Pion scattering in finite volume within the Inverse Amplitude Method

Abstract

We study the effect of a finite volume for pion-pion scattering within Chiral Perturbation Theory (ChPT) and the Inverse Amplitude Method (IAM) in a $L^3$ box (rest frame). Our full ChPT calculation takes into account the discretization not only in the $s$-channel loops but also in the $t,u$- channels and tadpole contributions. Hence, not only the unitarity right-hand cut but also the left-hand one continuum contributions are calculated in the finite volume. A proper extension of the standard Veltman-Pasarino identities is needed, as well as a suitable projection on the internal space spanned by the irreducible representations (irreps) of the octahedral group, based on either a finite set of cubic harmonics or the matrices which represent the irreps properly. From the ChPT we construct the IAM in the internal space, which provides the full volume dependence of the interacting energy levels of two-pions scattering in the finite volume. Our results for various low-energy constants sets show sizable corrections with respect to previous analyses in the literature for $m_{\pi }L\lesssim 2$, being compatible with energy levels lattice data. We expect that our analysis and results will help to optimize the process of determination of energy levels and phase-shifts with higher accuracy.

References in corpus (52)

• Chiral symmetry amplitudes in the s-wave isoscalar and isovector channels and the $\sigma ,f_0(980),a_0(980)$ scalar mesons
• Chiral Symmetry Amplitudes in the S-Wave Isoscalar and Isovector Channels and the σ, f_0(980), a_0(980) Scalar Mesons
• FLAG Review 2021
• N/D Description of Two Meson Amplitudes and Chiral Symmetry
• Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
• Finite-Volume Effects for Two-Hadron States in Moving Frames
• Domain wall QCD with physical quark masses
• Scattering processes and resonances from lattice QCD
• The inverse amplitude method in Chiral Perturbation Theory
• On the structure of the scalar mesons $f_0(975)$ and $a_0(980)$
• A relativistic, model-independent, three-particle quantization condition
• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• Scattering phases for meson and baryon resonances on general moving-frame lattices
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• Three particles in a finite volume
• Toward the excited isoscalar meson spectrum from lattice QCD
• Three-particle scattering amplitudes from a finite volume formalism
• Unitarized Chiral Perturbation Theory in a finite volume: scalar meson sector
• A global fit of $\pi \pi$ and $\pi K$ elastic scattering in ChPT with dispersion relations
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Three-body Unitarity in the Finite Volume
• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• Resonance properties from the finite-volume energy spectrum
• Three-body spectrum in a finite volume: the role of cubic symmetry
• Scalar mesons moving in a finite volume and the role of partial wave mixing
• Improving the Volume Dependence of Two-Body Binding Energies Calculated with Lattice QCD
• Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD
• The pi+ pi+ scattering length from maximally twisted mass lattice QCD
• Rho resonance parameters from lattice QCD
• The Inverse Amplitude Method and Adler Zeros
• Three-body unitarity versus finite-volume ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ spectrum from lattice QCD
• Topological phases for bound states moving in a finite volume
• Extraction of isoscalar $\pi \pi$ phase-shifts from lattice QCD
• Finite volume corrections to pi-pi scattering
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Scattering of two and three physical pions at maximal isospin from lattice QCD
• A cross-channel study of pion scattering from lattice QCD
• Pion scattering in the isospin I=2 channel from elongated lattices
• Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875{)}^{+}$ from finite volume energy levels
• Fitting two nucleons inside a box: exponentially suppressed corrections to the Luscher's formula
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: The $\rho$-resonance
• Pole position of the $a_1(1260)$ resonance in a three-body unitary framework
• Finite Temperature Pion Scattering to one-loop in Chiral Perturbation Theory
• Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory
• The pion-pion Interaction in the rho Channel in Finite Volume
• Finite volume treatment of pi pi scattering and limits to phase shifts extraction 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
• Two-loop Sunset Integrals at Finite Volume
• Lattice QCD calculation of $\pi \pi$ scattering length
• Pole trajectories of the $\Lambda (1405)$ helps establish its dynamical nature
• The pion-kaon scattering amplitude and the $K^0(700)$ and $K^{\ast }(892)$ resonances at finite temperature