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 ($ππ, K \bar{K}$, S-wave), and the influences from the various dynamical structures: poles, roots, branch cuts, and Riemann sheets, are examined.
We study the width of a two-body resonance in a coupled-channel system. We demonstrate how the width does not come only determined by the available phase space for its decay to the detection channel, but it greatly depends on the relative position of the mass of the resonance with respect to the masses of the coupled-channels generating the state. Our results are consistent with the experimental observation of narrow hadrons lying well above their lowest decay threshold.
A local coupled-channels Kbar N-pi Sigma-pi Lambda potential is constructed, equivalently reproducing the scattering amplitude in chiral SU(3) dynamics. By analyzing the wave function of the Lambda(1405), we show the Kbar N dominance of the upper pole within the two-pole structure of the Lambda(1405). The resulting potential will be useful for investigating Kbar few-nucleon systems including their coupled channels.
Spin-$\ffh$ resonance contributions in pion-nucleon scattering are investigated within the coupled channel $K$-matrix approach for c.m. energies up to $\sqrt s=$ 2 GeV. All previously studied $πN$, $2πN$, $ηN$, $K Λ$, $K Σ$, and $ωN$ final states are included. We find a significant improvement of $χ^2$ in almost all channels by inclusion of the spin-$\ffh$ states. The obtained coupling parameters are discussed.
The origin of the poles generated by chiral coupled-channel dynamics and applied to $\bar{K}N$ interactions is related to the nonzero diagonal couplings in the $πΣ$, $\bar{K}N$ and $KΞ$ channels. An evolution of the poles from the zero coupling limit and from a limit of restored SU(3) symmetry is discussed.
We present several possible hadronic states found in coupled-channel models within the on-shell approximation. The interaction potential is constructed as a sum of the tree-level Feynman diagrams calculated with the effective Lagrangians. Based on the recent empirical data, we illustrate the possible existence of several baryonic and mesonic states with definite quantum numbers in the model. We give their properties for the purpose of further study and discuss the potential of finding them in future experiments.
The meson-baryon interaction in s-wave in the strangeness S=-1 sector has been studied, employing a chiral SU(3) Lagrangian up to next-to-leading order (NLO) and implementing unitarization in coupled channels. The parameters of the Lagrangian have been fitted to a large set of experimental data in different two-body channels, paying special attention to the $\bar{K} N \rightarrow K Ξ$ reaction, which is particularly sensitive to the NLO terms. With the aim of improving the model in the $KΞ$ production channels, effects of the high spin hyperon resonances $Σ(2030)$ and $Σ(2250)$ have been taken…
In this paper we develop a formalism to evaluate wave functions in momentum and coordinate space for the resonant states dynamically generated in a unitary coupled channel approach. The on shell approach for the scattering matrix, commonly used, is also obtained in Quantum Mechanics with a separable potential, which allows one to write wave functions in a trivial way. We develop useful relationships among the couplings of the dynamically generated resonances to the different channels and the wave functions at the origin. The formalism provides an intuitive picture of the resonances in the coup…
The pi N --> eta N and eta N --> eta N partial wave T-matrices for the eight lowest partial waves have been obtained in a three coupled channel model with unitarity manifestly imposed. The two physical channels are pi_N and eta_N, and the third channel, pi_pi_N is an effective, but unphysical two body channel which represents all remaining processes. The pi_N elastic phase shifts and the weighted data base of the pi- p --> eta n total and differential cross sections are chosen as the input for the fitting procedure. A model containing a single resonance in each of the three partial waves that …
The momentum correlation functions of S = -2 baryon pairs (p Xi^- and Lambda Lambda) produced in high-energy pp and pA collisions are investigated on the basis of the coupled-channel formalism. The strong interaction is described by the coupled-channel HAL QCD potential obtained by the lattice QCD simulations near physical quark masses, while the hadronic source function is taken to be a static Gaussian form. The coupled-channel effect, the threshold difference, the realistic strong interaction, and the Coulomb interaction are fully taken into account for the first time in the femtoscopic anal…
We describe the pi N -> omega N cross section from threshold to a center of mass energy of 2 GeV in a unitary coupled-channel model and analyze it in terms of rescattering and resonance excitations. The amplitude is mainly composed of D13, P13, and P11 contributions, where the D13 dominates over the complete considered energy range. We also outline the generalization of the standard partial-wave formalism necessary for the decomposition of the omega N final state.
