$I = 3$ three-pion scattering amplitude from lattice QCD

Meson-Nucleon Scattering Amplitudes from Lattice QCD

“…2 applies also to coupled two-hadron scattering channels which are relevant for the Λ(1405) resonance. Furthermore, extension of the finite-volume formalism to treat meson-meson-baryon channels and the corresponding lattice QCD computation of the spectra have not yet been completed, although first calculations of three-pion scattering amplitudes are encouraging [59,84,85]. Nonetheless, the range of impact of the two-to-two scattering amplitudes can be increased by using lattice QCD scattering data as an input to effective field theories and EFT-inspired models.…”

Relativistic-invariant formulation of the NREFT three-particle quantization condition

“…In fact, these investigations go back to the 1950's and have been re-activated recently with the use of the modern technique of the non-relativistic effective Lagrangians [11,30,[46][47][48][49][50][51][52][53][54]. Furthermore, in quite a few recent papers, the theoretical approaches mentioned above have been successfully used to analyze data from lattice calculations [38,53,[55][56][57][58][59][60][61][62][63][64][65]. Last but not least, a three-body analog of the Lellouch-Lüscher formula for the finite-volume matrix elements [66] has been recently derived in two different settings [67,68].…”

“…As a cure to the problem, within the RFT approach, it was proposed to modify the three-body propagator, bringing it to a manifestly invariant form (the pertinent formulae are given, e.g., in Ref. [58]) 2 . We shall briefly consider this prescription below, in Sect.…”

On the three-particle analog of the Lellouch-Lüscher formula

“…It should be mentioned that the above theoretical developments have largely boosted the study of the three (and more particles) on the lattice, be this in QCD or other fieldtheoretical models [11][12][13][14][15][16][17][18][19]. In view of these activities, the need for the three-particle analog of the LL formula, which should be used for the extraction of the matrix elements, becomes obvious.…”