Resonance Poles Research Articles

Radiative resonance couplings in γπ→ππ

Studies of the reaction $\gamma\pi\to\pi\pi$, in the context of the ongoing Primakoff program of the COMPASS experiment at CERN, give access to the radiative couplings of the $\rho(770)$ and $\rho_3(1690)$ resonances. We provide a vector-meson-dominance estimate of the respective radiative width of the $\rho_3$, $\Gamma_{\rho_3\to\pi\gamma}=48(18)$ keV, as well as its impact on the $F$-wave in $\gamma\pi\to\pi\pi$. For the $\rho(770)$, we establish the formalism necessary to extract its radiative coupling directly from the residue of the resonance pole by analytic continuation of the $\gamma\pi\to\pi\pi$ amplitude to the second Riemann sheet, without any reference to the vector-meson-dominance hypothesis.

Trapped modes and resonance wave transmission in a plate with a system of notches

The paper deals with guided wave propagation and diffraction in an elastic plate with two and more parallel grooves (notches). It is a continuation of the preceding studies of a single-notch diffraction focused on the manifestation of the trapped mode and resonance transmission effects in the case of several obstacles. Those effects occur at the frequencies close to the nearly real scattering resonance poles, and the forms of wave localization near the notches are predetermined by the eigenforms associated with these poles. Therefore, the change of location of nearly real poles with additional notches and its dependence on their spacing are the issues of prime concern. The increase in number and assembling in groups of resonance poles and transmission peaks, which was known for multi-obstacle guides of other nature, have also been revealed and experimentally confirmed. The theoretical research is conducted on the basis of low-cost semi-analytical models, and the numerical simulation is experimentally validated through the laser Doppler vibrometry.

Threshold energies and poles for hadron physical problems by a model-independent universal algorithm

In this work we show how by using a Padé type analytical continuation scheme, based on the Schlessinger point method, it is possible to find higher production thresholds in hadron physical problems. Recently, an extension of this numerical approach to the complex energy plane enabled the calculations of auto-ionization decay resonance poles in atomic and molecular systems. Here we use this so-called Resonances via Padé (RVP) method, to show its convergence beyond the singular point in hadron physical problems. In order to demonstrate the capabilities of the RVP method, two illustrations for the ability to identify singularities and branch points are given. In addition, two applications for hadron physical problems are given. In the first one, we identify the decay thresholds from a numerically calculated spectral function. In the second one, we use experimental data. First, we calculate the resonance pole of the f0(500) or σ meson using the S0 partial wave amplitude for ππ scattering in very good agreement with the literature. Second, we use data on the cross section ratio R(s) for e+e− collisions and discuss the prediction of decay thresholds which proves to be difficult if the data is noisy.

Potential for α -induced nuclear scattering, reaction and decay, and a resonance-pole-decay model with exact explicit analytical solutions

The decay of $\alpha$ particle from a nucleus is viewed as a quantum resonance state of a two-body scattering process of the $\alpha$+daughter nucleus pair governed by a novel nucleus-nucleus potential in squared Woods-Saxon form. By the application of the rigorous optical model (OM) potential scattering (S-matrix) theory the genuineness of the potential for the system is established by giving good explanation of the elastic scattering and reaction cross sections data of the $\alpha$+nucleus pair. From the pole position in the complex momentum (k) plane of the S-matrix defined above, the energy and width of the resonance state akin to the decaying state of emission of $\alpha$ particle are extracted and from this width, the result of $\alpha$-decay half-life is derived to account for the experimental result of half-life in the cases of large number of $\alpha$-emitters including heavy and super-heavy nuclei. The S-matrix of the full OM calculation above is replaced by an analytical function expressed in terms of exact Schr\"{o}dinger solutions of a global potential that closely represents the Coulomb-nuclear interaction in the interior and the pure Coulomb wave functions outside, and the resonant poles of this S-matrix in the complex momentum plane are used to give satisfactory results of decay half-lives of $\alpha$ coming out from varieties of nuclei.

Pseudo-Linear Time-Invariant Magnetless Circulators Based on Differential Spatiotemporal Modulation of Resonant Junctions

In this paper, we present voltage- and current-mode differential magnetless non-reciprocal devices obtained by pairing two single-ended (SE) circulators, each consisting of three first-order bandpass or bandstop LC filters, connected in either a wye or a delta topology. The resonant poles of each SE circulator are modulated in time with 120 deg phase-shifted periodic signals, resulting in synthetic angular-momentum biasing achieved through spatiotemporal modulation (STM). We tailor the two SE circulators to exhibit a constant 180 deg phase difference between their STM biases. Unlike conventional differential time-variant circuits, for which only the even or odd spurs are rejected, we show that the proposed configuration cancels out all intermodulation (IM) products, thus making them operate alike linear time-invariant (LTI) circuits for an external observer. In turn, this property enhances all metrics of the resulting circulator, overcoming the limitations of SE architectures, and improving insertion loss, impedance matching, bandwidth and noise figure. We show that this differential architecture also significantly relaxes the required modulation parameters, both in frequency and amplitude. We develop a rigorous small-signal model to guide the design of the proposed circuits and to get insights into their pseudo-LTI characteristics. Then, we validate the theory with simulations and measurements showing remarkable performance compared to the current state of the art of magnetless non-reciprocal devices.