As a step toward performing a complete coupled-channels analysis of the world data of pi N, gamma^* N --> pi N, eta N, pi pi N reactions, the pi N --> pi pi N reactions are investigated starting with the dynamical coupled-channels model developed in Phys. Rev. C76, 065201 (2007). The channels included are pi N, eta N, and pi pi N which has pi Delta, rho N, and sigma N resonant components. The non-resonant amplitudes are generated from solving a set of coupled-channels equations with the meson-baryon potentials defined by effective Lagrangians. The resonant amplitudes are generated from 16 bare…
Two-particle momentum correlation functions as measured in heavy ion collisions or in high-energetic proton-proton collisions are studied. Special emphasis is put on systems like $ΛΛ$ or $K^-p$ where effects from the coupling to other channels could be relevant. In both cases other channels open at relatively low momenta or are already open at the reaction threshold. To have a solid basis, realistic coupled-channel interactions for $ΛΛ-ΞN-ΛΣ-ΣΣ$ and $πΛ-πΣ-\bar KN$ are utilized in the actual calculations. It is found that the opening of the $ΞN$ channel leaves a trace in the $ΛΛ$ correlation f…
We compare and review the theoretical predictions for the $\bar{K}N$ and $ηN$ elastic amplitudes where sizable variations are found among the considered approaches, especially at subthreshold energies relevant for studies of kaonic atoms and meson-nuclear quasi-bound states. Conditions for an appearance of dynamically generated states in meson-baryon multi-channel interactions are established and discussed for the $\bar{K}N$ and $ηN$ systems.
Within a dynamical coupled-channels model which has already been fixed from analyzing the data of the pi N -> pi N and gamma N -> pi N reactions, we present the predicted double pion photoproduction cross sections up to the second resonance region, W< 1.7 GeV. The roles played by the different mechanisms within our model in determining both the single and double pion photoproduction reactions are analyzed, focusing on the effects due to the direct gamma N -> pi pi N mechanism, the interplay between the resonant and non-resonant amplitudes, and the coupled-channels effects. The model parameters…
By means of a coupled channel non-perturbative unitary approach, it is possible to extend the strong constrains of Chiral Perturbation Theory to higher energies. In particular, it is possible to reproduce the lowest lying resonances in meson-meson scattering up to 1.2 GeV using the parameters of the O(p^2) and O(p^4) Chiral Lagrangian. We report on an update of these results examining their possible relevance for meson spectroscopy.
A new tool which combines chiral perturbation theory and unitarity in coupled channels is applied with success to the study of the meson-meson interaction, extending the theoretical predictions up to sqrt{s} = 1.2 GeV, hence improving considerably the convergence radius of conventional chiral perturbation theory. The method is applied to obtain the meson-meson phase shifts and inelasticities as well as the isoscalar pion-pion scattering amplitude inside a nuclear medium.
From dispersion relation approach, a formalism that describes final state interaction among three particles in a coupled-channel system is presented in this work. Different representations of coupled-channel three-body formalism with only spinless particles in both initial and final states are derived.
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 $\bar{K}N$ 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 gradua…
We review our recent efforts for determining resonance parameters associated with light-quark baryons ($N^*$, $Δ^*$, $Λ^*$, $Σ^*$) through comprehensive analyses of various meson production reactions off the nucleon within the ANL-Osaka dynamical coupled-channels approach.
