Two-particle scattering from finite-volume quantization conditions using the plane wave basis

Understand

We propose an alternative approach to L\"uscher's formula for extracting two-body scattering phase shifts from finite volume spectra with no reliance on the partial wave expansion.

• We use an effective-field-theory-based Hamiltonian method in the plane wave basis and decompose the corresponding matrix elements of operators into irreducible representations of the relevant point groups.
• The proposed approach allows one to benefit from the knowledge of the long-range interaction and avoids complications from partial wave mixing in a finite volume.
• We consider spin-singlet channels in the two-nucleon system and pion-pion scattering in the $\rho$-meson channel in the rest and moving frames to illustrate the method for non-relativistic and relativistic systems, respectively.