  We find the analytic expression of the trace of powers of the reduced density
matrix on an interval of length L, for a massive boson field in 1+1 dimensions.
This is given exactly (except for a non universal factor) in terms of a finite
sum of solutions of non linear differential equations of the Painlev\'e V type.
Our method is a generalization of one introduced by Myers and is based on the
explicit calculation of quantities related to the Green function on a plane,
where boundary conditions are imposed on a finite cut. It is shown that the
associated partition function is related to correlators of exponential
operators in the Sine-Gordon model in agreement with a result by Delfino et al.
We also compute the short and long distance leading terms of the entanglement
entropy. We find that the bosonic entropic c-function interpolates between the
Dirac and Majorana fermion ones given in a previous paper. Finally, we study
some universal terms for the entanglement entropy in arbitrary dimensions
which, in the case of free fields, can be expressed in terms of the two
dimensional entropy functions.
