  This paper is devoted to the spatial analyticity of the solution of the BBM
equation on the real line with an analytic initial data. It is shown that the
analytic radius has a lower bound like $t^{-\frac{2}{3}}$ as time $t$ goes to
infinity, which is an improvement of previous results. The main new ingredient
is a higher order almost conservation law in analytic spaces. This is proved by
introducing an equivalent analytic norm with smooth symbol and establishing
some algebra identities of higher order polynomials.
