Pionic and radiative decay widths of charmed hadrons in a badly broken SU(4) symmetry

The width of ψ(4.414) is surprisingly small for a c$\text{c}$ state far above the charm threshold, Γ_exp ≈ 33 MeV. This fact can be qualitatively understood if one makes the conservative assignment 4 ³S₁. The nodes of the wave function reflect as zero's of the decay amplitude in the momentum of the decay products, and are responsible for the suppression of the couplings to the ground state charmed mesons, Γ(ψ(4.414)→D$\text{D}$+ D$\text{D}$¹ + $\text{D}$D¹ + D¹$\text{D}$¹ + F$\text{F}$ + F$\text{F}$¹ + $\text{F}$F¹ + F¹$\text{F}$¹) ≈ 15 MeV. All the modes are suppressed by factors of the order of 10³ with respect to the k³ spin counting prediction. The dominant modes are predicted to be D¹$\text{D}$¹, F$\text{F}$¹ + $\text{F}$F¹ and D$\text{D}$. Moreover, we show that the contributions from P-wave charmed mesons are reasonably expected to be suppressed either by phase space or by the nodes if their masses lie within certain range. We emphasize however that the smallness of the photon coupling remains to be understood.