Coupled-channel System Research Articles

Tunneling time in coupled-channel systems

In present work, we present a couple-channel formalism for the description of tunneling time of a quantum particle through a composite compound with multiple energy levels or a complex structure that can be reduced to a quasi-one-dimensional multiple-channel system. Published by the American Physical Society 2024

Triangle and box diagrams in coupled-channel systems from the chiral Lagrangian

Triangle and box diagrams in coupled-channel systems from the chiral Lagrangian

Charmoniumlike resonant explanation on the newly observed X(3960)

Motivated by the recent observation of X(3960) by the LHCb collaboration, we adopt the one-boson-exchange model to study the DsD¯s/D⁎D¯⁎/Ds⁎D¯s⁎ interactions with I(JPC)=0(0++) after considering both the S−D wave mixing effects and the coupled channel effects. Our analysis yields the phase shifts for these coupled channel systems, and indicate the existence of a charmoniumlike resonance, whose mass and width align well with the experimental data for the newly discovered X(3960). Furthermore, our investigation reveals the significant role played by the D⁎D¯⁎ system in the formation of the X(3960) resonance, and the Ds⁎D¯s⁎ system notably contributes to the resonance's width. As a byproduct, we perform a coupled channel analysis on the D⁎D¯⁎/DsD¯s⁎/Ds⁎D¯s⁎ interactions with I(JPC)=0(1+−), our results can predict the existence of a DsD¯s⁎ molecule with 1+− and another Ds⁎D¯s⁎ molecule with 1+−. Their widths are around several and several to several tens MeV, respectively. We encourage experimental investigations to search for these two possible charmoniumlike molecular candidates, as such findings would serve to validate our research findings and proposals.

Coupled-channel system with anomalous thresholds and unitarity

We consider the isospin one-half example system, with $D \,\pi , D\,\eta, D_s \bar K, D^* \pi , D^*\eta, D^*\bar K$ coupled channels in the $J^P = 1^-$ partial wave, chosen such that various phenomena that come with the opening of an anomalous threshold can be illustrated in a step-wise procedure by a suitable variation of up, down and strange quark masses. We use a set of LEC in the chiral Lagrangian that were adjusted to a large set of Lattice QCD results. The six phase shifts and inelasticity parameters are presented for various choices of the pion mass. For a pion mass of 150 MeV there are no anomalous thresholds encountered. The small change from 150 MeV to 145 MeV pion mass causes a dramatic impact of the anomalous threshold on the phase shifts.

A new R-matrix module for multi-channel calculations with GECCCOS

A versatile new R-matrix module for multi-channel reaction calculations was introduced into the code GECCCOS (GEneral Coupled-Channel COde System) which has been developed by the nuclear data group at TU-Wien to perform nuclear reaction calculations especially for light nuclear systems. It provides a tool for phenomenological R-matrix analyses of reaction data combined with calculations of a potential-based calculable R-matrix using the Lagrange-mesh technique. In addition it provides a platform for the development of non-standard extensions of R-matrix theory such as Reduced R-matrix analyses and the Hybrid R-matrix. A successful run of the code yields the complete S-matrix (collision matrix) as well as observables for unpolarized beams, angle-differential cross sections, excitation functions and, if existing, angle-integrated cross sections. Recently, extensions to polarization observables for spin-1/2 and spin-1 particles were implemented and tested. For phenomenological R-matrix analyses a separate module assembles calculated and available experimental values, automatically performs transformations with regard to reference frame and matching radii. Furthermore it allows to switch between incident channel and compound nucleus representation and provides the necessary feedback for the chi2 fitting process.

