Interpretation of the observed hybrid candidates by the QGC Model Farida IDDIR Laboratoire de Physique Théorique d’Oran - L.P.T.O - Ecole de Physique Avancée au Maghreb 26 Mars-03 Avril, Taza, Maroc E P A M 2011 07:56

Summary I- Introduction The experimental hybrid candidates II- The Quark-Gluon Constituent Model Structure of the hybrid meson The constituent gluon The gluon mass Representation of the hybrid states The quantum numbers The wave functions The Hamiltonian III-Masses and decay widths The masses The decay into two standard mesons The decay widths Selection rules for the decay channels IV- The results V- Conclusion 22:30

Introduction 07:56

SU(3)-Color singlets systems  mésons and baryons “NAÏVE” QUARK MODEL “ Standard Hadrons”   SU(3)-Color singlets systems Glueballs QCD predictions  Hybrids diquonia “ Exotic Hadrons”   Hadron + HYBRID MESON but Many good candidates no absolute confirmation 07:56

JPC =1-+ 1-+ p1 (1400) 1-+ p1(1600) 1-+ p1(2000) The candidates Y -Anomaly : 1-- Y (4040) and Y (4160)  not compatible with . mixed states? (Ono, Close , Page  OCP scénario) 1-- cannot mix with (Iddir, Pène , Safir) Charmonium(-like) resonance Y(4260): not compatible with . (1998) 07:56

IHEP , KEK , CERN , BNL Several exotic resonances have been claimed to be identified, especially and have received great interest, but some doubts are raised about the later one. In the Charm sector, the most interesting new states observed are the and the (BELLE, BABAR). 07:56

Constituent Gluon Model In the present work Hybrid mesons are studied from different models: Lattice QCD, Flux Tube Model, Bag Model, QCD Sum Rules, Constituent Gluon Model In the present work Calculations of masses and decay widths of hybrid mesons in the context of Constituent Gluon Model. Comparison with experimental data

The Quark-Gluon Constituent Model 07:56

interacting through a phenomenological potential STRUCTURE OF THE HYBRID MESON Hybrid meson  bound state of quark-antiquark-constituent gluon (Coulomb + linear) + spin-spin , spin-orbit , tensor corrections terms 07:56

Models with Constituent Gluon A pair, color-octet, neutralized by a constituent gluon. The gluon contributes to the quantum numbers of hybrid meson, to construct exotic states. Models with Constituent Gluon Tube Flux Model Or a pair, color-octet, and gluonic excitations Standard méson Hybrid méson 07:56

 vector of the strong interaction The Constituent Gluon  vector of the strong interaction May interact with other gluons and construct color singlet objects ( ex: glueballs, … ,…)  The gluon  have a color charge  QCD predict existence of color singlets containing gluons Espace de Fock 07:56

Gauge Invariance Principle !!! The Gluon Mass  1980 : effective mass proposed for the gluon : ~ 800 MeV J/y photodecay Pb: m(g)  0 Gauge Invariance Principle !!! Higgs Mechanism (1973) Introduction of new particles (Higgs) in the hadronic spectrum Introduction of possibles electric gluonic charges ! Solutions :  Dynamic mass for the gluon (1982) Propagator of the effective gluon (LQCD) 0++ (lightest) glueball (gg) LQCD  mgg ~ 1.7 GeV  mg ~ 850 MeV 07:56

REPRESENTATION OF THE HYBRID STATES The bound states: quark-antiquark-gluon THE QUANTUM NUMBERS  the quark-excited (QE) mode  the gluon-excited (GE) mode QE-mode GE-mode 07:56

THE WAVE FUNCTION ( space-spin coupling ) The sum runs over the values of excluding those not consistent with P and C . Jacobi coordinates 07:56

A THE HAMILTONIAN The kinetic term Not valid for the light systems M ( Martin-Inequality) A This equality occurs for a particular M value : 07:56

