  The discussion of renormalization group flows in four-dimensional conformal
field theories has recently focused on the $a$-anomaly. It has been shown that
there is a monotonic decreasing function which interpolates between the
ultraviolet and infrared fixed points such that $\Delta a=a_{UV}-a_{IR}>0$. In
that context Komargodski and Schwimmer showed that $\Delta a$ could be studied
by means of dilaton-dilaton scattering. In this paper we examine the
$a$-theorem using these methods for a four-dimensional interacting theory: the
O(N) vector model, considered to leading order in the 1/N expansion and all
orders in the coupling constant $\lambda$.
