  We study I=0 $d$ wave $\pi\pi$ scattering phase shift using a proper
unitarization approach. It is verified that the $f_2(1270)$ resonance
corresponds to a twin pole structure: one on the second sheet, another one on
the third sheet. Also we find fair agreement on $f_2(1270)$ pole's mass and
width between our results and the PDG values. Besides, our analysis reveals the
existence of a virtual state in this channel. Its pole location is determined
by fitting experimental data and it is found to be in good agreement with the
prediction from chiral perturbation theory. Our analysis demonstrates that
partial wave amplitudes calculated in chiral perturbation theory are reliable
in the small $|s|$ region, contrary to some unitarization models.