Pseudoscalar charmonium pair interactions via the Pomeron exchange mechanism

Following the observation of the fully-heavy tetraquark candidates $X(6900)$ and possible $X(6300)$ in the di-$J/\psi$ spectrum by the LHCb Collaboration, we investigate the near-threshold dynamics of the pseudoscalar quarkonium pairs in a coupled-channel approach in the di-$\eta_c$ channel. We show that the Pomeron exchange mechanism should be a general dynamics in the near-threshold heavy quarkonium pair interactions. In the di-$\eta_c$ channel, a coupled-channel system involving the di-$\eta_c$, $\eta_c$-$\eta_c(2S)$ and di-$\eta_c(2S)$ interactions can be established. Their $S$-wave interactions near threshold via the Pomeron exchange potential can produce near-threshold resonance poles similar to the di-$J/\psi$, $J/\psi$-$\psi(2S)$ and di-$\psi(2S)$ coupled channels. Interestingly, we find here that the pole positions are more shifted to the corresponding thresholds and turn out to be different from those seen in the di-$J/\psi$ spectrum. Taking into account the suppression of the heavy quark spin flips in the transitions between two vector and two pseudoscalar heavy quarkonium systems, the enhancements in the di-$\eta_c$ spectrum should be different from those seen in the di-$J/\psi$ channel. Experimental study of the di-$\eta_c$ channel should be useful for disentangling the nature of the fully-heavy tetraquark systems.

D+D− hadronic atom and its production in pp and pp¯ collisions

There must be Coulomb bound states of a pair of hadrons, which are stable against the strong interaction, with opposite electric charges. Such bound states are hadronic atoms. We study the properties and the production of the ground-state $D^+D^-$ hadronic atom $A_{D^+D^-}$, called dionium, with quantum numbers $J^{PC}=0^{++}$. Using a nonrelativistic effective field theory for the $D^0\bar{D}^0$-$D^+D^-$ coupled-channel system, the mass of the ground-state dionium is predicted to be $(3739.3 \pm 0.1)~\text{MeV}$, with the binding energy reduced by about 10% compared to the Coulomb binding energy due to the strong interaction. Its width for the decay into the neutral $D^0\bar D^0$ channel is predicted to be $1.8^{+1.4}_{-0.6}$ keV using lattice inputs for the $D\bar D$ strong interaction. The cross section for the inclusive prompt production of the dionium at CMS and LHCb and that for the direct production $p\bar p\to A_{D^+D^-}$ at PANDA are estimated at an order-of-magnitude level. In particular, we expect that $\mathcal{O}(10^3\sim 10^5)$ events of the reaction chain $p\bar p\to A_{D^+D^-}\to D^0\bar D^0 \to K^-\pi^+K^+\pi^-$ can be collected at PANDA, and valuable information on the charmed meson interaction and on understanding charmoniumlike states will be obtained.

SU(3) flavor symmetry considerations for the [formula omitted] coupled channels system

We study the impact of SU(3) flavor symmetry breaking on the properties of dynamically generated Λ⁎ states within an effective separable potential model describing the coupled channels K¯N system. The model is based on the chiral meson-baryon Lagrangian at next-to-leading order, and constitutes an improvement over a previous model developed by our group, with its applicability being extended to higher energies covering the Λ(1670) resonance region. It is demonstrated that the ratios of channel couplings to the resonant states can vary dramatically when the flavor breaking is gradually switched off, tracing a path to the restored SU(3) symmetry. We conclude that the couplings determined from physical observables cannot be used to reliably relate a given resonance to a specific flavor multiplet.

Decay processes of a pseudoscalar D(2900)

We study the decay properties of a $D(2900)$ state, with spin parity ${0}^{\ensuremath{-}}$, whose existence was proposed in an earlier study of the $DK\overline{K}$ and coupled-channel system. It was found in the former work that a $D$ meson appears with a mass of about 2900 MeV from the three-body dynamics while the charmless subsystem of the pseudoscalar mesons forms the ${f}_{0}(980)$ resonance. Motivated by the recent experimental investigations of $D$ mesons around 3000 MeV, we now study the two-body decays of $D(2900)$. We find that the nature of the said state sets the main decay channels to be ${D}^{*}\ensuremath{\pi}$, ${D}_{s}^{*}\overline{K}$ and ${D}_{s0}^{*}(2317)\overline{K}$. It turns out that decay width to the last one is the largest, making the ${D}_{s0}^{*}(2317)\overline{K}$ system to be the most favorable one to look for a signal of $D(2900)$. We compare the decay properties of our state with those of the $D$-meson states, proposed within quark models, near 3000 MeV. We hope that our findings and discussions can be useful for the future experimental investigations of charm mesons around 3000 MeV.

