It is shown that in order to explain the ratios $x$ and $y$ of the helicity amplitudes for the process $\frac{J}{\psi }\to \gamma +f_2\mathrm{}\left(1270\right)\mathrm{}$ and the experimental datum $R=\frac{B\left({\psi }^{\prime }\mathrm{}\right(3685)\mathrm{}\to \gamma +f_2\mathrm{}(1270\left)\right)}{B(\frac{J}{\psi }\to \gamma +f_2\mathrm{}(1270\left)\right)}=(9\mathrm{}\pm 3)\%$ in terms of the mixture between the meson $f_2\mathrm{}\left(1270\right)\mathrm{}$ and a $2^{++}$ glueball, two $D$-wave components have to be considered in addition to the $S$-wave component of the $2^{++}$ glueball.

• Received 18 April 1989

DOI:https://doi.org/10.1103/PhysRevD.40.1517