Use of Dipole Sum Rules to Estimate Upper and Lower Bounds for Radiative and Total Widths ofχ(3414),χ(3508), andχ(3552)

Upper and lower bounds on the widths for ${\chi }_J\to \gamma \psi \mathrm{}\left(3095\right)\mathrm{}$ can be estimated by assuming $E1\mathrm{}$ transitions and approximate Russell-Saunders coupling for the $c\overline{c}$ system. Experimental widths for $\psi \mathrm{}\left(3684\right)\mathrm{}\to \gamma {\chi }_J$ make the lower bound more restrictive, giving radiative widths of 160 → 240, 230 → 400, and 280 → 480 keV for 3414-, 3508-, and 3552-MeV states, respectively. Cascade branching ratio data permit estimation of the total widths as > 1.6, 0.3-1.5, and 0.6-4 MeV, respectively.