Semi-classical scalar products in the generalised $SU$(2) model

Abstract : In these notes we review the field-theoretical approach to the computation of the scalar product of multi-magnon states in the Sutherland limit where the magnon rapidities condense into one or several macroscopic arrays. We formulate a systematic procedure for computing the 1/$M$ expansion of the on-shell/off-shell scalar product of $M$-magnon states in the generalised integrable model with $SU$(2)-invariant rational $R$-matrix. The coefficients of the expansion are obtained as multiple contour integrals in the rapidity plane.