Properties of the tensor mesons $f_2(1270)$ and $f^\prime_2(1525)$

In the $f_2(1270)-f^\prime_2(1525)$ mixing framework, the isoscalar singlet-octet mixing angle for 1$^3P_2$ tensor nonet is determined to be the value of $27.5^\circ$ and the decays of the two states are investigated. Comparing the predicted results of the decays of the two states with the available experimental data, we find that the predicted results are in good agreement with the experimental data, which shows that the $f_2(1270)$ and $f^\prime_2(1525)$ wave functions don't need other components such as glueballs or the 2 $^3P_2$,3 $^3P_2$,...$q\bar{q}$.