  It is shown that the uniform radius of spatial analyticity $\sigma(t)$ of
solutions at time $t$ to the KdV equation cannot decay faster than $|t|^{-4/3}$
as $|t| \to \infty$ given initial data that is analytic with fixed radius
$\sigma_0$. This improves a recent result of Selberg and Da Silva, where they
proved a decay rate of $|t|^{-(4/3 + \varepsilon) }$ for arbitrarily small
positive $\varepsilon$. The main ingredients in the proof are almost
conservation law for the solution to the KdV equation in space of analytic
functions and space-time dyadic bilinear $L^2$ estimates associated with the
KdV equation.
