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

Abstract

We propose an alternative approach to Lüscher’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 ρ-meson channel in the rest and moving frames to illustrate the method for non-relativistic and relativistic systems, respectively. For the two-nucleon system, the long-range interaction due to the one-pion exchange is found to make the single-channel Lüscher formula unreliable at the physical pion mass. For S-wave dominated states, the single-channel Lüscher method suffers from significant finite-volume artifacts 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 effects prevent the application of the single-channel Lüscher formula regardless of the box size (except for the near-threshold region). Using a toy model to generate synthetic data for finite-volume energies, we show that our effective-field-theory-based approach in the plane wave basis is capable of a reliable extraction of the phase shifts. For pion-pion scattering, we employ a phenomenological 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 the experimental results.

Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules

“…In literature, the pole in the interaction potential was often called the CDD pole, e.g. [508,509,510]. One should be cautious about the different meanings of the "CDD pole" according to the context.…”

“…-EFT based frameworks to extract the interactions and structures from the lattice QCD data (see [863,1144,510,897] for examples) should be further developed, especially for the coupled-channel systems.…”

Three relativistic neutrons in a finite volume

“…[66][67][68][69][70]. Other finite-volume approaches, which we do not discuss, include formulating EFTs in finite volume [71][72][73][74][75], the finite-volume Hamiltonian method (see, e.g., ref. [76]), and the HAL-QCD method [15].…”

Finite volume NN systems using plane wave expansion and eigenvector continuation

“…We use the projection operator technique (see Ref. [2] for details) to reduce the above equation into different irreps,…”

“…In our previous work [2], we proposed a approach based on plane wave expansion and chiral effective field theory (ChEFT). The plane wave expansion renders the natural inclusion of the partial wave mixing effect and explicit OPE interaction in ChEFT make it work well for small box.…”