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We propose an alternative approach to L\"uscher's formula for extractingtwo-body scattering phase shifts from finite volume spectra with no reliance onthe partial wave expansion. We use an effective-field-theory-based Hamiltonianmethod in the plane wave basis and decompose the corresponding matrix elementsof operators into irreducible representations of the relevant point groups. Theproposed approach allows one to benefit from the knowledge of the long-rangeinteraction and avoids complications from partial wave mixing in a finitevolume. We consider spin-singlet channels in the two-nucleon system andpion-pion scattering in the $\rho$-meson channel in the rest and moving framesto illustrate the method for non-relativistic and relativistic systems,respectively. For the two-nucleon system, the long-range interaction due to theone-pion exchange is found to make the single-channel L\"uscher formulaunreliable at the physical pion mass. For S-wave dominated states, thesingle-channel L\"uscher method suffers from significant finite-volumeartifacts for a $L=3$~fm box, but it works well for boxes with $L>5$~fm.However, for P-wave dominated states, significant partial wave mixing effectsprevent the application of the single-channel L\"uscher formula regardless ofthe box size (except for the near-threshold region). Using a toy model togenerate synthetic data for finite-volume energies, we show that oureffective-field-theory-based approach in the plane wave basis is capable of areliable extraction of the phase shifts. For pion-pion scattering, we employ aphenomenological model to fit lattice QCD results at the physical pion mass.The extracted P-wave phase shifts are found to be in a good agreement with theexperimental results.

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