Differential cross section measurements for γn→π−p above the first nucleon resonance region

The quasi-free $\gamma d\to\pi^{-}p(p)$ differential cross section has been measured with CLAS at photon beam energies $E_\gamma$ from 0.445 GeV to 2.510 GeV (corresponding to $W$ from 1.311 GeV to 2.366 GeV) for pion center-of-mass angles $\cos\theta_\pi^{c.m.}$ from -0.72 to 0.92. A correction for final state interactions has been applied to this data to extract the $\gamma n\to\pi^-p$ differential cross sections. These cross sections are quoted in 8428 $(E_\gamma,\cos\theta_\pi^{c.m.})$ bins, a factor of nearly three increase in the world statistics for this channel in this kinematic range. These new data help to constrain coupled-channel analysis fits used to disentangle the spectrum of $N^*$ resonances and extract their properties. Selected photon decay amplitudes $N^* \to \gamma n$ at the resonance poles are determined for the first time and are reported here.

A compact diplexer with a split-ring resonator junction

Diplexers are three-port filtering devices with a junction connecting two channel filters; the common port connects to an antenna which serves the two channel filters bearing the second and the third port. In the design of diplexers, the technique used in connecting the two channel filters is of great importance to the designers. This is because it determines the size, the effectiveness of signal splitting and combining as well as the ease in implementation. In this paper, an asynchronously tuned double split-ring resonator (SRR) was used in joining the two channel filters. Without incurring any extra space for the junction, the SRR, being a dual-mode resonator, also functioned as a resonant pole for each channel filter. A diplexer operating at 2 GHz and 3 GHz with 4% fractional bandwidths and 20 dB return loss has been demonstrated. The interactions between the SRR and the channel filters were investigated. Good agreement between the simulated and the measured responses was achieved.

Nucleon resonance structure in the finite volume of lattice QCD

An approach for relating the nucleon resonances extracted from $\pi N$ reaction data to lattice QCD calculations has been developed by using the finite-volume Hamiltonian method. Within models of $\pi N$ reactions, bare states are introduced to parametrize the intrinsic excitations of the nucleon. We show that the resonance pole positions can be related to the probability $P_{N^*}(E)$ of finding the bare state, $N^*$, in the $\pi N$ scattering states in infinite volume. We further demonstrate that the probability $P_{N^*}^V(E)$ of finding the same bare states in the eigenfunctions of the underlying Hamiltonian in finite volume approaches $P_{N^*}(E)$ as the volume increases. Our findings suggest that the comparison of $P_{N^*}(E)$ and $P_{N^*}^V(E)$ can be used to examine whether the nucleon resonances extracted from the $\pi N$ reaction data within the dynamical models are consistent with lattice QCD calculation. We also discuss the measurement of $P_{N^*}^V(E)$ directly from lattice QCD. The practical differences between our approach and the approach using the L\"uscher formalism to relate LQCD calculations to the nucleon resonance poles embedded in the data are also discussed.

Fully coupled-channels complex scaling method for the K−pp system

We have developed a fully coupled-channels complex scaling method (ccCSM) for the study of the simplest (and thus most important) kaonic nucleus, $``{K}^{\ensuremath{-}}pp$'', which is a resonant state of a $\overline{K}NN\text{\ensuremath{-}}\ensuremath{\pi}\mathrm{\ensuremath{\Sigma}}N\text{\ensuremath{-}}\ensuremath{\pi}\mathrm{\ensuremath{\Lambda}}N$ coupled-channel system based on theoretical viewpoint. By employing the ccCSM and imposing the correct boundary condition for a resonance, the coupled-channel problem is solved using a phenomenological energy-independent potential. As a result of the ccCSM calculation of $``{K}^{\ensuremath{-}}pp$'', in which all three channels are treated explicitly, we have obtained a three-body resonance as a Gamow state. The resonance pole indicates that the binding energy of $``{K}^{\ensuremath{-}}pp$'' and the half value of its mesonic decay width are 51 and 16 MeV, respectively. In the analysis of the ccCSM resonant wave function, we clarify the spatial configuration and channel composition of $``{K}^{\ensuremath{-}}pp$''. Compared with past single-channel calculations based on effective $\overline{K}N$ potentials, the current study provides a guideline for the determination of the $\overline{K}N$ energy to be used in such effective potentials.

