Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions

A relation is presented between single-hadron long-range matrix elements defined in a finite Euclidean spacetime and the corresponding infinite-volume Minkowski amplitudes. This relation is valid in the kinematic region where any number of two-hadron states can simultaneously go on shell, so that the effects of strongly coupled intermediate channels are included. These channels can consist of nonidentical particles with arbitrary intrinsic spins. The result accommodates general Lorentz structures as well as nonzero momentum transfer for the two external currents inserted between the single-hadron states. The formalism, therefore, generalizes the work by Christ et al. [Phys. Rev. D 91, 114510 (2015)] and extends the reach of lattice quantum chromodynamics (QCD) to a wide class of new observables beyond meson mixing and rare decays. Applications include Compton scattering of the pion $(πγ^*→[ππ,K\overline{K}]→πγ^*)$, kaon $(Kγ^*→[πK,ηK]→Kγ^*)$, and nucleon $(Nγ^*→Nπ→Nγ^*)$, as well as double-$β$ decays, and radiative corrections to the single-$β$ decay, of QCD-stable hadrons. The framework presented will further facilitate generalization of the result to studies of nuclear amplitudes involving two currents from lattice QCD.