Energy shift of the three-particle system in a finite volume

Abstract

Using the three-particle quantization condition recently obtained in the particle-dimer framework, the finite-volume energy shift of the two lowest three-particle scattering states is derived up to and including order L −6 . Furthermore, assuming that a stable dimer exists in the infinite volume, the shift for the lowest particle-dimer scattering state is obtained up to and including order L −3 . The result for the lowest three-particle state agrees with the results from the literature, and the result for the lowest particle-dimer state reproduces the one obtained by using the Lüscher equation.

Pion scattering in the isospin I=2 channel from elongated lattices

“…[41,42] for a comprehensive calculation of meson-meson scattering lengths. * chrisculver@email.gwu.edu † maximmai@gwu.edu ‡ aalexan@gwu.edu § doring@gwu.edu ¶ fxlee@gwu.edu Systems of more than two pions with maximal isospin have been calculated in lattice QCD [43,44] and serve as a test ground for infinite-volume mapping techniques that are currently being developed [45][46][47][48][49][50][51][52][53][54]. In Ref.…”

Equivalence of three-particle scattering formalisms

“…Figure 5 illustrates diagrammatically the relations given in Eqs. (20), (21), and (23). It is useful to compare Fig.…”

“…Quantization conditions for three hadrons have been derived by various groups using different approaches [12][13][14][15][16][17][18][19][20][21][22][23], as recently reviewed in Ref. [24].…”

Opportunities for Lattice QCD in quark and lepton flavor physics

“…The first step, namely the derivation of a quantization condition, has been achieved for a relativistic system of three identical particles [135,136], including the possibility of mixing with states containing two particles [137] and resonant subprocesses [138]. Several important cross-checks of the formalism have been carried out [139][140][141][142][143][144][145]. A recent review can be found in Ref.…”

“…[146]. A simpler form has been derived for the three-particle case using a nonrelativistic effective field theory [145,147,148], while other relativistic approaches have also been considered [149,150]. Finite-volume energies now depend not only on two-particle scattering amplitudes but also on three-to-three amplitudes.…”