  It is well-known that several classical results about Calder\'{o}n-Zygmund
singular integral operators can be extended to \(X\)-valued functions if and
only if the Banach space \(X\) has the UMD property. The dependence of the norm
of an \(X\)-valued Calder\'{o}n-Zygmund operator on the UMD constant of the
space \(X\) is conjectured to be linear. We prove that this is indeed the case
for sufficiently smooth Calder\'{o}n-Zygmund operators with cancellation,
associated to an even kernel. Our method uses the Bellman function technique to
obtain the right estimates for the norm of dyadic Haar shift operators. We then
apply the representation theorem of T. Hyt\"{o}nen to extend the result to
general Calder\'{o}n-Zygmund operators.
