  We develop a framework of calculating entanglement entropy for non-conformal
field theories with the use of the dilaton effective action. To illustrate it,
we locate a theory on a cylinder $\mathbb{R} \times \mathbb{S}^{2}$ and compute
entanglement entropy of a cap-like region perturbatively with respect to the
mass for a free massive scalar field. A renormalized entanglement entropy (REE)
is proposed to regularize the ultraviolet divergence on the cylinder. We find
that the REE decreases monotonically both in the small and large mass regions
as the mass increases. We confirm all of these behaviors by the numerical
calculations, which further shows the monotonic decrease of the REE in the
entire renormalization group flow.
