 3.- Constituent quark model 3.2.- Some recent applications N-N interaction D.R. Entem, F. Fern´ andez and A. Valcarce, Phys. Rev. C 62 , 034002 (2000) B. Julia-Diaz, J. Haidenbauer, A. Valcarce and F. Fern´ andez, Phys. Rev. C 65 , 034001 (2002) Baryon spectrum H. Garcilazo, A. Valcarce and F. Fern´ andez, Phys. Rev. C 63 , 035207 (2001) H. Garcilazo, A. Valcarce and F. Fern´ andez, Phys. Rev. C 64 , 058201 (2001) Meson spectrum J. Vijande, A. Valcarce and F. Fern´ andez, J. Phys. G 31 , 481 (2005) J. Segovia, D.R. Entem and F. Fern´ andez, Phys. Rev. D 78 114033 (2008) J. Segovia, D.R. Entem and F. Fern´ andez, accepted by Phys. Rev. D Molecular states P. G. Ortega, J. Segovia, D. R. Entem and F. Fern´ andez, Phys. Rev. D 81 , 054023 (2010) J. Segovia et al. segonza@usal.es Microscopic Model of Charmonium Strong Decays

Introduction Modeling strong decays Constituent quark model Microscopic decay model Results within charmonium sector Summary 3.- Constituent quark model 3.2.- Some recent applications (Continuation) Deuteron X(3872) Charmonium reactions CQM NijmII Bonn B Exp. 60 1.0 (a) (a) ǫ d (MeV) − 2 . 2242 − 2 . 2246 − 2 . 2246 − 2 . 224575 50 0.8 Number of events/2.5 MeV P D (%) 4 . 85 5 . 64 4 . 99 - 40 0.6 2 ) Q d (fm 0 . 276 0 . 271 0 . 278 0 . 2859 ± 0 . 0003 30 σ (nb) − 1 / 2 ) 0.4 A S (fm 0 . 891 0 . 8845 0 . 8860 0 . 8846 ± 0 . 0009 20 A D /A S 0 . 0257 0 . 0252 0 . 0264 0 . 0256 ± 0 . 0004 0.2 10 0.0 0 Light mesons 3850 3860 3870 3880 3890 -0.2 4.0 4.2 4.4 4.6 4.8 5.0 M(J/ ψπ + π - ) (MeV) M(D 0 D *- π + ) (GeV/c 2 ) 3000 2500 1.0 70 (b) 2000 (b) 60 M(MeV) 0.8 1500 Number of events/5 MeV 50 1000 0.6 500 40 σ (nb) 0.4 0 η ω h 1 f 0 f 1 f 2 ω 2 ω 3 η 2 h 3 f 3 f 4 η 4 ω 4 30 3000 0.2 2500 20 2000 0.0 10 M(MeV) 1500 0 1000 -0.2 4.0 4.2 4.4 4.6 4.8 5.0 3850 3860 3870 3880 3890 M(D 0 D - π + ) (GeV/c 2 ) 500 M(J/ ψπ + π - ) (MeV) 0 b 1 a 0 a 1 a 2 ρ 2 ρ 3 π 2 b 3 a 3 a 4 π 4 ρ 4 π ρ J. Segovia et al. segonza@usal.es Microscopic Model of Charmonium Strong Decays

Introduction Modeling strong decays Constituent quark model Microscopic decay model Results within charmonium sector Summary 3.- Constituent quark model 3.3.- Model parameters Quark masses m c (MeV) 1763 Confinement a c (MeV) 507 . 4 µ c (fm − 1 ) 0 . 576 ∆ (MeV) 184 . 432 a s 0 . 81 One-gluon exchange α 0 2 . 118 Λ 0 (fm − 1 ) 0 . 113 µ 0 (MeV) 36 . 976 r 0 (fm) ˆ 0 . 181 ˆ r g (fm) 0 . 259 J. Vijande et al. J. Phys. G 31 481 (2005) J. Segovia et al. segonza@usal.es Microscopic Model of Charmonium Strong Decays