We present the current status of a combined and simultaneous analysis of meson production reactions based on a dynamical coupled-channels (DCC) model, which is conducted at Excited Baryon Analysis Center (EBAC) of Jefferson Lab.
We give an overview of recent progress in the spectroscopic study of nucleon resonances within the dynamical coupled-channels analysis of meson-production reactions. The important role of multichannel reaction dynamics in understanding various properties of nucleon resonances is emphasized.
Dynamical coupled-channel approaches are a widely used tool in hadronic physics that allow to analyze different reactions and partial waves in a consistent way. In such approaches the basic interactions are derived within an effective Lagrangian framework and the resulting pseudo-potentials are then unitarized in a coupled-channel scattering equation. We propose a scheme that allows for a solution of the arising integral equation in discretized momentum space for periodic as well as twisted boundary conditions. This permits to study finite size effects as they appear in lattice QCD simulations…
We consider a unitary coupled channel model to describe the low energy proton-antiproton scattering and the lower Coulomb-like protonium states. The existence of deeper quasi-bound states of nuclear nature is found to be a consequence of the experimental data. The properties of these states as well as the protonium annihilation densities are described and the difference with respect to the optical models description are manifested.
Coupled-channel dynamics for scattering and production processes in partial-wave amplitudes is discussed from a perspective that emphasizes unitarity and analyticity. We elaborate on several methods that have driven to important results in hadron physics, either by themselves or in conjunction with effective field theory. We also develop and compare with the use of the Lippmann-Schwinger equation in near-threshold scattering. The final(initial)-state interactions are discussed in detail for the elastic and coupled-channel case. Emphasis has been put in the derivation and discussion of the meth…
We present in this talk a recent investigation on $ϕ$ photoproduction, emphasizing the rescattering effects of the $KΛ^*$ channel near the threshold region. We discuss the results of the differential cross section and the angular distributions.
Based on the Lippmann-Schwinger equation approach, a generalized Lüscher's formula in 1+1 dimensions for two particles scattering in both the elastic and coupled-channel cases in moving frames is derived. A 2D coupled-channel scattering lattice model is presented, the model represents a two-coupled-channel resonant scattering scalars system. The Monte Carlo simulation is performed on finite lattices and in various moving frames. The 2D generalized Lüscher's formula is used to extract the scattering amplitudes for the coupled-channel system from the discrete finite-volume spectrum.
A numerical analysis to the scalar form-factor in the $ππ$ and KK coupled--channel system is made by solving the coupled-channel dispersive integral equations, using the iteration method. The solutions are found not unique. Physical application to the $ππ$ central production in the $pp\to ppππ$ process is discussed based upon the numerical solutions we found.
The $ρρ$ scattering has been studied by two groups which both claimed a dynamical generated scalar meson, most likely to be $f_0(1370)$. Here we investigate the influence of coupled-channels of pseudoscalar mesons, i.e., $ππ$ and $\bar KK$, on this dynamical generated scalar state. With the coupled channel effect included, the pole and partial decay widths are found to be more close to PDG values for $f_0(1500)$.
Coupled-channel final-state-interaction effects for D and B weak decays into ππand K \bar{K} are discussed in a Regge framework. It is found that the inclusion of coupled-channel effects significantly affects the results obtained previously in a quasi-elastic approximation. It is also shown that in the isospin I=0 channel the inelastic final-state transitions (ππ)_{I=0} --> (K \bar{K})_{I=0} dramatically influence the phase of the B^0 --> (K \bar{K})_{I=0} amplitude.
