Coupled-channel Dynamics Research Articles

P-wave coupled-channel scattering ofBsπ,Bs*π,BK¯,B*K¯and the puzzlingX(5568)

The D0 Collaboration has recently reported a narrow peak structure in the $B_s^0\pi^\pm$ invariant-mass spectrum, that is called $X(5568)$. Its proposed quantum numbers $J^P=0^+/1^+$ are not determined unambiguously, and we show that one can fit the data assuming $J^P=1^-$ with the same mass and width for the resonance signal. The corresponding isovector $P$-wave coupled-channel scattering involving the states $B_s\pi$, $B_s^*\pi$, $B \overline{K}$ and $B^*\overline K$ is studied employing leading-order Heavy Meson Chiral Perturbation Theory, which is then unitarized making use of standard techniques from Unitary Chiral Perturbation Theory. The subtraction constants that appear in the unitarization process are determined by a $u$-channel crossing symmetry constraint or by naturalness arguments, being the numerical values obtained in both cases quite closed, and no further freedom is left in the model. A crucial point is that if the $X(5568)$ is $1^-$ and decaying into $B_s^0\pi^\pm$ then it should appear as a pole in the $T$-matrix elements. It finally turns out that no $X(5568)$ pole is found that can be qualified as dynamically generated from the isovector $P$-wave coupled-channel dynamics. This result disfavors the interpretation of the $X(5568)$ within a "molecular" picture.

Hindered magnetic dipole transitions between P -wave bottomonia and coupled-channel effects

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, $\chi_b(n P)$ 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 vertices $\chi_{b0}(nP)B\bar B$. A measurement of the hindered M1 transitions can shed light on the coupled-channel dynamics in these transitions and hence on the size of the coupling constants. We also suggest to check the coupled-channel effects by comparing results from quenched and fully dynamical lattice QCD calculations.

Multiquark contributions to charm baryon spectroscopy

We study possible multiquark contributions to the charm baryon spectrum by considering higher order Fock space components. For this purpose we perform two different calculations. In a first approach we do a coupled-channel calculation of the $ND$ system looking for molecular states. In a second step we allow for the coupling to a heavy baryon--light meson two-hadron system looking for compact exotic five--quark structures. Both calculations have been done within the framework of a chiral constituent quark model. The model, tuned in the description of the baryon and meson spectra as well as the $NN$ interaction, provides parameter-free predictions for charm $+1$ molecular or compact two-hadron systems. Unlike the $N \bar D$ system, no sharp quark-Pauli effects are found. However, the existence of different two-hadron thresholds for the five-quark system will make the coupled-channel dynamics relevant. Only a few channels are candidates to lodge molecular or compact hadrons with a five-quark structure, being specially relevant the $(T)J^P=(0)1/2^-$ and $(T)J^P=(2)5/2^-$ channels. The identification of molecular states and/or compact hadrons with multiquark components either with or without exotic quantum numbers is a challenge of different collaborations like $\bar {\rm P}$ANDA, LHCb, ExHIC or J-PARC.

NEW INSIGHTS IN $\bar{K}N$ SCATTERING AND THE Λ(1405)

We discuss in this talk aspects of [Formula: see text] plus coupled channels dynamics with special emphasis on the Λ(1405) resonance and isovector resonances in the same energy region. We comment on several experimental reactions giving rise to πΣ distributions with important implications on the spectroscopy. We also discuss recent theoretical models based con NLO SU(3) unitarized chiral perturbation theory.

Coupled-channel dynamics in the reactions πN → πN, ηN, KΛ, KΣ

Elastic πN scattering and the world data of the family of reactions π − p → ηn, K 0 Λ, K 0 Σ 0, K + Σ −, and π + p → K + Σ + 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 continuation, including resonance positions and branching ratios, and possible sources of uncertainties are discussed. The results provide the final-state interactions for the ongoing analysis of photo- and electroproduction data.

Improved Threshold Constraints on Coupled-Channels Chiral SU(3) Dynamics from Kaonic Hydrogen

\({\bar{K}}\)-nucleon interactions near threshold are investigated in the framework of coupled-channels dynamics based on the next-to-leading order chiral SU(3) meson-baryon effective Lagrangian. Accurate constraints are now provided by new high-precision kaonic hydrogen measurements. This constraint permits an updated analysis of the complex \({\bar{K}N}\) and πΣ coupled-channels amplitudes.

On the Origin and Movement of the Poles in the Coupled Channels Model for $${\bar{K}N}$$ Interactions

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 $\pi\Sigma$, $\bar{K}N$ and $K\Xi$ channels. An evolution of the poles from the zero coupling limit and from a limit of restored SU(3) symmetry is discussed.

