Finite volume treatment of pi pi scattering and limits to phase shifts extraction from lattice QCD

Abstract

We study theoretically the effects of finite volume for pipi scattering in order to extract physical observables for infinite volume from lattice QCD. We compare three different approaches for pipi scattering (lowest order Bethe-Salpeter approach, N/D and inverse amplitude methods) with the aim to study the effects of the finite size of the box in the potential of the different theories, specially the left-hand cut contribution through loops in the crossed t,u-channels. We quantify the error made by neglecting these effects in usual extractions of physical observables from lattice QCD spectra. We conclude that for pipi phase-shifts in the scalar-isoscalar channel up to 800 MeV this effect is negligible for box sizes bigger than 2.5m_pi^-1 and of the order of 5% at around 1.5-2m_pi^-1. For isospin 2 the finite size effects can reach up to 10% for that energy. We also quantify the error made when using the standard Luscher method to extract physical observables from lattice QCD, which is widely used in the literature but is an approximation of the one used in the present work.

10 pages, 8 figures

References in corpus (18)

• First results from 2+1 dynamical quark flavors on an anisotropic lattice: light-hadron spectroscopy and setting the strange-quark mass
• Light Hadron Masses from Lattice QCD
• Scalar mesons in a finite volume
• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• Identification of a Scalar Glueball
• Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD
• Scalar Mesons a0(1450) and sigma(600) from Lattice QCD
• Lattice study of light scalar tetraquarks with I=0,2,1/2,3/2: are sigma and kappa tetraquarks?
• On the size of the sigma meson and its nature
• The Inverse Amplitude Method and Adler Zeros
• Lattice QCD determination of patterns of excited baryon states
• A lattice study of the masses of singlet 0++ mesons
• Hadron Spectroscopy with Dynamical Chirally Improved Fermions
• Dynamical generation of pseudoscalar resonances
• The Delta-resonance in a finite volume
• Tetra-Quark Resonances in Lattice QCD
• Ordering of Spin-$\frac{1}{2}$ Excitations of the Nucleon in Lattice QCD
• Searching for tetraquarks on the lattice

Cited by in corpus (19)

• Hadronic molecules
• Towards a theory of hadron resonances
• A finite-volume matrix Hamiltonian model for a Delta -> nucleon-pion system
• Chiral study of the $a_0(980)$ resonance and $\pi \eta$ scattering phase shifts in light of a recent lattice simulation
• Finite-volume and partial quenching effects in the magnetic polarizability of the neutron
• Hidden charm molecules in finite volume
• Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD
• Light- and strange-quark mass dependence of the $\rho (770)$ meson revisited
• Two-particle scattering from finite-volume quantization conditions using the plane wave basis
• Bound states on the lattice with partially twisted boundary conditions
• Predicting the existence of a 2.9 GeV $D{f}_0(980)$ molecular state
• $P$-wave charmonium contribution to hidden-charm states from reanalysis of lattice QCD data
• Cross sections for inelastic meson-meson scattering via quark-antiquark annihilation
• Cross sections for inelastic meson-meson scattering
• On ambiguities of sign determination of the S-matrix from energy levels in a finite box
• Cross sections for 2-to-3 meson-meson scattering
• The pseudoscalar meson and baryon octet interaction with strangeness $S=-2$ in the unitary coupled-channel approximation
• Pion scattering in finite volume within the Inverse Amplitude Method
• Effective Field Theories in a Finite Volume