  The experimental isoscalar $\pi\pi\to\pi\pi$ S-wave amplitude squared below
1.75 GeV is characterized by a very broad structure $f_0(400-1200)$ with two
narrow dips due to its destructive interference with the $f_0(980)$ and
$f_0(1500)$. The $f_0(1370)$ and $f_0(1710)$ do not show up clearly in the
$\pi\pi\to\pi\pi$ S-wave amplitude due to their weak coupling to $\pi\pi$. This
paper is about the controversial nature of the broad $f_0(400-1200)$. We
decompose it into two parts, i.e., t-channel $\rho$ meson exchange plus an
additional s-channel resonance $f_0(X)$. With the t-channel $\rho$ meson
exchange fixed by the isotensor $\pi\pi\to\pi\pi$ S-wave scattering, we re-fit
the CERN-Munich (CM) data on $\pi\pi$ scattering to get parameters for the
$f_0(X)$. We find that the $f_0(X)$ is very broad with a nearby pole at
(1.67-0.26i) GeV, while the t-channel $\rho$ meson exchange part produces a
pole at (0.36-0.53i) GeV. The implication of our results for the study of
$\sigma$ and glueball is discussed.
