Related papers: No hidden physics in resonance pole residue phase
All resonances, from hydrogen nuclei excited by the high-energy gamma rays in deep space to newly discovered particles produced in Large Hadron Collider, should be described by the same fundamental physical quantities. However, two distinct…
We propose a simple formula for multichannel resonant scattering with parameters related to physical resonant properties. It can be used to predict residue phase from other resonant parameters and describe the shape of scattering amplitudes…
The resonant properties of excited hadrons are commonly identified with the complex pole positions and residues of the scattering amplitude. The mass and total decay width are given by position, whereas the partial width is given by the…
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…
We formulate the Born approximation for finding resonance poles in the complex plane for potential scattering problems. Using the method, we study the distribution of resonance poles for several scattering potentials. In particular, we find…
We show that the complex-plane structure of light hadron resonances is governed by a unified geometric framework where the threshold position plays a decisive role. By applying this framework to $\pi\pi$, $\pi K$, and $\pi N$ phase shifts,…
Many low energy hadrons, such as the rho, can be observed as resonances in scattering experiments. A proposal by L\"uscher enables one to determine infinite volume elastic scattering phases from the two-particle energy spectrum measured…
In a finite volume, resonances and multi-hadron states are identified by discrete energy levels. When comparing the results of lattice QCD calculations to scattering experiments, it is important to have a way of associating the energy…
Most particles in nature are unstable, manifesting as resonances in scattering processes. Using analyticity and unitarity, we show nonperturbatively that resonances, defined as poles on higher Riemann sheets of scattering amplitudes, share…
The scattering phase shift encodes a good amount of physical information which can be used to study resonances from scattering data. Among others, it can be used to calculate the continuum density of states and the collision time in a…
We consider a slow-fast Hamiltonian system with one fast angular variable (a fast phase) whose frequency vanishes on some surface in the space of slow variables (a resonant surface). Systems of such form appear in the study of dynamics of…
The construction of general amplitudes satisfying symmetries and $S$-matrix constraints has been the primary tool in studying the spectrum of hadrons for over half a century. In this work, we present a new parameterization, which can…
Resonances are uniquely characterized by their complex pole locations and the corresponding residues. In practice, however, resonances are typically identified experimentally as structures in invariant mass distributions, with branching…
A family of orbiting resonances in molecular scattering is globally described by using a single pole moving in the complex angular momentum plane. The extrapolation of this pole at negative energies gives the location of the bound states.…
A central issue in hadron spectroscopy is to deduce --- and interpret --- resonance parameters, namely pole positions and residues, from experimental data, for those are the quantities to be compared to lattice QCD or model calculations.…
We discuss in general terms pole trajectories of resonances coupling to a continuum channel as some strength parameter is varied. It is demonstrated that, regardless the underlying dynamics, the trajectories of poles that couple to the…
Excited hadrons are seen as resonances in the scattering of lighter stable hadrons like $\pi$, $K$ and $\eta$. Many decay into multiple final states necessitating coupled-channel analyses. Recently it has become possible to obtain…
When a resonance lies near the threshold of a heavier channel, an interesting feature can occur. The paradigmatic example employed here is the scalar isoscalar $f_0(980)$ resonance that couples to the lighter $\pi\pi$ and heavier $K\bar{K}$…
A reliable determination of the pole parameters and residues of nucleon resonances is notoriously challenging, given the required analytic continuation into the complex plane. We provide a comprehensive analysis of such resonance parameters…
For an exponentially decaying potential, analytic structure of the $s$-wave S-matrix can be determined up to the slightest detail, including position of all its poles and their residues. Beautiful hidden structures can be revealed by its…