Generalized Lüscher formula in multichannel baryon-meson scattering

Abstract

Lüscher's formula relates the elastic scattering phase shifts to the two-particle energy levels in a finite cubic box. The original formula was obtained for elastic scattering of two massive spinless particles in the center of mass frame. In this paper, we consider the case for the scattering of a spin 1/2 particle with a spinless particle in multi-channel scattering. A generalized relation between the energy of two particle system and the scattering matrix elements is established. We first obtain this relation using quantum-mechanics in both center-of-mass frame and in a general moving frame. The result is then generalized to quantum field theory using methods outlined in Ref. [1]. We verify that the results obtained using both methods are equivalent up to terms that are exponentially suppressed in the box size.

Nonlinear atom-photon-interaction-induced population inversion and inverted quantum phase transition of Bose-Einstein condensate in an optical cavity

“…Correspondingly the notation SP co (S − , N + ) means the SP of S − coexisting with N + since S − is the lower energy state. The bistable MMQSs observed in this paper agree with the dynamic study of nonequilibrium QPT [13,16]. In the area (yellow) between the line of U = 30 and curve g c+ we have only the single NP of N + with full population inversion, which induced by the nonlinear interaction is a new observation.…”

“…It has been shown that the nonlinear interaction, indeed, results in dynamically unstable phase [16]. Most recently the coexistence of NP and SP was found in the nonequilibrium QPT with time-dependent atom-field coupling [12,16] based on the numerical simulation of zero-points of the energy functional. In order to understand the mechanism of multiphase coexistence we revisit the generalized Dicke model of BEC-cavity experiment [14,17] with nonlinear interaction J z a † a in the whole region of experimental parameters to reveal the bistable NPs as well as the coexistence of NP and SP.…”

“…Since the effective frequency ω can be turned from positive to negative regions by the pump-cavity field detuning ∆ and the atom-photon interaction constant U , much more rich phases arise compared with the ordinary DM. We reinvestigate the MMQSs and related QPT based on the SCS variational method with advantage that both the normal (⇓) and inverted (⇑) pseudospin states revealed in the dynamic study [13] can be taken into account in order to see the multiple steady states observed in the nonequilibrium QPT [13,14,16]. Moreover, an energy functional with one-parameter only can be obtained and thus the stability of MMQSs is justified rigorously.…”

“…A significant achievement is the experimental study of the quantum behaviors of Bose-Einstein condensates (BECs) in ultrahigh-finesse optical cavities [2,9]. More recently the time-dependent nonequilibrium experiments were performed in an open cavity [10,11], which lead to the theoretical interpretations of nonequilibrium QPT [12][13][14][15][16].…”

The optical potential on the lattice

“…In case when only two-particle coupled channels appear, one can make use of the coupled-channel Lüscher equation [2][3][4][5][6][7][8][9] and fit a simple pole parameterization for the multi-channel K-matrix elements to the measured energy spectrum in the finite volume [10][11][12]. A more sophisticated parameterization of the K-matrix elements, which is applicable in a wider range of the energies, can be obtained using unitarized chiral perturbation theory (ChPT) [13][14][15][16][17].…”