Vector mesons as dynamical resonances in the Bethe-Salpeter framework

Abstract

We present the first dynamical calculation of the $\rho$-meson as a resonance in the Dyson-Schwinger/Bethe-Salpeter framework by including explicit two-pion exchange in addition to the t-channel one-gluon exchange of rainbow-ladder in the interaction kernel. The width is determined from the imaginary part of the resonance pole and is generated by the singularity structure of the integrand, treated by means of suitable path deformations. We find the resonant mass and width to be $640$ MeV and $100$ MeV respectively, corresponding to a coupling constant $g_{\rho \pi \pi }=5.7$; repulsive corrections beyond rainbow-ladder are known to bring these in alignment with experiment. Furthermore we present the dependence of these parameters on the pion mass and compare with results from lattice QCD.

6 pages, 4 figures

References in corpus (10)

• Baryons as relativistic three-quark bound states
• A novel quark-field creation operator construction for hadronic physics in lattice QCD
• Sketching the Bethe-Salpeter kernel
• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• Hadronic unquenching effects in the quark propagator
• Beyond the rainbow: effects from pion back-coupling
• Remarks on pole trajectories for resonances
• Recent developments in bound-state calculations using the Dyson-Schwinger and Bethe-Salpeter equations
• Electromagnetic decays of the neutral pion
• Excited mesons in a Bethe-Salpeter approach

Cited by in corpus (27)

• QCD at finite temperature and chemical potential from Dyson-Schwinger equations
• Diquark Correlations in Hadron Physics: Origin, Impact and Evidence
• Impressions of the Continuum Bound State Problem in QCD
• Light Baryon Spectroscopy
• Landau gauge Yang-Mills propagators in the complex momentum plane
• Masses of positive- and negative-parity hadron ground-states, including those with heavy quarks
• Scattering amplitudes and contour deformations
• Elucidating the effect of intermediate resonances in the quark interaction kernel on the time-like electromagnetic pion form factor
• Four-quark states from functional methods
• Four-quark states with charm quarks in a two-body Bethe-Salpeter approach
• The $\sigma$-meson: four-quark vs. two-quark components and decay width in a Bethe-Salpeter approach
• On the quark spectral function in QCD
• Hidden-flavour four-quark states in the charm and bottom region
• Theory introduction to baryon spectroscopy
• The light scalars: four- vs. two-quark states in the complex energy plane from Bethe-Salpeter equations
• Disentangling different structures in heavy-light four-quark states
• The time-like electromagnetic kaon form factor
• The analytic structure of three-point functions from contour deformations
• Deep reinforcement learning for complex evaluation of one-loop diagrams in quantum field theory
• Timelike form factor for the anomalous process ${\gamma }^{\ast }\pi \to \pi \pi$
• A comprehensive approach to the physics of mesons
• The rainbow modified-ladder approximation and degenerate pion
• Gauge Technique approximation to the $\pi \gamma$ production and the pion transition form factor
• Electromagnetic and strong isospin breaking in light meson masses
• Baryonic form factors of light pseudoscalar mesons
• Decay mechanisms in bound state interaction kernels
• Perturbative method to estimate meson masses in the framework of Bethe-Salpeter equation beyond its dominant interaction