On Friedrichs model with two continuum states

The Friedrichs model with one discrete state coupled to more than one continuum is studied. The exact eigenstates for the full Hamiltonian can be solved explicitly. The discrete state is found to generate more than one virtual state pole or more than one pair of resonance poles in different Riemann sheets in different situations. The form factors could also generate new states on different sheets. All these states can appear in the generalized completeness relation.

Wideband Shorted Patch Antenna Under Radiation of Dual-Resonant Modes

A novel design concept of enhancing the impedance bandwidth of a single-layer shorted microstrip patch antenna (MPA) is proposed under simultaneous radiation of the one- and three-quarter wavelength resonant modes (TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,1/2</sub> and TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,3/2</sub> modes). Initially, a conventional MPA with the shorting wall is studied to demonstrate that none of the redundant modes can be excited between the dual-resonant modes. Then, a pair of shorting pins are appropriately installed underneath the patch to progressively turn up the resonant frequency of TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,1/2</sub> mode without significant influence on that of TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,3/2</sub> mode. After that, a V-shaped slot is etched out on the patch to dramatically reduce the resonant frequency of TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,3/2</sub> mode with little effect on that of TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,1/2</sub> mode. With the use of these arrangements, the dual-desired radiative resonant modes are gradually moved in proximity to each other, thus widening the impedance bandwidth under emergence of dual resonant poles. In order to validate the principle and design method, the proposed antenna is designed, fabricated, and measured. The measured results demonstrate that the impedance bandwidth of the proposed shorted patch antenna has been extended to about 11.8%, and it is about 1.82 times of 6.5% of the traditional shorted MPA. Meanwhile, the fabricated antenna exhibits other attractive performances including stable radiation pattern, same polarization, and a low-profile property with the height of 0.042 free-space wavelength.

Cosmic abundances of SIMP dark matter

Thermal production of light dark matter with sub-GeV scale mass can be attributed to 3 → 2 self-annihilation processes. We consider the thermal average for annihilation cross sections of dark matter at 3 → 2 and general higher-order interactions. A correct thermal average for initial dark matter particles is important, in particular, for annihilation cross sections with overall velocity dependence and/or resonance poles. We apply our general results to benchmark models for SIMP dark matter and discuss the effects of the resonance pole in determining the relic density.

Pseudo-orbit approach to trajectories of resonances in quantum graphs with general vertex coupling: Fermi rule and high-energy asymptotics

The aim of the paper is to investigate resonances in quantum graphs with a general self-adjoint coupling in the vertices and their trajectories with respect to varying edge lengths. We derive formulae determining the Taylor expansion of the resonance pole position up to the second order, which represent, in particular, a counterpart to the Fermi rule derived recently by Lee and Zworski for graphs with the standard coupling. Furthermore, we discuss the asymptotic behavior of the resonances in the high-energy regime in the situation where the leads are attached through δ or δs′ conditions, and we prove that in the case of δs′ coupling the resonances approach to the real axis with the increasing real parts as O((Rek)−2).

De Sitter Space as a Resonance.

A quantum mechanical formulation of de Sitter cosmological spacetimes still eludes string theory. In this Letter we conjecture a potentially rigorous framework in which the status of de Sitter space is the same as that of a resonance in a scattering process. We conjecture that transition amplitudes between certain states with asymptotically supersymmetric flat vacua contain resonant pole characteristic metastable intermediate states. A calculation employing constrained instantons illustrates this idea.

De Sitter harmonies: Cosmological spacetimes as resonances

The aim of this work is to provided the details of a calculation summarized in the recent paper by Maltz and Susskind which conjectured a potentially rigorous framework where the status of de Sitter space is the same as that of a resonance in a scattering process. The conjecture being that transition amplitudes between certain states with asymptotically supersymmetric flat vacua contain resonant poles characteristic metastable intermediate states. A calculation employing constrained instantons is presented that illustrates this idea.

Resonant Scattering Characteristics of Homogeneous Dielectric Sphere

In the present article the classical problem of electromagnetic scattering by a single homogeneous sphere is revisited. Main focus is the study of the scattering behavior as a function of the material contrast and the size parameters for all electric and magnetic resonances of a dielectric sphere. Specifically, the Pad\'e approximants are introduced and utilized as an alternative system expansion of the Mie coefficients. Low order Pad\'e approximants can give compact and physically insightful expressions for the scattering system and the enabled dynamic mechanisms. Higher order approximants are used for predicting accurately the resonant pole spectrum. These results are summarized into general pole formulae, covering up to fifth order magnetic and forth order electric resonances of a small dielectric sphere. Additionally, the connection between the radiative damping process and the resonant linewidth is investigated. The results obtained reveal the fundamental connection of the radiative damping mechanism with the maximum width occurring for each resonance. Finally, the suggested system ansatz is used for studying the resonant absorption maximum through a circuit-inspired perspective.

