Finite-volume matrix elements in multiboson states

We derive the relations necessary for the extraction of matrix elements of multihadron systems from finite-volume lattice QCD calculations. We focus on systems of $n\ge 2$ weakly interacting identical particles without spin. These results will be useful in extracting physical quantities from lattice QCD measurements of such matrix elements in many-pion and many-kaon systems.

Figure 1

Representative contributions in the calculation of the finite-volume matrix elements. The solid lines correspond to the boson propagators, and the vertices indicate either strong scattering (dark square) or one- and two-body currents (light and dark circles, respectively). The contribution of a given topology is shown up to combinatoric factors. The combinations $\mathcal{U}=Q_1^{\prime }+Q_1^{\prime \prime }$ and $\mathcal{V}=R_1^{\prime }+R_1^{\prime \prime }$ are used in the final expression.