When hadrons become unstable: a novel type of non-analyticity in chiral extrapolations

Abstract

Hadron masses show a specific dependence on the quark masses. Therefore, the variation of these masses can cause a resonance in a hadronic scattering amplitude to become a bound state. Consequently, the amplitude exhibits a non-analytic behavior at this transition. Crossed amplitudes, where the resonance can be exchanged in the t-channel, can be shown to exhibit the same phenomenon by s-->t analytic continuation. This entails possible kinks in lattice quark mass extrapolations needed to compute hadronic observables.

14 pages, 6 figures

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• Light quark mass dependence in heavy quarkonium physics
• Chiral behavior of vector meson self energies
• $\theta$-dependence of the lightest meson resonances in QCD
• Chiral symmetry constraints on resonant amplitudes
• Gravitational form factors of pions, kaons and nucleons from dispersion relations
• On pion and kaon decay constants and chiral SU(3) extrapolations
• Low-energy $N\varphi$ scattering from a pole-enhanced triangle diagram