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 non-identical particles with arbitrary intrinsic spins. The result accommodates general Lorentz structures as well as non-zero 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. D91 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 ($\pi \gamma^\star \to [\pi \pi, K \overline K] \to \pi \gamma^\star$), kaon ($K \gamma^\star \to [\pi K, \eta K] \to K \gamma^\star$) and nucleon ($N \gamma^\star \to N \pi \to N \gamma^\star$), as well as double-$\beta$ decays, and radiative corrections to the single-$\beta$ 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.