Decomposition of scattering phase shifts of coupled-channels systems in the complex scaling method

The decomposition of scattering phase shifts in single-channel systems is extended to coupled-channels systems in the complex scaling method. The present method describes the contribution of the resonant states to the phase shift separately from the background in each channel phase shift of the coupled-channels system. We apply this method to the ($^{3}\mathrm{H}+p)+(^{3}\mathrm{He}+n)$ model for $^{4}\mathrm{He}$, and show that the decomposition of phase shifts in coupled-channels systems provides useful information about the structure of scattering states.

Exchange effects in nucleus-nucleus reactions

We present a scattering model for nuclei with similar masses. In this three-body model, the projectile has a core+valence structure, whereas the target is identical to the core nucleus. The three-body wave functions must be symmetrized for the exchange of the cores. This property gives rise to non-local potentials, which are computed without approximation. The present model is an extension of the Continuum Discretized Coupled Channel (CDCC) formalism, with an additional treatment of core exchange. We solve the coupled-channel system, including non-local terms, by the $R$-matrix method using Lagrange functions. This model is applied to the $^{13}{\rm C}+^{12}$C, $^{13}{\rm N}+^{12}$C and $^{16}{\rm O}+^{12}$C systems. Experimental scattering cross sections are fairly well reproduced without any parameter fitting. The backward-angle enhancement of the elastic cross sections is due to the non-local potential. We discuss in more detail the various non-local contributions and present effective local potentials.

Thermal study of a coupled-channel system: a brief review

We demonstrate the construction of a density of states from the S-matrix describing a coupled-channel (S-wave pi pi , K {bar{K}}) system, and examine the influences from various structures of particle dynamics: poles, roots, and Riemann sheets.

Density of states of a coupled-channel system

We demonstrate how an effective density of states can be derived from the S-matrix describing a coupled-channel system. Besides the locations of poles, the phase of the determinant of the S-matrix encodes essential details in characterizing the dynamics of resonant and non-resonant interactions. The density of states is computed for the two channel scattering problem ($\pi\pi, K \bar{K}$, S-wave), and the influences from the various dynamical structures: poles, roots, branch cuts, and Riemann sheets, are examined.

Equivalent Local Potentials for the coupled channel system and the optical potential

The explicit formulae of the equivalent local potentials for a coupled channel problem are calculated. We prove that the equivalent local potential of the coupled channel system coincides with the equivalent local potential of the Feshbach optical potential.

Structure, formation, and decay of system by Faddeev-AGS calculations

The Faddeev AGS equations for the coupled-channels system with quantum numbers I= 1/2 and S= 0 are solved. Using separable potentials for the interaction, we calculate the transition probability for the reaction. The possibility to observe the trace of the quasi-bound state in mass spectra was studied. Various types of chiral-based and phenomenological potentials are used to describe the interaction. Finally, we show that we can observe the signature of the quasi-bound state in the mass spectra, as well as the trace of branch points in the observables.

Phase shift and spectral function from PWA

I illustrate a robust method for extracting an effective phase shift and an effective spectral weight for a coupled-channel system. These quantities are useful for describing the thermodynamics of an interacting hadron gas within the S-matrix formulation.

On coupled-channel dynamics in the presence of anomalous thresholds

We explore a general framework to treat coupled-channel systems in the presence of overlapping left- and right-hand cuts as well as anomalous thresholds. Such systems are studied in terms of a generalized potential, where we exploit the known analytic structure of $t$- and $u$-channel forces as the exchange masses approach their physical values. Given an approximate generalized potential the coupled-channel reaction amplitudes are defined in terms of nonlinear systems of integral equations. For large exchange masses, where there are no anomalous thresholds present, conventional $N/D$ methods are applicable to derive numerical solutions to the latter. At a formal level a generalization to the anomalous case is readily formulated by use of suitable contour integrations with amplitudes to be evaluated at complex energies. However, it is a considerable challenge to find numerical solutions to anomalous systems set up on a set of complex contours. By suitable deformations of left-hand and right-hand cut lines we manage to establish a framework of linear integral equations defined for real energies. Explicit expressions are derived for the driving terms that hold for an arbitrary number of channels. Our approach is illustrated in terms of schematic three-channel systems. It is demonstrated that despite the presence of anomalous thresholds the scattering amplitude can be represented in terms of three phase shifts and three inelasticity parameters, as one would expect from the coupled-channel unitarity condition.

