Existence and analyticity of bound states of a two-particle Schrodinger operator on a lattice

We consider the two-particle discrete Schrodinger operator H-mu(K) corresponding to a system of two arbitrary particles on a d-dimensional lattice Zd, d = 3, interacting via a pair contact repulsive potential with a coupling constant mu > 0 (K. Td is the quasimomentum of two particles). We find that the upper (right) edge of the essential spectrum can be either a virtual level (for d = 3, 4) or an eigenvalue (for d = 5) of H-mu(K). We show that there exists a unique eigenvalue located to the right of the essential spectrum, depending on the coupling constant mu and the two-particle quasimomentum K. We prove the analyticity of the corresponding eigenstate and the analyticity of the eigenvalue and the eigenstate as functions of the quasimomentum K. Td in the domain of their existence.