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.

45 pages, 4 figures, 16 tables

References in corpus (36)

• Is X(3872) {\sl Really} a Molecular State?
• Is X(3872) a molecule?
• Hadron Loops: General Theorems and Application to Charmonium
• X(3872) as a hadronic molecule and its decays to charmonium states and pions
• $D_{sJ}(2860)$ and $D_{sJ}(2715)$
• Strong decays of heavy-light mesons in a chiral quark model
• Decay channels and charmonium mass-shifts
• Heavy quarkonium hybrids from Coulomb gauge QCD
• Isospin breaking, coupled-channel effects, and X(3872)
• The newly observed open-charm states in quark model
• Canonical Interpretation of the D_{sJ}(2860) and D_{sJ}(2690)
• Nature of X(3872) from data
• Pionic Decays of $D_{sj}(2317)$, $D_{sj}(2460)$ and $B_{sj}(5718)$, $B_{sj}(5765)$
• Dynamics of Hadronic Molecule in One-Boson Exchange Approach and Possible Heavy Flavor Molecules
• Ambiversion of X(3872)
• B_{s1}(5830) and B_{s2}^*(5840)
• Newly observed D_{sJ}(3040) and the radial excitations of P-wave charmed-strange mesons
• Newly observed D(2550), D(2610), and D(2760) as 2S and 1D charmed mesons
• Strong decays of the newly observed $D(2550)$, $D(2600)$, $D(2750)$, and $D(2760)$
• Possible 2S and 1D charmed and charmed-strange mesons
• Spectra and decays of hybrid charmonia
• $X(1835)$ and $\eta (1760)$ observed by the BES Collaboration
• On two- and three-body descriptions of hybrid mesons
• Hybrid meson properties in Lattice QCD and Flux Tube Models
• Hadronic molecules with both open charm and bottom
• Radiative decay of the X(3872) as a mixed molecule-charmonium state in QCD Sum Rules
• The Strong Decay Patterns of the $1^{-+}$ Exotic Hybrid Mesons
• B meson spectroscopy
• Recoupling matrix elements and decay
• Coupling constants and transition potentials for hadronic decay modes of a meson
• 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
• Looking for a gift of Nature: Hadron loops and hybrid mixing
• Charmonium production in e+e- to ψ+ X(c\bar c) and e+e- to D*D_J
• Light meson decay in the c3p0 model

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