Resonances in a finite volume

Abstract

International audienceWe review applications of effective field theory methods in a finite volume for the extraction of the characteristics of unstable particles from lattice QCD calculations. In particular, the scalar mesons f0(980),a0(980) are considered. We formulate criteria that distinguish between hadronic molecules and tightly bound quark states, as well as between the ordinary qq̄ and the tetraquark states. Using these criteria will enable one to study the nature of scalar mesons on the lattice. Further, we also formulate a procedure to calculate resonance matrix elements on the lattice by using the background field method

S-waveKK*interactions in a finite volume and thefGeng1, Ren2, Zhou3 et al. 2015Phys. Rev. D282330View full textAdd to dashboardCite

“…Inclusion of high-order kernels in the chiral unitary approach is found to have negligible effects 1 Although in the present work we only need to tackle a single channel problem, it should be noted that the Lüscher method has been generalized to the case of multichannel scattering [19][20][21][22]. A thorough study of the coupled πK and ηK channels has recently been done in Refs.…”

Two-particle elastic scattering in a finite volume including QED

“…Recently, Lüscher's formalism has been extended to coupled-channels systems (i.e. channels that are coupled in infinite-volume), and to systems comprised of particles with non-zero spin [26][27][28][29][30][31][32][33][34][35][36][37][38]. Further, the FV formalism describing nucleon-nucleon (NN) systems with arbitrary CM momenta, spin, angular momentum, isospin and twisted boundary conditions has been developed, providing the quantization conditions (QCs) for the energy eigenvalues in irreducible representations (irreps) of the FV symmetry groups [39].…”

Resonance Extraction from the Finite Volume

“…If G is only given by the phase space factor (purely imaginary above threshold and real below), one has a K-matrix approach. Dispersive real contributions to G can be included by writing a dispersion relation, but also then the amplitude can be recast in the K-matrix formulation [4]. The imaginary part of G ensures also coupled-channel two-body unitarity.…”

“…In Refs. [4,5] it was proposed to modify the boundary conditions for the strange quark to remove the influence of the threshold. In the notation used here, this results in a modifiedG.…”

“…In the volume-dependent spectrum of eigenvalues, "avoided level crossing" is usually taken as a signal of a resonance, but this criterion has been shown insufficient for resonances with larger widths [1][2][3][4][5]. For resonances with a single, two-body decay channel, one often uses Lüscher's approach to extract phase shifts from the discrete energy levels in the box [6,7].…”