Finite-volume effects for two-hadron states in moving frames

Abstract

We determine the finite-volume corrections to the spectrum and matrix elements of twohadron states in a moving frame, i.e. one in which the total momentum of the twohadrons is non-zero. The analysis is performed entirely within field theory and the results are accurate up to exponential corrections in the volume. Our results for the spectrum are equivalent to those of Rummukainen and Gottlieb which had been obtained using a relativistic quantum mechanical approach. A technical step in our analysis is a simple derivation of the summation formulae relating the loop summations over the momenta of the two hadrons in finite volume to the corresponding integrals in infinite volume.

Baryons as relativistic three-quark bound states

“…It turns out that the energies of these states can be used to extract phase shifts in the infinite volume, which allow for a reconstruction of the S-matrix as a function of energy and consequently a determination of the resonance pole positions. In the literature this is known as the Lüscher method [260,266]; originally formulated for the case of a particle at rest, the framework has been generalised to moving frames [267][268][269] and to multi-channel problems, see e.g. [270][271][272][273][274][275] and references therein.…”

Coupled-channel Dπ, Dη and D s K ¯ $$ {D}_s\overline{K} $$ scattering from lattice QCD

“…In particular, the Lüscher method and its extensions for relating finite-volume spectra to scattering amplitudes are now well established for elastic [5][6][7][8][9][10][11][12][13][14] and coupled-channel [15][16][17][18][19] hadron-hadron scattering. These methods have been demonstrated in a number of applications, notably for the ρ-resonance seen in P -wave ππ scattering [20][21][22][23][24][25][26][27][28][29], and for the σ resonance seen in S-wave ππ scattering [30].…”

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

“…The problem has been thoroughly studied in Ref. [18] and it is particularly relevant when one performs lattice simulations for particles in a moving frame [22,[35][36][37][38][39][40][41][42][43][44]. The formulation for moving frames along the lines of Ref.…”