  We consider the rational six-vertex model on an L-by-L lattice with domain
wall boundary conditions and restrict N parallel-line rapidities, N < L/2, to
satisfy length-L XXX spin-1/2 chain Bethe equations. We show that the partition
function is an (L-2N)-parameter extension of Slavnov's scalar product of a
Bethe eigenstate and a generic state, with N magnons each, on a length-L XXX
spin-1/2 chain.
  Decoupling the extra parameters, we obtain a third determinant expression for
the scalar product, where the first is due to Slavnov [1], and the second is
due to Kostov and Matsuo [2]. We show that the new determinant is a discrete KP
tau-function in the inhomogeneities, and consequently that tree-level N = 4 SYM
structure constants that are known to be determinants, remain determinants at
1-loop level.