We extend the study of a JP=2+, I=3/2 pion-Lambda-nucleon quasibound state [Phys. Rev. D 78, 014013 (2008)] by solving nonrelativistic Faddeev equations, using 3S1-3D1, Lambda N - Sigma N coupled channels Chiral Quark Model local interactions, and pion-nucleon and coupled pion-Lambda - pion-Sigma separable interactions fitted to the position and decay parameters of the Delta(1232) and Sigma(1385) resonances, respectively. The results exhibit a strong sensitivity to the p-wave pion-hyperon interaction, with a pion-Lambda-nucleon quasibound state persisting over a wide range of acceptable parame…
We demonstrate that partial wave amplitudes extracted from $D^+\to K^-π^+π^+$ Dalitz plot with a unitary coupled-channel model are significantly different from those obtained with an isobar model. The unitary coupled-channel model takes account of hadronic rescattering mechanisms involving all three mesons that have been missed in conventioanl isobar model analyses. The rescattering mechanisms contribute largely, and can triplicate the $D^+\to {K}^-π^+π^+$ decay width within our analysis. These findings deliver a warning that analysis results obtained with isobar models should be looked with a…
We review a global analysis of meson production reactions off the nucleons by a collaboration at Excited Baryon Analysis Center of Jefferson Lab. The analysis is pursued with a dynamical coupled-channels approach, within which the dynamics of multi-channel reaction processes are taken into account in a fully consistent way with the two-body as well as three-body unitarity of the S-matrix. With this approach, new features of nucleon excitations are revealed as resonant particles originating from the non-trivial multi-channel reaction dynamics, which cannot be addressed by static hadron models w…
Pion and eta electroproduction data are jointly analyzed for the first time, up to a center-of-mass energy of 1.6 GeV. The framework is a dynamical coupled-channel model, based on the recent Jülich-Bonn-Washington analysis of pion electroproduction data for the same energy range. Comparisons are made to a number of single-channel eta electroproduction fits. By comparing multipoles of comparable fit quality, we find some of these amplitudes are well determined over the near-threshold region, while others will require fits over an extended energy range.
The mass spectrum and the two-body open-charm decays of the $J^{PC}=1^{--}$ charmonium states are studied with the coupled-channel effects taken into account. The coupled-channel-induced mixing effects among the excited vector charmonia are studied. Based on our calculations of the masses and the decay widths, we find that the tension between the observed properties of $Y(4260)/Y(4360)$ and their conventional charmonia interpretations could be softened.
We calculated the coupled channel photoproduction amplitudes of the scalar isovector resononace $a_0(980)$, which include the $πη$, $K^+K^-$ and $K^0\overline{K^0}$ intermediate states. Based on them we obtained the mass distribution in the $πη$ channel at photon energy $E_γ$=7 GeV, corresponding to energy accissible in new JLab experiments CLAS12 and GlueX. We also analyzed the shape of mass distribution as a function of the phase of the background amplitude.
Recent results on the study of light-quark baryons with the ANL-Osaka dynamical coupled-channels (DCC) approach are presented, which contain the N* and Delta* spectroscopy via the analysis of pi N and gamma N reactions and the Lambda* and Sigma* spectroscopy via the analysis of K- p reactions. A recent application of our DCC approach to neutrino-nucleon reactions in the resonance region is also presented.
