  In this letter we study the exponentially decaying corrections to saturation
of the second R\'enyi entropy of one interval of length L in minimal E8 Toda
field theory. It has been known for some time that the entanglement entropy of
a massive quantum field theory in 1+1 dimensions saturates to a constant value
for m1 L <<1 where m1 is the mass of the lightest particle in the spectrum.
Subsequently, results by Cardy, Castro-Alvaredo and Doyon have shown that there
are exponentially decaying corrections to this behaviour which are
characterised by Bessel functions with arguments proportional to m1 L. For the
von Neumann entropy the leading correction to saturation takes the precise
universal form -K0(2m1 L)/8 whereas for the R\'enyi entropies leading
corrections which are proportional to K0(m1 L) are expected. Recent numerical
work by P\'almai for the second R\'enyi entropy of minimal E8 Toda has found
next-to-leading order corrections decaying as exp(-2m1 L) rather than the
expected exp(-m1 L). In this paper we investigate the origin of this result and
show that it is incorrect. An exact form factor computation of correlators of
branch point twist fields reveals that the leading corrections are proportional
to K0(m1 L) as expected.
