Related papers: Probabilistic interpretation of compositeness rela…
We generalize the time-honored Weinberg's compositeness relations by including the range corrections through considering a general form factor. In Weinberg's derivation, he considered the effective range expansion up to $\mathcal{O}(p^2)$…
We study the internal structure of exotic hadrons, especially focusing on the relation between the compositeness and physical observables. Defined as the probability of finding hadronic molecular components in the wave function,…
Whether one starts form the analytic S-matrix definition or the requirement of gauge parameter independence in renormalization theory, a relativistic resonance is given by a pole at a complex value s of energy squared. The complex number s…
We use a near-threshold parameterization with explicit inclusion of the Castillejo-Dalitz-Dyson poles, which is more general than the effective range expansion, to study the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$. In terms of…
In the absence of a half-bound state, a compactly supported potential of a Schr\"odinger operator on the line is determined up to a translation by the zeros and poles of the meropmorphically continued left (or right) reflection coefficient.…
We establish a one-to-one correspondance between the ''composite particles'' with $N$ particles and the Young tableaux with at most $N$ rows. We apply this correspondance to the models of Calogero-Sutherland and Ruijsenaars-Schneider and we…
A version of the bound state soliton model which allows both $\eta$ and $K$ bound states is used to study low partial wave octet baryon resonances. It is found that negative parity $S-$wave resonances are well described within this…
Relativistic resonances and decaying states are described by representations of Poincar\'e transformations, similar to Wigner's definition of stable particles. To associate decaying state vectors to resonance poles of the $S$-matrix, the…
We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized…
Resonances, or scattering poles, are complex numbers which mathematically describe meta-stable states: the real part of a resonance gives the rest energy, and its imaginary part, the rate of decay of a meta-stable state. This description…
Effects of resonant single-particle (s.p.) states on the pairing correlations are investigated by an exact treatment of the pairing Hamiltonian on the Gamow shell model basis. We introduce the s.p. states with complex energies into the…
We study the structure of two-body s-wave bound states as well as resonances in the threshold energy region. We focus on the single-channel scattering where the scattering length and the effective range are given by real numbers. It is…
For compact and for convex co-compact oriented hyperbolic surfaces, we prove an explicit correspondence between classical Ruelle resonant states and quantum resonant states, except at negative integers where the correspondence involves…
Potential resonances are usually investigated either directly in the complex energy plane or indirectly in the complex angular momentum plane. Another formulation complementing these two is presented in this work. It is an indirect method…
We calculate resonances which are formed by a particle in a potential which is either Coulombian or quadratic when the particle is strongly coupled to a massless boson, taking only two energy levels into consideration. From these…
We investigate the internal structure of near-threshold states in a system with a repulsive Coulomb interaction combined with a short-range potential, using the compositeness. We construct a model in which the eigenmomentum is expressed in…
We study the compositeness of unstable hadrons which lie near the two-hadron threshold. In the framework of the effective field theory, we derive the relation between the compositeness of stable bound states with observables. We then extend…
We establish a relation between the solution of a relativistic bound state equation in quantum mechanics and the field representation of a bound state with the aid of creation and annihilation operators. We show that a bound system can be…
We develop a theoretical framework to quantify the structure of unstable hadron resonances. With the help of the corresponding system in a finite volume, we define the compositeness of resonance states which can be interpreted as a…
The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided…