We revisit the construction of the eigenvectors of the single and double-row
transfer matrices associated with the Zamolodchikov-Fateev model, within the
algebraic Bethe ansatz method. The left and right eigenvectors are constructed
using two different methods: the fusion technique and Tarasov's construction. A
simple explicit relation between the eigenvectors from the two Bethe ans\"atze
is obtained. As a consequence, we obtain the Slavnov formula for the scalar
product between on-shell and off-shell Tarasov-Bethe vectors.Comment: 28 pages; v2: 30 pages, added proof of (4.40) and (5.39), minor
changes to match the published versio
