Coupled-channel Dynamics Research Articles

Molecular pentaquarks with hidden charm and double strangeness

We analyze theoretically the coupled-channel meson-baryon interaction with global flavor c¯cssn and c¯csss, where mesons are pseudoscalars or vectors, and baryons have JP=1/2+ or 3/2+. The aim is to explore whether the nonlinear dynamics inherent in the unitarization process within coupled channels can dynamically generate double- and triple-strange pentaquark-type states (Pcss and Pcsss, respectively), for which there is no experimental evidence to date. We evaluate the s-wave scattering matrix by implementing unitarity in coupled channels, using potential kernels obtained from t-channel vector meson exchange. The required PPV and VVV vertices are obtained from Lagrangians derived through appropriate extensions of the local hidden gauge symmetry approach to the charm sector, while capitalizing on the symmetry of the spin and flavor wave function to evaluate the BBV vertex. We find four different poles in the double strange sector, some of them degenerate in spin. For the triple-strange channel, we find the meson-baryon interaction insufficient to generate a bound or resonance state through the unitary coupled-channel dynamics. Published by the American Physical Society 2024

Double strangeness molecular-type pentaquarks from coupled channel dynamics

Abstract. The existence of the nucleonic pentaquark resonances Pc (4312), Pc(4380), Pc(4440) and Pc(4457), established by the LHCb collaboration, has been one of the major discoveries in hadron physics in the latest years. This has been followed by the discovery of pentaquarks with one unit of strangeness, Pcs(4338) and Pcs(4457). Most of these states can be understood as hadronic molecules, namely bound states of a sufficiently attractive meson-baryon interaction. A widely used model, based on unitarized meson-baryon amplitudes obtained from vector meson exchange interactions derived from the hidden gauge formalism, which predicted these states prior to their discovery, is also predicting the existence of pentaquarks with double strangeness content, at around 4500 MeV and 4600 MeV [1]. Our model also suggest that one of these double strangeness pentaquarks can be seen in the weak decay of the Eb baryon into J/ΨϕΞ. A detailed study of this reaction is still under investigation, but in these proceedings we shall show some preliminary results, which confirm the possibility of observing traces of S=-2 pentaquark in invariant mass spectra of J/ΨΞ pairs produced in the decays Ξb → J/ΨϕΞ.

Two-pole structures as a universal phenomenon dictated by coupled-channel chiral dynamics

Two-pole structures as a universal phenomenon dictated by coupled-channel chiral dynamics

Molecular states in systems* *Supported by the Doctoral Program of Tian Chi Foundation of Xinjiang Uyghur Autonomous Region of China (51052300506), the NSFC and the Deutsche Forschungsgemeinschaftn(DFG, German Research Foundation) through the funds provided to the Sino-German Collaborative Research Center TRR110 “Symmetries and the Emergence of Structure in QCD” (NSFC 12070131001, DFG Project-ID 196253076 - TRR 110), the NSFC (11835015,

The possible hadronic molecules in systems with , and are investigated with interactions described by light meson exchanges. By varying the cutoff in a phenomenologically reasonable range of GeV, we find ten near-threshold (bound or virtual) states in the single-channel case. After introducing the coupled-channel dynamics of ----- systems, these states, except those below the lowest channels in each sector, move into the complex energy plane and become resonances in the mass range GeV. Their spin-parities and nearby thresholds are , , , , , , , , , and . The impact of the -term in the one-boson-exchange model on these states is presented. Setting GeV as an illustrative value, it is found that is a stable bound state (becoming unstable if the coupling to lower channels is turned on), and are physical resonances in cases where the -term is included or excluded, and the other seven states are physical resonances or "virtual-state-like" poles near thresholds, depending on whether the -term is included. In addition, the partial decay widths of the physical resonances are provided. These double-charm hidden-strangeness pentaquark states, as the partners of the experimentally observed and states, can be searched for in the final states in the future.

Efficiency of charge transfer in changing the dissociation dynamics of OD+ transients formed after the photo-fragmentation of D2O.

We present an investigation of the relaxation dynamics of deuterated water molecules after direct photo-double ionization at 61eV. We focus on the very rare D+ + O+ + D reaction channel in which the sequential fragmentation mechanisms were found to dominate the dynamics. Aided by theory, the state-selective formation and breakup of the transient OD+(a1Δ, b1Σ+) is traced, and the most likely dissociation path-OD+: a1Δ or b1Σ+ → A 3Π → X 3Σ- → B 3Σ--involving a combination of spin-orbit and non-adiabatic charge transfer transitions is determined. The multi-step transition probability of this complex transition sequence in the intermediate fragment ion is directly evaluated as a function of the energy of the transient OD+ above its lowest dissociation limit from the measured ratio of the D+ + O+ + D and competing D+ + D+ + O sequential fragmentation channels, which are measured simultaneously. Our coupled-channel time-dependent dynamics calculations reproduce the general trends of these multi-state relative transition rates toward the three-body fragmentation channels.

Understanding the [formula omitted] and [formula omitted] charmonium(-like) states near 3.9 GeV

We propose that the X(3915) observed in the J/ψω channel is the same state as the χc2(3930), and the X(3960), observed in the Ds+Ds- channel, is an S-wave Ds+Ds- hadronic molecule. In addition, the JPC=0++ component in the B+→D+D-K+ assigned to the X(3915) in the current Review of Particle Physics has the same origin as the X(3960), which has a mass around 3.94 GeV. To check the proposal, the available data in the DD¯ and Ds+Ds- channels from both B decays and γγ fusion reaction are analyzed considering both the DD¯-DsD¯s-D*D¯*-Ds*D¯s* coupled channels with 0++ and a 2++ state introduced additionally. It is found that all the data in different processes can be simultaneously well reproduced, and the coupled-channel dynamics produce four hidden-charm scalar molecular states with masses around 3.73, 3.94, 3.99 and 4.23 GeV, respectively. The results may deepen our understanding of the spectrum of charmonia as well as of the interactions between charmed hadrons.

ABC+D: A time-independent coupled-channel quantum dynamics program for elastic and ro-vibrational inelastic scattering between atoms and triatomic molecules in full dimensionality.

We discuss the details of a time-independent quantum mechanical method and its implementation for full-dimensional non-reactive scattering between a closed-shell triatomic molecule and a closed-shell atom. By solving the time-independent Schrödinger equation within the coupled-channel framework using a log-derivative method, the state-to-state scattering matrix (S-matrix) can be determined for inelastic scattering involving both the rotational and vibrational modes of the molecule. Various approximations are also implemented. The ABC+D code provides an important platform for understanding an array of physical phenomena involving collisions between atoms and molecules.

P_{cc}^N states in a unitarized coupled-channel approach

Starting from an effective Lagrangian with heavy quark spin symmetry embedded, the coupled-channel dynamics of the doubly charmed systems D^{(*)} Sigma _c^{(*)} is investigated. The potential underlying our investigation includes t-channel pseudoscalar and vector meson exchanges. A series of S-wave bound states with isospin I=1/2 is found by applying the first iterated solution of the N/D method: one state with binding energy 23 MeV in the 5/2^-D^*Sigma _c^* channel, three states with binding energy 26, 30 and 7 MeV (relative to the thresholds from low to high, respectively) in the 3/2^-DSigma _c^*-D^*Sigma _c-D^*Sigma _c^* system and three states with binding energy 32, 8 and 16 MeV in the 1/2^-DSigma _c-D^*Sigma _c-D^*Sigma _c^* system. Those P_{cc}^N states serve as the open-charm partners of the hidden charm pentaquarks P_{psi }^N observed by the LHCb Collaboration.

Coupled-channel dynamics with chiral long-range forces in the open-charm sector of QCD

We perform an analysis of lattice QCD data in the open-charm sector based on the chiral SU(3) Lagrangian. The low-energy constants are adjusted to recover the open-charm meson masses on lattice QCD ensembles from HPQCD, ETMC, and HSC with pion and kaon masses smaller than 550 MeV. A significant set of low-energy parameters is obtainable only if the most recent information from HSC on scattering observables is included in our global fit. For the first time our analysis considers the effect of left-hand cuts as developed in terms of a generalized potential approach previously by one of the authors. Here we use coupled-channel interaction terms at the one-loop level. The elastic s-wave and p-wave $D\ensuremath{\pi}$, $DK$, and $D\overline{K}$ scattering phase shifts on ensembles with nominal pion masses of about 239 and 391 MeV are reproduced faithfully. Based on such low-energy parameters we predict s- and p-wave phase shifts and inelasticities at physical quark masses, where the statistical uncertainties in the phase shifts are smaller than 1 degree always. Most striking would be the exotic s-wave ${D}_{s}\ensuremath{\pi}$ channel, for which we predict a resonance state at about 2.287 GeV where the phase shift passes through 90 degrees.

Exploring the NΛ–NΣ coupled system with high precision correlation techniques at the LHC

The interaction of Λ and Σ hyperons (Y) with nucleons (N) is strongly influenced by the coupled-channel dynamics. Due to the small mass difference of the NΛ and NΣ systems, the sizable coupling strength of the NΣ↔NΛ processes constitutes a crucial element in the determination of the NΛ interaction. In this letter we present the most precise measurements on the interaction of pΛ pairs, from zero relative momentum up to the opening of the NΣ channel. The correlation function in the relative momentum space for pΛ⊕p‾Λ‾ pairs measured in high-multiplicity triggered pp collisions at s=13 TeV at the LHC is reported. The opening of the inelastic NΣ channels is visible in the extracted correlation function as a cusp-like structure occurring at relative momentum k⁎=289MeV/c. This represents the first direct experimental observation of the NΣ↔NΛ coupled channel in the pΛ system. The correlation function is compared with recent chiral effective field theory calculations, based on different strengths of the NΣ↔NΛ transition potential. A weaker coupling, as possibly supported by the present measurement, would require a more repulsive three-body NNΛ interaction for a proper description of the Λ in-medium properties, which has implications on the nuclear equation of state and for the presence of hyperons inside neutron stars.

Analysis on the composite nature of the light scalar mesons f0(980) and a0(980)

We study the weight or compositeness of the $\pi\pi$-$K\bar{K}$ and $\pi\eta$-$K\bar{K}$ in the composition of the $f_0(980)$ and $a_0(980)$ resonances, respectively. Either we use the saturation of the total width and compositeness, or we use a Flatt\'e parameterization taking also into account the spectral function of a near-threshold resonance. We make connections and compare between these two methods. We take input values for the pole mass and width from several determinations in the literature. In addition, we take as third input either the total compositeness or the decay-width branching ratio to the lighter channel for each resonance. It turns out that for the poles considered the meson-meson components are dominant for the $f_0(980)$, while for the $a_0(980)$ resonance they are subdominant. We also provide partial decay widths and partial compositeness coefficients, so that the $K\bar{K}$ component is the most important one for the $f_0(980)$. Additionally, this study stresses the need to distinguish between the bare and dressed couplings and widths in a Flatt\'e parameterization. We elaborate on the connection between the partial-decay widths calculated in terms of the dressed couplings and the actual measured ones. Due to the coupled-channel dynamics when the pole lies near the heavier threshold in the second Riemann sheet some changes are needed with respect to standard relations.

Coupled-channel effects of the Σc(*)D¯(*)−Λc(2595)D¯ system and molecular nature of the Pc pentaquark states from one-boson exchange model

The effects of the $\Sigma_c\bar{D}^*$-$\Lambda_{c}(2595)\bar{D}$ coupled-channel dynamics and various one-boson-exchange (OBE) forces for the LHCb pentaquark states, $P_c(4440)$ and $P_c(4457)$, are reinvestigated. Both the pion and $\rho$-meson exchanges are considered for the $\Sigma_c\bar{D}^*$-$\Lambda_{c}(2595)\bar{D}$ coupled-channel dynamics. It is found that the role of the $\Lambda_{c}(2595)\bar{D}$ channel in the descriptions of the $P_c(4440)$ and $P_c(4457)$ states is not significant with the OBE parameters constrained by other experimental sources. The naive OBE models with the short-distance $\delta(\vec{r})$ term of the one-pion exchange (OPE) keep failing to reproduce the $P_c(4440)$ and $P_c(4457)$ states simultaneously. The OPE potential with the full $\delta(\vec{r})$ term results in a too large mass splitting for the $J^P=1/2^-$ and $3/2^-$ $\Sigma_c\bar{D}^*$ bound states with total isospin $I=1/2$. The OBE model with only the OPE $\delta(\vec{r})$ term dropped may fit the splitting much better but somewhat underestimates the splitting. Since the $\delta(\vec r)$ potential is from short-distance physics, which also contains contributions from the exchange of mesons heavier than those considered explicitly, we vary the strength of the $\delta(\vec r)$ potential and find that the masses of the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ can be reproduced simultaneously with the $\delta(\vec r)$ term in the OBE model reduced by about 80\%. While two different spin assignments are possible to produce their masses, in the preferred description, the spin parities of the $P_c(4440)$ and $P_c(4457)$ are $3/2^-$ and $1/2^-$, respectively.

The P_{cs}(4459) pentaquark from a combined effective field theory and phenomenological perspective

The observation of the P_{cs}(4459) by the LHCb collaboration adds a new member to the set of known hidden-charm pentaquarks, which includes the P_c(4312), P_c(4440) and P_c(4457). The P_{cs}(4459) is expected to have the light-quark content of a Lambda baryon (I=0, S=-1), but its spin is unknown. Its closeness to the {bar{D}}^* Xi _c threshold – 4478,{mathrm{MeV}} in the isospin-symmetric limit – suggests the molecular hypothesis as a plausible explanation for the P_{cs}(4459). While in the absence of coupled-channel dynamics heavy-quark spin symmetry predicts the two spin-states of the {bar{D}}^* Xi _c to be degenerate, power counting arguments indicate that the coupling with the nearby {bar{D}} Xi _c' and {bar{D}} Xi _c^* channels might be a leading order effect. This generates a hyperfine splitting in which the J=tfrac{3}{2}{bar{D}}^* Xi _c pentaquark will be lighter than the J=tfrac{1}{2} configuration, which we estimate to be of the order of 5-15,{mathrm{MeV}}. We also point out an accidental symmetry between the P_{cs}(4459) and P_c(4440/4457) potentials. Finally, we argue that the spectroscopy and the J/psi Lambda decays of the P_{cs}(4459) might suggest a marginal preference for J = tfrac{3}{2} over J = tfrac{1}{2}.

Peaks within peaks and the possible two-peak structure of the Pc(4457) : The effective field theory perspective

The LHCb pentaquarks -- the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ -- have been theorized to be $\Sigma_c \bar{D}$ and $\Sigma_c \bar{D}^*$ S-wave molecules. Here we explore the possibility that two of these pentaquarks -- the $P_c(4440)$ and $P_c(4457)$ -- contain in addition a $\Lambda_c(2595) \bar{D}$ component in P-wave. We will analyze the effects of this extra channel within two effective field theories: the first one will be a standard contact-range effective field theory and the second one will include the non-diagonal pion dynamics connecting the $\Sigma_c \bar{D}^*$ and $\Lambda_c(2595) \bar{D}$ channels, which happens to be unusually long-ranged. The impact of the coupled-channel dynamics between the $\Sigma_c \bar{D}^*$ and $\Lambda_c(2595) \bar{D}$ components is modest at best for the $P_c(4440)$ and $P_c(4457)$, which will remain to be predominantly $\Sigma_c \bar{D}^*$ molecules. However, if the quantum numbers of the $P_c(4457)$ are $J^P = \frac{1}{2}^-$, the coupled-channel dynamics is likely to induce the binding of a $\Lambda_c(2595) \bar{D}$ S-wave molecule (coupled to $\Sigma_c \bar{D}^*$ in P-wave) with $J^P = \frac{1}{2}^+$ and a mass similar to the $P_c(4457)$. If this is the case, the $P_c(4457)$ could actually be a double peak containing two different pentaquark states.

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.

Coupled channels dynamics in the generation of the Omega (2012) resonance

We look into the newly observed Omega (2012) state from the molecular perspective in which the resonance is generated from the bar{K} Xi ^*, eta Omega and bar{K} Xi channels. We find that this picture provides a natural explanation of the properties of the Omega (2012) state. We stress that the molecular nature of the resonance is revealed with a large coupling of the Omega (2012) to the bar{K} Xi ^* channel, that can be observed in the Omega (2012) rightarrow bar{K} pi Xi decay which is incorporated automatically in our chiral unitary approach via the use of the spectral function of Xi ^* in the evaluation of the bar{K} Xi ^* loop function.

Ω(2012) as a hadronic molecule

Recently the Belle collaboration has discovered a narrow $S=-3$ baryon, the $\Omega(2012)$. We explore the possibility that the $\Omega(2012)$ is a $\Xi(1530)\,\bar K$ molecule, where the binding mechanism is the coupled channel dynamics with the $\Omega\,\eta$ channel. The characteristic signature of a molecular $\Omega(2012)$ will be its decay into the three body channel $\Xi \pi \bar{K}$, for which we expect a partial decay width of $2-3\,{\rm MeV}$. The partial decay width into the $\Xi \bar{K}$ channel should lie in the range of $1-11\,{\rm MeV}$, a figure compatible with experiment and which we have deduced from the assumption that the coupling involved in this decay is of natural size. For comparison purposes the decay of a purely compact $\Omega(2012)$ into the $\Xi \bar{K}$ and $\Xi \pi \bar{K}$ channels is of the same order of magnitude as and one order of magnitude smaller than in the molecular scenario, respectively. This comparison indicates that the current experimental information is insufficient to distinguish between a compact and a molecular $\Omega(2012)$ and further experiments will be required to determine its nature. A molecular $\Omega(2012)$ will also imply the existence of two- and three-body molecular partners. The two-body partners comprise two $\Lambda$ hyperons located at $1740$ and $1950\,{\rm MeV}$ respectively, the first of which might correspond to the $\Lambda(1800)$ while the second to the $\Lambda(2000)$ or the $\Lambda(2050)$. The three-body partners include a $\Xi(1530) K\bar{K}$ and a $\Xi(1530) \eta \bar{K}$ molecule, with masses of $M = 2385-2445\,{\rm MeV}$ and $M = 2434-2503\,{\rm MeV}$ respectively. We might be tempted to identify the first with the $\Xi(2370)$ and the latter with the $\Omega(2470)$ listed in the PDG.

On chiral extrapolations of charmed meson masses and coupled-channel reaction dynamics

We perform an analysis of QCD lattice data on charmed meson masses. The quark-mass dependence of the data set is used to gain information on the size of counter terms of the chiral Lagrangian formulated with open-charm states with J^P= 0^- and J^P =1^- quantum numbers. Of particular interest are those counter terms that are active in the exotic flavour sextet channel. A chiral expansion scheme where physical masses enter the extrapolation formulae is developed and applied to the lattice data set. Good convergence properties are demonstrated and an accurate reproduction of the lattice data based on ensembles of PACS-CS, MILC, ETMC and HSC with pion and kaon masses smaller than 600 MeV is achieved. It is argued that a unique set of low-energy parameters is obtainable only if additional information from HSC on some scattering observables is included in our global fits. The elastic and inelastic s-wave pi D and eta D scattering as considered by HSC is reproduced faithfully. Based on such low-energy parameters we predict 15 phase shifts and in-elasticities at physical quark masses but also for an additional HSC ensemble at smaller pion mass. In addition we find a clear signal for a member of the exotic flavour sextet states in the eta D channel, below the bar K D_s threshold. For the isospin violating strong decay width of the D_{s0}(2317) we obtain the range (104-116) keV.

Heavy Quark Coupled Channel Dynamics from Thermal Shifts

QCD at finite temperature below the phase transition should be determined in terms of colour singlet states such as hadrons and strings. We show how quark-hadron duality allows extracting sensible information concerning heavy quark and string breaking coupled channel dynamics from Polyakov loop correlators.

Quark-mass dependence of the H dibaryon in ΛΛ scattering

We study the quark mass dependence of the H-dibaryon in the strangeness $S=-2$ baryon-baryon scattering. A low-energy effective field theory is used to describe the coupled-channel scattering, in which the quark mass dependence is incorporated so as to reproduce the lattice QCD data by the HAL QCD collaboration in the SU(3) limit. We point out the existence of the Castillejo-Dalitz-Dyson (CDD) pole in the $\Lambda\Lambda$ scattering amplitude below the threshold in the SU(3) limit, which may cause the Ramsauer-Townsend effect near the $N\Xi$ threshold at the physical point. The H-dibaryon is unbound at the physical point, and a resonance appears just below the $N\Xi$ threshold. As a consequence of the coupled-channel dynamics, the pole associated with the resonance is not continuously connected to the bound state in the SU(3) limit. Through the extrapolation in quark masses, we show that the unitary limit of the $\Lambda\Lambda$ scattering is achieved between the physical point and the SU(3) limit. We discuss the possible realization of the "H-matter" in the unphysical quark mass region.