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For the integrable higher-spin XXX and XXZ spin chains we presentmultiple-integral representations for the correlation function of an arbitraryproduct of Hermitian elementary matrices in the massless ground state. We givea formula expressing it by a single term of multiple integrals. In particular,we explicitly derive the emptiness formation probability (EFP). We assume$2s$-strings for the ground-state solution of the Bethe ansatz equations forthe spin-$s$ XXZ chain, and solve the integral equations for the spin-$s$Gaudin matrix.  In terms of the XXZ coupling $\Delta$ we define $\zeta$ by $\Delta=\cos\zeta$, and put it in a region $0 \le \zeta < \pi/2s$ of the gapless regime:$-1 < \Delta \le 1$ ($0 \le \zeta < \pi$), where $\Delta=1$ ($\zeta=0$)corresponds to the antiferromagnetic point. We calculate the zero-temperaturecorrelation functions by the algebraic Bethe ansatz, introducing the Hermitianelementary matrices in the massless regime, and taking advantage of the fusionconstruction of the $R$-matrix of the higher-spin representations of the affinequantum group.

Correlation functions of the integrable higher-spin XXX and XXZ spin chains through the fusion method