Fully coupled-channel study of K−pp resonance in a chiral SU(3)-based [formula omitted] potential

We have investigated the most essential kaonic nucleus “K−pp” as a resonant state of the K¯NN-πΣN- πΛN coupled-channel system using a chiral SU(3)-based K¯N potential. We treat the “K−pp” resonance adequately with a fully coupled-channel complex scaling method (full ccCSM). Self-consistency needs to be considered for the energy dependence of the chiral SU(3)-based potential. In the present study, we propose a simple prescription for the treatment of self-consistency, considering the averaged threshold and averaged binding energy of mesons. With this prescription, we have successfully found the self-consistent solutions of the “K−pp” three-body resonance. The results indicate that the “K−pp” system is bound rather shallowly. In particular, when the potential parameters are constrained with the latest K¯N scattering length, the binding energy and half of the mesonic decay width are obtained as 14–50 MeV and 8–19 MeV, respectively.

Degenerate two-body and three-body coupled-channels systems: Renormalized effective Alt-Grassberger-Sandhas equations and near-threshold resonances

Motivated by the existence of candidates for exotic hadrons whose masses are close to both two-body and three-body hadronic thresholds lying close to each other, we study degenerate two-body and three-body coupled-channels systems. We first formulate the scattering problem of non-degenerate two-body and three-body coupled channels as an effective three-body problem, i.e., as effective Alt-Grassberger-Sandhas (AGS) equations. We next investigate the behavior of $S$-matrix poles near the threshold when two-body and three-body thresholds are degenerate. We solve the eigenvalue equations of the kernel of AGS equations instead of AGS equations themselves to obtain the $S$-matrix pole energy. We then face a problem of unphysical singularity: although the physical transition amplitudes have physical singularities only, the kernels of AGS equations have unphysical singularities. We show, however, that these unphysical singularities can be removed by appropriate reorganization of the scattering equations and mass renormalization. The behavior of $S$-matrix poles near the degenerate threshold is found to be universal in the sense that the complex pole energy, $E$, is determined by a real parameter, $c$, as $c+Elog\left(\ensuremath{-}E\right)=0$, or equivalently, $c+\mathrm{Re}\phantom{\rule{0.16em}{0ex}}Elog\left(\mathrm{Re}\phantom{\rule{0.16em}{0ex}}E\right)=0$ and $\mathrm{Im}\phantom{\rule{0.16em}{0ex}}E=\ensuremath{\pi}\mathrm{Re}\phantom{\rule{0.16em}{0ex}}E/log\left(\mathrm{Re}\phantom{\rule{0.16em}{0ex}}E\right)$. This behavior is different from that of either two-body or three-body systems and is characteristic of the degenerate two-body and three-body coupled-channels system. We expect that this new class of universal behavior might play a key role in understanding exotic hadrons.

Four-body extension of the continuum-discretized coupled-channels method

I develop an extension of the continuum-discretized coupled-channels (CDCC) method to reactions where both nuclei present a low breakup threshold. This leads to a four-body model, where the only inputs are the interactions describing the colliding nuclei, and the four optical potentials between the fragments. Once these potentials are chosen, the model does not contain any additional parameter. First I briefly discuss the general formalism, and emphasize the need for dealing with large coupled-channel systems. The method is tested with existing benchmarks on $4\ensuremath{\alpha}$ bound states with the Ali-Bodmer potential. Then I apply the four-body CDCC to the $^{11}\mathrm{Be}+d$ system, where I consider the $^{10}\mathrm{Be}({0}^{+},{2}^{+})+n$ configuration for $^{11}\mathrm{Be}$. I show that breakup channels are crucial to reproduce the elastic cross section, but that core excitation plays a weak role. The $^{7}\mathrm{Li}+d$ system is investigated with an $\ensuremath{\alpha}+t$ cluster model for $^{7}\mathrm{Li}$. I show that breakup channels significantly improve the agreement with the experimental cross section, but an additional imaginary term, simulating missing transfer channels, is necessary. The full CDCC results can be interpreted by equivalent potentials. For both systems, the real part is weakly affected by breakup channels, but the imaginary part is strongly modified. I suggest that the present wave functions could be used in future DWBA calculations.