  In this paper we generalise the main result of a recent work by J. L. Cardy
and the present authors concerning the bi-partite entanglement entropy between
a connected region and its complement. There the expression of the leading
order correction to saturation in the large distance regime was obtained for
integrable quantum field theories possessing diagonal scattering matrices. It
was observed to depend only on the mass spectrum of the model and not on the
specific structure of the diagonal scattering matrix. Here we extend that
result to integrable models with backscattering (i.e. with non-diagonal
scattering matrices). We use again the replica method, which connects the
entanglement entropy to partition functions on Riemann surfaces with two branch
points. Our main conclusion is that the mentioned infrared correction takes
exactly the same form for theories with and without backscattering. In order to
give further support to this result, we provide a detailed analysis in the
sine-Gordon model in the coupling regime in which no bound states (breathers)
occur. As a consequence, we obtain the leading correction to the sine-Gordon
partition function on a Riemann surface in the large distance regime.
Observations are made concerning the limit of large number of sheets.