We study coupled channel effects upon isospin I=2 and I=0 $ππ$ S-wave interaction. With introduction of the $ππ\toρρ\toππ$ coupled channel box diagram contribution into $ππ$ amplitude in addition to $ρ$ and $f_2 (1270)$ exchange, we reproduce the $ππ$ I=2 S-wave and D-wave scattering phase shifts and inelasticities up to 2 GeV quite well in a K-matrix formalism. For I=0 case, the same $ππ\toρρ\toππ$ box diagram is found to give the largest contribution for the inelasticity among all possible coupled channels including $ππ\toωω\toππ$, $ππ\to K \bar{K}\toππ$. We also show why the broad $σ$ appea…
The $f_0(1710)$ was previously proposed to be dynamically generated state by interactions between vector mesons. We extend the study of $f_0(1710)$ by including its coupling to channels of pseudoscalar mesons within coupled-channel approach. The channels involved are $K^*\bar{K}^*,ρρ,ωω,ϕϕ, ωϕ,ππ,K\bar{K},ηη$. We show that the pole assigned to $f_0(1710)$ does not change much. Then we calculate the partial decay widths of $f_0(1710) \to K^*\bar{K}^* \to ππ,K\bar{K},ηη$ as the coupled channel dynamically generated state as well as assuming it to be pure $K^*\bar{K}^*$ molecule. In both cases th…
We study the $Λ(1520)$ resonance in a coupled channel approach involving the $πΣ(1385)$, $KΞ(1530)$, $\bar{K}N$ and $πΣ$ channels. Implementing unitarity in coupled channels, we make an analysis of the relative importance of the different mechanisms which contribute to the dynamical structure of this resonance. From experimental information on some partial wave amplitudes and constraints imposed by unitarity, we get a comprehensive description of the amplitudes and hence the couplings to the different channels. We test these amplitudes in different reactions like $K^-p\toΛππ$, $γp\to K^+K^-p$,…
We present a coupled channel partial wave analysis of nondiffractive S-wave pi+ pi- and K+ K- photoproduction focusing on the KK threshold. Final state interactions are included. We calculate total cross sections, angular and effective mass distributions in both pion-pion and kaon-antikaon channels. Our results indicate that these processes are experimentally measurable and valuable information on the f0(980) resonance structure can be obtained.
The resonance D*_sJ (2317) which is considered to be the 1^3P_0 state composed of charm and strange quarks has been discovered recently. The measured mass, which is about 160 MeV lower than the mass of the 1^3P_0 state obtained from the potential model calculation by Godfrey and Isgur, was considered surprisingly low and attracted a lot of theoretical investigations. We calculate the mass shift of the 1^3P_0 state by using the coupled channel e#ect. Our result shows that the coupled channel e#ect naturally explains the low mass of D*_sJ (2317).
In the hindered magnetic dipole transitions of heavy quarkonia, the coupled-channel effects originating from the coupling of quarkonia to a pair of heavy and anti-heavy mesons can play a dominant role. Here, we study the hindered magnetic dipole transitions between two $P$-wave bottomonia, $χ_b(n P)$ and $h_b(n^\prime P)$, with $n\neq n^\prime$. In these processes the coupled-channel effects are expected to lead to partial widths much larger than the quark model predictions. We estimate these partial widths which, however, are very sensitive to unknown coupling constants related to the vertice…
The decays eta, eta-prime -> pi^+ pi^- gamma are investigated within an approach that combines one-loop chiral perturbation theory with a coupled channel Bethe-Salpeter equation which satisfies unitarity constraints and generates vector mesons dynamically from composite states of two pseudoscalar mesons. It is furthermore shown that the inclusion of the eta-prime as a dynamical degree of freedom does not renormalize the Wess-Zumino-Witten term.
The Jülich-Bonn dynamical coupled-channel approach is extended to include $KΣ$ photoproduction off the proton. Differential cross section and (double) polarization data for $K^+Σ^0$ and $K^0Σ^+$ are analysed simultaneously with the pion- and photon-induced production of $πN$, $ηN$, $KΛ$, and $KΣ$ final states, totaling more than 67,000 data points for center-of-mass energies $W<2.4$ GeV. Based on the fit results the spectrum of $N^*$ and $Δ$ resonances is extracted in terms of pole positions and residues. We discuss the impact of the $γp\to KΣ$ channels in detail and investigate the influence …
