On the computation of hadron-to-hadron transition matrix elements in lattice QCD

We discuss the accurate determination of matrix elements < f vertical bar h(w)vertical bar i > where neither vertical bar i > nor vertical bar f > is the vacuum state and h(w) is some operator. Using solutions of the Generalized Eigenvalue Problem (GEVP) we construct estimators for matrix elements which converge rapidly as a function of the Euclidean time separations involved. vertical bar i > and vertical bar f > may be either the ground state in a given hadron channel or an excited state. Apart from a model calculation, the estimators are demonstrated to work well for the computation of the B*B pi-coupling in the quenched approximation. They are also compared to a standard ratio as well as to the "summed ratio method" of [1-3]. In the model, we also illustrate the ordinary use of the GEVP for energy levels.