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 3 P0 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 pseudoscalarmeson 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.

Charmed-strange mesons revisited: Mass spectra and strong decays

“…As for D s (1D (2 − )), the situation is opposite to D s (1D(2 − )), D s (1D (2 − )) strongly couples with DK * via a P wave. Our present calculations are consistent with the conclusion of the heavy quark limit [101,102] and the results are model independent in the heavy quark limit. In addition, The total decay widths of D s (1D(2 − )) and D s (1D (2 − )) can reach up to 240 MeV and 147 MeV, respectively.…”

Phenomenology of Pc(4380)+, Pc(4450)+ and related states

“…The computed values assume point-like pion-emission, but as shown in ref. [40], the same values arise in other models for the pion vertex, including the 3 P 0 , flux tube, and microscopic models, so conclusions based on RBNs are rather general. )…”

“…For simplicity, in this paper the spatial part will be treated as a common factor for the different channels. A similar approach has been applied to meson strong decays by quark-pair creation [40,[58][59][60].…”

Molecular interpretation of the Pc(4440) and Pc(4457) sta

“…Although our potentials are derived with the specific vertex model shown in Eq. (4), the relative signs and magnitudes of the central potentials are the same using other models for the vertex, such as the 3 P 0 model or flux tube model [64]. Hence the problem we identify is rather general in nature.…”