Toward establishing low-lyingΛandΣhyperon resonances with theK¯+d→π+Y+Nreaction

A model for the $\bar K d \to \pi Y N$ reactions with $Y=\Lambda, \Sigma$ is developed, aiming at establishing the low-lying $\Lambda$ and $\Sigma$ hyperon resonances through analyzing the forthcoming data from the J-PARC E31 experiment. The off-shell amplitudes generated from the dynamical coupled-channels (DCC) model, which was developed in Kamano et al. [Phys. Rev. C 90, 065204 (2014)], are used as input to the calculations of the elementary $\bar K N \to \bar K N$ and $\bar K N \to \pi Y$ subprocesses in the $\bar K d \to \pi Y N$ reactions. It is shown that the cross sections for the J-PARC E31 experiment with a rather high incoming-$\bar{K}$ momentum, $|\vec p_{\bar K}|= 1$ GeV, can be predicted reliably only when the input $\bar K N \to \bar K N$ amplitudes are generated from a $\bar KN$ model, such as the DCC model used in this investigation, which describes the data of the $\bar K N$ reactions at energies far beyond the $\bar K N$ threshold. We find that the data of the threefold differential cross section $d\sigma/(dM_{\pi\Sigma}d\Omega_{p_n})$ for the $K^- d \to \pi \Sigma n$ reaction below the $\bar K N$ threshold can be used to test the predictions of the resonance poles associated with $\Lambda(1405)$. We also find that the momentum dependence of the threefold differential cross sections for the $K^- d \to \pi^- \Lambda p$ reaction can be used to examine the existence of a low-lying $J^P=1/2^+$ $\Sigma$ resonance with a pole mass $M_R = 1457 -i39$ MeV, which was found from analyzing the $K^-p$ reaction data within the employed DCC model.

Dynamics of phase oscillators with generalized frequency-weighted coupling.

Heterogeneous coupling patterns among interacting elements are ubiquitous in real systems ranging from physics, chemistry to biology communities, which have attracted much attention during recent years. In this paper, we extend the Kuramoto model by considering a particular heterogeneous coupling scheme in an ensemble of phase oscillators, where each oscillator pair interacts with different coupling strength that is weighted by a general function of the natural frequency. The Kuramoto theory for the transition to synchronization can be explicitly generalized, such as the expression for the critical coupling strength. Also, a self-consistency approach is developed to predict the stationary states in the thermodynamic limit. Moreover, Landau damping effects are further revealed by means of linear stability analysis and resonance poles theory below the critical threshold, which turns to be far more generic. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the synchronization transition in general networks with heterogenous couplings.

General considerations on the nature ofZb(10610)andZb(10650)from their pole positions

The nature of the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ is studied by calculating the $B^{(*)}\overline B^{*}$ compositeness ($X$) in those resonances. We first consider uncoupled isovector $S$-wave scattering of $B^{(*)}\overline B^{*}$ within the framework of effective-range expansion (ERE). Expressions for the scattering length ($a$) and effective range ($r$) are derived exclusively in terms of the masses and widths of the two $Z_b$ states. We then develop compositeness within ERE for the resonance case and deduce the expression $X=1/\sqrt{2r/a-1}$, which is then applied to the systems of interest. Finally, the actual compositeness parameters are calculated in terms of resonance pole positions and their experimental branching ratios into $B^{(*)}\overline{B}^*$ by using the method of Ref.[1]. We find the values $X=0.66\pm 0.11$ and $0.51\pm 0.10$ for the $Z_b(10610)$ and $Z_b(10650)$, respectively. We also compare the ERE with Breit-Wigner and Flatt\'e parameterizations to discuss the applicability of the last two ones for near-threshold resonances with explicit examples.

Isospin decomposition ofγN→N*transitions within a dynamical coupled-channels model

By extending the dynamical coupled-channels analysis performed in our previous work [Phys. Rev. C 88, 035209 (2013)] to include the available data of photoproduction of pi meson off the neutron, the transition amplitudes for the photo-excitation of the neutron to nucleon resonances, gamma n --> N*, at the resonance pole positions are determined. The combined fits to the data for both the proton- and neutron-target reactions also revise our results for the resonance pole positions and the gamma p --> N* transition amplitudes. Our results allow an isospin decomposition of the gamma N --> N* transition amplitudes for the isospin I=1/2 N* resonances, which is necessary for testing hadron structure models and gives crucial inputs for constructing models of neutrino-induced reactions in the nucleon resonance region.