Feynman-Hellmann theorem for resonances and the quest for QCD exotica

Abstract

The generalization of the Feynman-Hellmann theorem for resonance states in quantum field theory is derived. On the basis of this theorem, a criterion is proposed to study the possible exotic nature of certain hadronic states emerging in QCD. It is shown that this proposal is supported by explicit calculations in Chiral Perturbation Theory and by large-$N_c$ arguments. Analyzing recent lattice data on the quark mass dependence in the pseudoscalar, vector meson, baryon octet and baryon decuplet sectors, we conclude that, as expected, these are predominately quark-model states, albeit the corrections are non-negligible.

26 pages, 2 figures

References in corpus (13)

• Hadronic Uncertainties in the Elastic Scattering of Supersymmetric Dark Matter
• A Theory of Scalar Mesons
• Mesonic low-energy constants
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Scalar mesons in a finite volume
• Nucleon mass and sigma term from lattice QCD with two light fermion flavors
• Chiral extrapolations of baryon masses for unquenched three-flavor lattice simulations
• Improved predictions for $\mu \to e$ conversion in nuclei and Higgs-induced lepton flavor violation
• The electric dipole moment of the deuteron from the QCD $\theta$-term
• Large-$N_c$ naturalness in coupled-channel meson-meson scattering
• Non-ordinary light meson couplings and the $1/N_c$ expansion
• Chiral power counting of one- and two-body currents in direct detection of dark matter
• On the sigma sigma term

Cited by in corpus (5)

• Toward a First-Principles Calculation of Electroweak Box Diagrams
• Radiative corrections to semileptonic beta decays: Progress and challenges
• The Large $N_c$ limit of QCD on the lattice
• Chiral symmetry constraints on resonant amplitudes
• $N_C$ evolution of the light meson resonances