The problem of describing low-energy two-body scattering for systems with two open channels with different thresholds is addressed in the context of an effective field theory. In particular, the problem where the threshold is unnaturally small and the cross section at low energy is unnaturally large is considered. It is shown that the lowest-order point coupling associated with the mixing of the channels scales as $Λ^{-2}$ rather than $Λ^{-1}$ (the scaling of the same-channel coupling and the scaling in a single-channel case) where $Λ$ is the ultraviolet cutoff. The renormalization of the theo…
We perform a systematic analysis of the mass and strong decays of the $Ω(2012)$ resonance in a coupled-channel approach of a bare three-quark state and a composite meson-baryon state. Besides the coupling of the bare state and $Ξ^* \bar K$ channel, the effective meson-baryon interactions are also included. We find a pole with mass of $2008$ MeV by solving the Bethe-Salpeter equation. The calculated decay widths and its ratios of branching fractions $\mathcal {R}_{Ξ\bar K}^{Ξπ\bar K}$ agree well with the new experimental measurement by Belle Collaboration. Our results suggest that both three-qu…
Elastic piN scattering and the world data of the family of reactions pi^- p --> eta n, K^0 Lambda$, K^0 Sigma^0, K^+ Sigma^-, and pi^+ p --> K^+ Sigma^+ are described simultaneously in an analytic, unitary, coupled-channel approach. SU(3) flavor symmetry is used to relate both the t- and the u- channel exchanges that drive the meson-baryon interaction in the different channels. Angular distributions, polarizations, and spin-rotation parameters are compared with available experimental data. Partial-wave amplitudes are determined and the resonance content is extracted from the analytic continuat…
The enigmatic charged states $Z_c(3900)$, $Z_c(4020)$, $Z_c(4050)$, $Z_b(10610)$, and $Z_b(10650)$ are studied within a coupled-channel Schrödinger model, where radially excited quark-antiquark pairs, with the same angular momenta and isospin as the $a_1(1260)$ and $b_1(1235)$, are strongly coupled to their Okubo-Zweig-Iizuka - allowed decay channels $D\bar{D}^*+\bar{D}D^*$ and $D^*\bar{D}^*$, or $B\bar{B}^*+\bar{B}B^*$ and $B^*\bar{B}^*$, in $S$ and $D$-wave. Poles, matching the experimental mass and width of all the above states, are found by varying only two free parameters. From the wave-f…
We report our recent effort on the extraction of N*- and Delta*-resonance parameters (pole masses, coupling constants, etc.) through the comprehensive analysis of pion- and photon-induced pi N, eta N, K Lambda, and K Sigma production reactions. The analysis was performed with the ANL-Osaka dynamical coupled-channels approach, which satisfies the multichannel unitarity of the S-matrix in the channel space spanned by pi N, eta N, K Lambda, K Sigma, and also three-body pi pi N that contains rho N, pi Delta, and sigma N resonant components. Ongoing projects and future plans are also discussed.
A coupled channel model is used to study the nature of the scalar mesons produced in the decay phi - gamma pi pi. The KKbar molecular picture of f0(980) is found to be in a good agreement with the recent experimental data from SND and CMD-2. The structure of the light scalar mesons is elucidated by investigating the S-matrix poles and the qqbar spectral density.
We study the process $γγ\toπ^0π^0$ involving the principle mechanisms, the structure of its cross section and the role of individual isoscalar-tensor resonances in the saturation of its energy spectrum.
Based on the Hamiltonian formalism approach, a generalized Lüscher's formula for two particle scattering in both the elastic and coupled-channel cases in moving frames is derived from a relativistic Lippmann-Schwinger equation. Some strategies for extracting scattering amplitudes for a coupled-channel system from the discrete finite-volume spectrum are discussed and illustrated with a toy model of two-channel resonant scattering. This formalism will, in the near future, be used to extract information about hadron scattering from lattice QCD computations.
The complete spectrum of $c\bar{b}$ states is obtained in a phenomenological non relativistic quark model(NRQM), which consists of a confinement potential and one gluon exchange potential (OGEP) as effective quark - antiquark potential with coupled channel effects. We make predictions for the radiative decay (E1 and M1) widths and weak decay widths of $c\bar{b}$ states in the framework of NRQM formalism.
Systematic and careful studies are made on the properties of the IJ=00 $ππ$ and $K\bar K$ coupled-channel system, using newly derived dispersion relations between the phase shifts and poles and cuts. The effects of nearby branch point singularities to the determination of the $f_0(980)$ resonance are estimated and and discussed.