The phenomenological potential Light flavours Charm sector 07:56

Masses and Decay Widths 07:56

THE MASSES Hyperspherical coordinates: 07:56

For a state we calculate the energy function: and minimize it to respect of the parameters and to have both masses and parameters of the corresponding wavefunctions. The spin dependant corrections will calculated as perturbation: 07:56

A  B + C THE DECAY INTO TWO STANDARD MESONS Selection rules l Spin conservation Spin conservation Charge conjugation G-Parity Isospin Parity 07:56

THE DECAY WIDTHS The decay process occurs through the quark pair creation mechanism, annihilating the constituent gluon. Original quarks being spectators. The interaction Hamiltonian : 07:56

The hybrid meson state: The final meson state: The hybrid meson state: The decay of the hybrid meson A into two mesons B and C is described by the matrix element of the Hamiltonian: Where representing the decay amplitude by: flavour color spin space 07:56

The spatial overlap is given by: The partial decay width : 07:56

SELECTION RULES FOR THE DECAY CHANNELS for lB =lC=0 ״S + S ״ channel : two fundamental mesons QE for lB =1 and lC=0 ״ S + P ״ channel GE 07:56

Then the possible decay channels for the two cases: For the hybrid meson: QE-mode : GE-mode : QE-mode : 07:56

The Results 07:56

our results coincide with those calculated by LQCD. THE PARAMETERS Light flavours S,P,D states for light mesons Kaons masses Heavy flavours 1–- states spectrum for charmonium and bottomonium mesons for our results coincide with those calculated by LQCD. 07:56

RESULTS: MASSES Models with gluonic excitations 1-+ 1(1400) Candidate 1-+ 1(1600) Candidate 1-+ 1(2000) Candidate Pure GE-mode with spin effects F.Iddir and L.Semlala, Int. J. Mod.Phys.A23(2008)5229 1--Y(4260) Candidate QE and GE –modes mixing (+spin effects) QE - GE mixing coefficients 07:56

No resonance in this channel RESULTS: DECAY WIDTHS (I) ״S + S ״ Channel ״S + P ״ Channel Resonances ״S + S ״ Channel ״S + P ״ Channel No resonance in this channel 07:56

RESULTS: DECAY WIDTHS (II) Canal ״S + S ״ Large Canal ״S + P ״ Resonance 07:56

Conclusion 07:56

diquonium interpretation The mass results : in good agreement with the other models. For the pure GE-mode, perfect agreement with LQCD and FTM. Significant mixing between QE and GE-modes: u,d: 1.40 ~ 1.90 s: 1.66 ~ 2.21 c: 4.27 ~ 4.48 b: 10.50 ~ 10.80 (GeV) F.Iddir et al, Phys.LettB205(1988)564 Experimental 1-+ candidates diquonium interpretation mass 500 MeV non hybrid meson 1-+ 1(1400) Candidate 1-+ 1(1600) Candidate 1-+ 1(2000) Candidate Possible non exotic interpretation mass 330 MeV doubts Good agreement good hybrid candidate Our Г=361 MeV for [1-+ nng(2000),L=1]  f1 (1285)  agreement with exp=333 MeV Molecular resonance (two standard mesons) I.General , hep-ph/0707.128 Note that the possible mixing of and corresponding is excluded The charmed 1-- candidate (P+S-channel) 1--Y(4260) Candidate Good agreement good hybrid candidate 07:56

Decay widths calculations being non relativistic Spin conservation We find (1-+ hybrid   or ’ )=0, Observed channels! Decay widths calculations being non relativistic Spin conservation  = 0 2nd approximation Hadrons: unstable resonances (non bound states) coupled channel formalism Decay cannot be considered as perturbation 07:56

New results from the updated and parameters F.Iddir and L.Semlala, ArXiv 1101.2431 [hep-ph] We have used ~ 800 MeV Recent Lattice data  ~ 600 MeV 07:56

The parameter We have used ~ 1  order of magnitude for the decay rates. We can use more convincing value available from recent Schwinger-Dyson equations and Lattice QCD data.  ~ 0.85 The results () will be multiplied by a factor ~ 0.68 07:56

Merci de votre attention 07:56