A study on the correlation between poles and cuts in $\pi \pi$ scattering

Abstract

In this paper we propose a dispersive method to describe two-body scattering with unitarity imposed. This approach is applied to elastic $\pi \pi$ scattering. The amplitudes keep single-channel unitarity and describe the experimental data well, and the low-energy amplitudes are consistent with that of chiral perturbation theory. The pole locations of the $\sigma$, $f_0(980)$, $\rho (770)$ and $f_2(1270)$ and their couplings to $\pi \pi$ are obtained. A virtual state appearing in the isospin-two S-wave is confirmed. The correlations between the left (and right) hand cut and the poles are discussed. Our results show that the poles are more sensitive to the right hand cut rather than the left hand cut. The proposed method could be used to study other two-body scattering processes.

arXiv comment10 pages, 4 figures

References in corpus (28)

• ππscattering
• Exotica
• Two-pion contribution to hadronic vacuum polarization
• Mass and width of the lowest resonance in QCD
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Elastic $\pi \pi$ scattering to two loops
• Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis
• Mesonic low-energy constants
• Unitarized Chiral Perturbation Theory in a finite volume: scalar meson sector
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• B_l4 decays and the extraction of |V_ub|
• The pi pi S-wave scattering lengths
• tau -> pi pi pi nu_tau decays and the a_1(1260) off-shell width revisited
• Dispersive analysis of the $\gamma {\gamma }^{\ast }\to \pi \pi$ process
• The pole structure of the unitary, crossing symmetric low energy $\pi \pi$ scattering amplitudes
• A new parametrization for the scalar pion form factors
• Left Hand Singularities, Hadron Form Factors and the Properties of the Sigma Meson
• Two photon couplings of the lightest isoscalars from BELLE data
• Lattice QCD study of the s-wave $\pi \pi$ scattering lengths in the I=0 and 2 channels
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: isospin-2 $\pi \pi$ scattering length
• The branching ratio $\omega \to {\pi }^{+}{\pi }^{-}$ revisited
• Pole analysis on unitarized $SU(3)\times SU(3)$ one loop $\chi$PT amplitudes
• Pole Analysis of Unitarized One Loop $\chi$PT Amplitudes - A Triple Channel Study
• Observation of the decay ${\Lambda }_c^{+}\to {\Sigma }^{-}{\pi }^{+}{\pi }^{+}{\pi }^0$
• ${\eta }^{\prime }\to \eta \pi \pi$ decays in unitarized resonance chiral theory
• A new method to study the number of colors in the final-state interactions of hadrons
• Light $O^{++}$ Mesons: Scalargators in Florida
• A Critical Examination to the Unitarized $\pi \pi$ Scattering Chiral Amplitudes

Cited by in corpus (3)

• A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation
• Study the molecular nature of $\sigma$, $f_0(980)$, and $a_0(980)$ states
• Signatures of the two $K_1(1270)$ poles in $D^{+}\to \nu e^{+}VP$ decay