Chiral dynamics and baryon resonances

The structure of baryon resonance in coupled-channel meson-baryon scattering is studied from the viewpoint of chiral dynamics. The meson-baryon scattering amplitude can be successfully described together with the properties of the resonance in the scattering, by implementing the unitarity condition for the amplitude whose low energy structure is constrained by chiral theorem. Recently, there have been a major progress in the study of the structure of the resonance in chiral dynamics. We review the methods to clarify the structure of the resonance by focusing on the Lambda(1405) resonance.Comment: 6 pages, talk give at 4th International Symposium on Symmetries in Subatomic Physics (SSP2009), June 2-5, 2009, National Taiwan University, Taipe

Hadron mass scaling near the s-wave threshold

The influence of a two-hadron threshold is studied for the hadron mass scaling with respect to some quantum chromodynamics parameters. A quantum mechanical model is introduced to describe the system with a one-body bare state coupled with a single elastic two-body scattering. The general behavior of the energy of the bound and resonance state near the two-body threshold for a local potential is derived from the expansion of the Jost function around the threshold. It is shown that the same scaling holds for the nonlocal potential induced by the coupling to a bare state. In p or higher partial waves, the scaling law of the stable bound state continues across the threshold describing the real part of the resonance energy. In contrast, the leading contribution of the scaling is forbidden by the nonperturbative dynamics near the s-wave threshold. As a consequence, the bound state energy is not continuously connected to the real part of the resonance energy. This universal behavior originates in the vanishing of the field renormalization constant of the zero-energy resonance in the s wave. A proof is given for the vanishing of the field renormalization constant, together with a detailed discussion.Comment: 11 pages, 4 figures. v4: Published versio

Monodromy and local-global compatibility for l=p

We strengthen the compatibility between local and global Langlands correspondences for GL_{n} when n is even and l=p. Let L be a CM field and \Pi\ a cuspidal automorphic representation of GL_{n}(\mathbb{A}_{L}) which is conjugate self-dual and regular algebraic. In this case, there is an l-adic Galois representation associated to \Pi, which is known to be compatible with local Langlands in almost all cases when l=p by recent work of Barnet-Lamb, Gee, Geraghty and Taylor. The compatibility was proved only up to semisimplification unless \Pi\ has Shin-regular weight. We extend the compatibility to Frobenius semisimplification in all cases by identifying the monodromy operator on the global side. To achieve this, we derive a generalization of Mokrane's weight spectral sequence for log crystalline cohomology.Comment: 34 page

Model-independent determination of the compositeness of near-threshold quasibound states

We study the compositeness of near-threshold states to clarify the internal structure of exotic hadron candidates. Within the framework of effective field theory, we extend the Weinberg's weak-binding relation to include the nearby CDD (Castillejo-Dalitz-Dyson) pole contribution with the help of the Pade approximant. Finally, using the extended relation, we conclude that the CDD pole contribution to the Lambda(1405) baryon in the Kbar N amplitude is negligible.Comment: 5 pages, Proceedings of the 14th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU2016), July 25-30, 2016, Kyoto, Japa

Generalized weak-binding relations of compositeness in effective field theory

We study the compositeness of near-threshold states to investigate the internal structure of exotic hadron candidates. Within the framework of effective field theory, Weinberg's weak-binding relation is extended to more general cases by easing several preconditions. First, by evaluating the contribution from the decay channel, we obtain the generalized relation for unstable quasibound states. Next, we generalize the relation to include the nearby CDD (Castillejo-Dalitz-Dyson) pole contribution with the help of the Pade approximant. The validity of the estimation with the generalized weak-binding relations is examined by numerical calculations. The method to systematically evaluate the error in the weak-binding relation is presented. Finally, by applying the extended relation to Lambda(1405), f0(980) and a0(980), we discuss their internal structure, in comparison with other approaches.Comment: 46 pages, 12 figures, published versio