Scattering of unstable particles in a finite volume: The case ofπρscattering and thea1(1260)resonance

Abstract

We present a way to evaluate the scattering of unstable particles quantized in a finite volume with the aim of extracting physical observables for infinite volume from lattice data. We illustrate the method with the πρ scattering which generates dynamically the axial-vector a1(1260) resonance. Energy levels in a finite box are evaluated both considering the ρ as a stable and unstable resonance and we find significant differences between both cases. We discuss how to solve the problem to get the physical scattering amplitudes in the infinite volume, and hence phase shifts, from possible lattice results on energy levels quantized inside a finite box.

S-waveKK*interactions in a finite volume and thefGeng1, Ren2, Zhou3 et al. 2015Phys. Rev. D292330View full textAdd to dashboardCite

“…[48][49][50]. For two-body systems with one unstable particle, one can use a formalism in which the self-energy of the unstable particle is discretized in the moving frame [11]. We shall not do this here, although when more refined lattice calculations are available it would be interesting to tackle this problem.…”

“…It is true that the consideration of the decay channels of the particles involved in a problem leads to changes in the spectrum [11,46,53] and that to get the proper spectrum multihadron interpolators should be used [54], but also, as mentioned in Ref. [54] , one can and must restrict oneself to lower energies if the interpolators accounting for the inelastic spectrum are not used.…”

“…In recent years, however, it has been suggested to be a dynamically generated state made from the KK * interaction, together with its axial-vector counterparts [2,3]. Such a picture has been extensively tested in the past decade [4][5][6][7][8][9][10][11][12][13][14]. All these studies yield consistent results that the ground-state axial-vector mesons can be understood as dynamically generated states or at least contain large pseudoscalar meson-vector meson components.…”

“…[26], the authors have developed a new effective approach to connect the LQCD discrete energy levels with the physical phase shifts (energies) by keeping the full relativistic two-body propagator, from which the Lüscher formulation can be derived. This new approach has been applied to study finite volume effects in the meson-baryon interaction in the Jülich model [27]; the KD, ηD s interaction [28,29]; the pion-kaon scattering [30,31]; the DN, πΣ c interaction [32]; the πρ interaction [11]; the ππ interaction [33]; and theKN interaction [34].…”

Resonance Extraction from the Finite Volume

“…Theoretical developments addressing finite-volume effects for three-body systems are pioneered in Refs. [48][49][50][51][52][53][54], although much conceptual work, including three-body unitarity constraints, remains to be done.…”