Scattering phases for meson and baryon resonances on general moving-frame lattices

Abstract

A proposal by Lüscher enables one to compute the scattering phases of elastic two-body systems from the energy levels of the lattice Hamiltonian in a finite volume. In this work we generalize the formalism to S-, P -and D-wave meson and baryon resonances, and general total momenta.Employing nonvanishing momenta has several advantages, among them making a wider range of energy levels accessible on a single lattice volume and shifting the level crossing to smaller values of m π L.

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

“…[70], which is generalized in Ref. [71] to moving frames. The case of 1/2 + , 1/2 + interacting particles is studied in Ref.…”

“…If lattice data become more precise, a coupledchannel calculation including the S-wave and the two D-waves will be necessary. At nonzero total momentum, which is not considered here, the mixing can become more complicated [71].…”

Finite-Volume Hamiltonian Method for ππ Scattering in Lattice QCD

“…In Ref. [9], the coefficients, C Γ,Γ n ,L,m , between basis state |Γ, Γ n > of the little group and the usual |L, m > are given. In the Hamiltonian model, H 0 is the same as before, while the interaction part is: ( for the P-wave of ππ scattering, neglecting the v potential)…”

Matrix elements of unstable states

“…Finally, in ref. [35], a full group-theoretical analysis of the resulting equation has been performed, including the case of particles with spin. Below, we shall briefly re-derive this result within the non-relativistic EFT along the lines similar to refs.…”

“…We do not, however, address this problem here. A full-fledged group-theoretical analysis of the Gottlieb-Rummukainen formula with the inclusion of the spin of the particles forms the subject of a separate investigation [35].…”