Massive corrections to entanglement in minimal E8 Toda field theory

In this letter we study the exponentially decaying corrections to saturation of the second Renyi entropy of one interval of length l in minimal E-8 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 m(1)l >> 1 where m(1) 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 characterized by Bessel functions with arguments proportional to m(1). For the von Neumann entropy the leading correction to saturation takes the precise universal form -1/8K(0) (2m(1)l) whereas for the Renyi entropies leading corrections which are proportional to K-0 (m(1)l) are expected. Recent numerical work by Palmai for the second Renyi entropy of minimal E-8 Toda has identified next-to-leading order corrections which decay as e(-2m1l) rather than the expected e(-m1l). 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 K-0(m(1)l) as expected.