Angular momentum coefficients for meson strong decay and unquenched quark models

Abstract

In most meson strong decay and unquenched (coupled-channel) quark models, the pair-creation operator is a scalar product of vectors in the spin and spatial degrees of freedom. While differing in the spatial part, most models have the same spin part, which creates a qq* pair coupled to spin triplet, with the spins of the initial quarks as spectators. This is a basic assumption of the 3P0 model, and is well-known to arise also in the flux tube model, starting from the strong coupling expansion of lattice QCD. In this article the same structure is shown to emerge in the Cornell model, in the dominant contributions of a more general microscopic decay model, and in the pseudoscalar-meson emission model. A solution is obtained for arbitrary matrix elements in these ``non-flip, triplet'' models, expressed as a weighted sum over spatial matrix elements. The coefficients in the expansion, which involve the spin degrees of freedom and the associated angular momentum algebra, are model-independent. Tables of the angular momentum coefficients are presented which can be used in future calculations, avoiding tedious Clebsch-Gordan sums. The symmetry and orthogonality properties of the coefficients are discussed, as well as their application to transitions involving hybrid mesons and states of mixed spin. New selection rules are derived, and existing ones generalised. The coefficients lead to model-independent relations among decay amplitudes and widths which can be tested in experiment and lattice QCD. They can also be used to explain how mass shifts in the unquenched quark model do not spoil successful predictions of the ordinary (quenched) quark model.

arXiv comment45 pages, 4 figures, 16 tables

References in corpus (113)

