  We evaluate the "$\sigma$" exchange contribution to the $\bar{K}N\to\bar{K}N$
scattering within a chiral unitary approach. We show that the chiral transition
potentials for $\pi \pi \to K \bar{K}$ in the $t$-channel lead to a "$\sigma$"
contribution that vanishes in the $\bar{K}$ forward direction and, hence, would
produce a null "$\sigma$" exchange contribution to the $K^-$ optical potential
in nuclear matter in a simple impulse approximation. This is a consequence of
the fact that the leading order chiral Lagrangian gives an I=0 $\pi\pi\to
K\bar{K}$ amplitude proportional to the squared momentum transfer, $q^2$. This
finding poses questions on the meaning or the origin of "$\sigma$" exchange
potentials used in relativistic mean field approaches to the $K^-$ nuclear
selfenergy. This elementary "$\sigma$" exchange potential in
$\bar{K}N\to\bar{K}N$ is compared to the Weinberg-Tomozawa term and is found to
be smaller than present theoretical uncertainties but will be relevant in the
future when aiming at fitting increasingly more accurate data.