• Higher Charmonia
• Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson
• From the Deuteron to Deusons, an Analysis of Deuteronlike Meson-Meson Bound States
• Short Range Structure in the X(3872)
• Quasi-Two-Body Decays of Nonstrange Baryons
• The D*0 D0bar threshold resonance
• On the Mechanism of Open-Flavor Strong Decays
• Exotic QQ\qbar\qbar States in QCD
• Charmonium Options for the X(3872)
• Charmonium levels near threshold and the narrow state $X(3872) \to π^{+}π^{-}\jpsi$
• Higher Quarkonia
• Strong Decays of Excited Heavy Mesons In Chiral Perturbation Theory
• The X(3872) boson: Molecule or charmonium
• The Production and Decay of Hybrid Mesons by Flux-Tube Breaking
• Dynamics and Decay of Heavy-Light Hadrons
• Is X(3872) {\sl Really} a Molecular State?
• Diagnostic Decays of the X(3872)
• Is X(3872) a molecule?
• X(3872): Hadronic Molecules in Effective Field Theory
• Decay width of light quark hybrid meson from the lattice
• Hybrid and Conventional Mesons in the Flux Tube Model: Numerical Studies and their Phenomenological Implications
• Coupled-channel model for charmonium levels and an option for X(3872)
• Strong Decays of Strange Quarkonia
• New states above charm threshold
• Properties of Orbitally Excited Heavy-Light Mesons
• Hadron Loops: General Theorems and Application to Charmonium
• Hybrid Meson Decay Phenomenology
• QCD phenomenology of static sources and gluonic excitations at short distances
• Interpretation of the X(3872) as a charmonium state plus an extra component due to the coupling to the meson-meson continuum
• The lightest hybrid meson supermultiplet in QCD
• X(3872) as a hadronic molecule and its decays to charmonium states and pions
• Coupled-Channel and Screening Effects in Charmonium Spectrum
• The $\xi (2220)$ Revistited
• $D_{sJ}(2860)$ and $D_{sJ}(2715)$
• Strong decays of heavy-light mesons in a chiral quark model
• Decay channels and charmonium mass-shifts
• X(3915) and X(4350) as new members in P-wave charmonium family
• Distinguishing Among Strong Decay Models
• On Deusons or Deuteronlike Meson-Meson Bound States
• Heavy quarkonium hybrids from Coulomb gauge QCD
• Isospin breaking, coupled-channel effects, and X(3872)
• On the hidden charm state at 3872 MeV
• The newly observed open-charm states in quark model
• Canonical Interpretation of the D_{sJ}(2860) and D_{sJ}(2690)
• Scaling of the 3P0 strength in heavy meson strong decays
• Mass of D*_sJ(2317) and Coupled Channel Effect
• Nature of X(3872) from data
• Pionic Decays of $D_{sj}(2317)$, $D_{sj}(2460)$ and $B_{sj}(5718)$, $B_{sj}(5765)$
• Evidence for the eta_b(2S) and observation of h_b(1P) -> eta_b(1S) gamma and h_b(2P) -> eta_b(1S) gamma
• Higher bottom and bottom-strange mesons
• Unquenched quark model for baryons: magnetic moments, spins and orbital angular momenta
• Precision Measurement of the Mass of the h_c(1P1) State of Charmonium
• Properties of the Charmed P-wave Mesons
• Dynamics of Hadronic Molecule in One-Boson Exchange Approach and Possible Heavy Flavor Molecules
• The Photoproduction of Hybrid Mesons from Cebaf to HERA
• Ambiversion of X(3872)
• Properties of the Strange Axial Mesons in the Relativized Quark Model
• B_{s1}(5830) and B_{s2}^*(5840)
• Newly observed D_{sJ}(3040) and the radial excitations of P-wave charmed-strange mesons
• Channel coupling in heavy quarkonia: energy levels, mixing, widths and new states
• Newly observed D(2550), D(2610), and D(2760) as 2S and 1D charmed mesons
• Strong decays of newly observed $D_{sJ}$ states in a constituent quark model with effective Lagrangians
• X(3872) is not a true molecule
• Molecular structures in charmonium spectrum: The $XYZ$ puzzle
• Strong decays of the newly observed $D(2550)$, $D(2600)$, $D(2750)$, and $D(2760)$
• Excited Charmonium Decays by Flux-Tube Breaking and the ${\psi }^{{}^{\prime }}$ Anomaly at CDF
• Newly observed $D_J(3000{)}^{+,0}$ and $D_J^{\ast }(3000{)}^0$ as $2P$ states in $D$ meson family
• The 2^-+ assignment for the X(3872)
• Possible 2S and 1D charmed and charmed-strange mesons
• Spectra and decays of hybrid charmonia
• Implication of BaBar's new data on the $D_{s1}(2710)$ and $D_{sJ}(2860)$
• Bottomonium Spectrum with Coupled-Channel Effects
• $X(1835)$ and $\eta (1760)$ observed by the BES Collaboration
• A relativistic chiral quark model for pseudoscalar emission from heavy mesons
• Towards two-body strong decay behavior of higher $\rho$ and ${\rho }_3$ mesons
• Axial resonances a1(1260), b1(1235) and their decays from the lattice
• Hadronic molecules with both open charm and bottom
• Hybrid meson properties in Lattice QCD and Flux Tube Models
• On two- and three-body descriptions of hybrid mesons
• Delicate interplay between the D0-D*0, rho0-J/psi, and omega-J/psi channels in the X(3872) resonance
• Are the $X$(4160) and $X$(3915) charmonium states?
• Radiative decay of the X(3872) as a mixed molecule-charmonium state in QCD Sum Rules
• Hybrid Decays
• The Strong Decay Patterns of the $1^{-+}$ Exotic Hybrid Mesons
• Multichannel calculation for Ds* vector states and the Ds(2632) resonance
• B meson spectroscopy
• The Decay Properties of the 1^{-+} Hybrid State
• Meson Decays In A Quark Model
• Do $1^{-}c\bar{c}g$ hybrid meson exist, do they mix with charmonium ?
• Strong charmonium decays in a microscopic model
• Recoupling matrix elements and decay
• Distinguishing Hybrids from Radial Quarkonia
• Study of the D^0 \to pi^-pi^+pi^-pi^+ decay
• Comment on the Nature of the $D_{s1}^{\ast }(2710)$ and $D_{sJ}^{\ast }(2860)$ Mesons
• Coupling constants and transition potentials for hadronic decay modes of a meson
• On the nature of the $π_2(1880)
• Quasi-bound states in the continuum: a dynamical coupled-channel calculation of axial-vector charmed mesons
• Excited flux tube from $q\bar{q}g$ hybrid mesons
• Meson decay in a corrected $3_0^P$ model
• Dynamics of hadron strong production and decay
• The "forbidden" decays of hybrid mesons to $\pi \rho$ can be large
• Hyperfine splitting and the experimental candidates for η_b(2S)
• How the small hyperfine splitting of P-wave mesons evades large loop corrections
• Reaction $e^{+}{e}^{-}\to \bar{D}D$ and ${\psi }^{\prime }$ mesons
• Looking for a gift of Nature: Hadron loops and hybrid mixing
• Towards a Relativistic Description of Exotic Meson Decays
• Charmonium production in e+e- to ψ+ X(c\bar c) and e+e- to D*D_J
• Fine Splitting in Charmonium Spectrum with Channel Coupling Effect
• Light meson decay in the c3p0 model
• Quarkonium Mass Splitting Revisited: Effects of Closed Mesonic Channels
• Using pi_2(1670) -> b_1(1235) pi to Constrain Hadronic Models
• The X(3872) and other X,Y,Z Resonances as Hidden Charm Meson-Meson Molecules
• Study on the mechanism of open-flavor strong decays

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• Charmed-strange mesons revisited: mass spectra and strong decays
• Molecular Interpretation of the $P_c(4440)$ and $P_c(4457)$ States
• Production of $P_c$ states in ${\Lambda }_b$ decays
• Modern meson spectroscopy: the fundamental role of unitarity
• Exploring open-charm decay mode ${\Lambda }_c{\bar{\Lambda }}_c$ of charmonium-like state $Y(4630)$
• Model-independent predictions for decays of hidden-heavy hadrons into pairs of heavy hadrons
• Axial-vector $D_1$ hadrons in $D^{\ast }\pi$ scattering from QCD
• Tetraquark mass relations in quark and diquark models
• Gluon-pair-Creation Production Model of Strong Interaction Vertices