Resonances Generated by the Vector Meson-Baryon Dynamics

We have recently studied vector meson-octet baryon (VB) interactions with the aim to find dynamical generation of resonances in such systems. For this, we consider the s-, t-, u-channel diagrams along with a contact interaction originating from the hidden local symmetry Lagrangian. We find the contribution from all these sources, except the s-channel, to be important. The amplitudes obtained by solving the coupled channel Bethe–Salpeter equations for the systems with total strangeness zero show generation of one isospin 3/2, spin 1/2 resonance and three isospin 1/2 resonances: two with spin 3/2 and one with spin 1/2. We identify these resonances with Δ (1900) S31, N*(2080) D13, N* (1700) D13, and N*(2090) S11, respectively. Further, we briefly discuss the results of our investigation of the VB systems when coupled to the pseudoscalar meson-baryon (PB) channels. We find that the low-lying resonances couple strongly to the VB channels, a result which can be useful in studying the reactions involving pseudoscalar and vector meson exchanges. In case of the higher mass resonances (in the 1,800–2,200 MeV region), we find that some of the states claimed as dynamically generated states in the VB system can disappear due to their coupling to the PB channels. We also find that new states can appear from PB–VB coupled channel dynamics; for example, we find that a Σ resonance near 1,400 MeV gets developed due to such an effect.

Chiral SU(3) theory of antikaon–nucleon interactions with improved threshold constraints

$\bar{K}$-nucleon interactions are investigated in the framework of coupled-channels dynamics based on the next-to-leading order chiral SU(3) meson-baryon effective Lagrangian. A recent determination of the 1s shift and width of kaonic hydrogen enables us to set accurate constraints on the coupled-channels meson-baryon amplitudes in the strangeness $S=-1$ sector. Theoretical uncertainties in the subthreshold extrapolation of the coupled-channels amplitudes are discussed. Using this framework, we give predictions for $K^-$-neutron interactions and for the spectrum of the $\Lambda(1405)$ resonance. A simplified, effective three-channel model using leading order chiral SU(3) meson-baryon interactions is also constructed for convenient application in $\bar{K}$-nuclear few-body calculations.

Combined large-Ncand heavy-quark operator analysis of two-body meson-baryon counterterms in the chiral Lagrangian with charmed mesons

The chiral SU(3) Lagrangian with pseudoscalar and vector $D$ mesons and with the octet and decuplet baryons is considered. The leading two-body counter terms involving two baryon fields and two $D$ meson fields are constructed in the open-charm sector. There are 26 terms. A combined expansion in the inverse of the charm quark mass and in the inverse of the number of colors provides sum rules that reduce the number of free parameter down to 5 only. Our result shows the feasibility of a systematic computation of the open-charm baryon spectrum based on coupled-channel dynamics.

Improved constraints on chiral SU(3) dynamics from kaonic hydrogen

A new improved study of K−–proton interactions near threshold is performed using coupled-channels dynamics based on the next-to-leading order chiral SU(3) meson–baryon effective Lagrangian. Accurate constraints are now provided by new high-precision kaonic hydrogen measurements. Together with threshold branching ratios and scattering data, these constraints permit an updated analysis of the complex K¯N and πΣ coupled-channels amplitudes and an improved determination of the K−p scattering length, including uncertainty estimates.

Nonadiabatic quantum dynamics of C(1D)+H2→CH+H: Coupled-channel calculations including Renner-Teller and Coriolis terms

The Renner-Teller (RT) coupled-channel dynamics for the C((1)D)+H(2)(X(1)Σ(g) (+))→CH(X(2)Π)+H((2)S) reaction has been investigated for the first time, considering the first two singlet states ã̃(1)A' and b(1)A'' of CH(2) dissociating into the products and RT couplings, evaluated through the ab initio matrix elements of the electronic angular momentum. We have obtained initial-state-resolved probabilities, cross sections and thermal rate constants via the real wavepacket method for both coupled electronic states. In contrast to the N((2)D)+H(2)(X(1)Σ(g)(+)) system, RT effects tend to reduce probabilities, cross sections, and rate constants in the low energy range compared to Born-Oppenheimer (BO) ones, due to the presence of a repulsive RT barrier in the effective potentials and to long-lived resonances. Furthermore, contrary to BO results, the rate constants have a positive temperature dependence in the 100-400 K range. The two-state RT rate constant at 300 K, lower than the BO one, remains inside the error bars of the experimental value.

Level structure and production cross section ofΞ12Be studied with coupled-channels antisymmetrized molecular dynamics

A theoretical framework of coupled-channels antisymmetrized molecular dynamics that describes the multistrangeness system with mixing between different baryon species is developed and applied to ${}_{\mathrm{\ensuremath{\Lambda}}}^{12}\mathrm{C}$ and ${}_{\mathrm{\ensuremath{\Xi}}}^{12}\mathrm{Be}$. By introducing a minor modification to the YN G-matrix interaction derived from the Nijmegen model-D, the low-lying level structure and production cross section of ${}_{\mathrm{\ensuremath{\Lambda}}}^{12}\mathrm{C}$ are reasonably described. It is found that the low-lying states of ${}_{\mathrm{\ensuremath{\Xi}}}^{12}\mathrm{Be}$ are dominated by the ${}^{11}\mathrm{B}\ensuremath{\bigotimes}{\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ channel and their order strongly depends on $\mathrm{\ensuremath{\Xi}}N$ effective interactions used in the calculation. The calculated peak position of the production cross section depends on the $\mathrm{\ensuremath{\Xi}}N$ effective interaction and the magnitude of spin-flip and non-spin-flip cross sections of ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}^{+}{\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ elemental processes. We suggest that the ${}^{12}\mathrm{C}({K}^{\ensuremath{-}},{K}^{+}){}_{\mathrm{\ensuremath{\Xi}}}^{12}\mathrm{Be}$ reaction possibly provides us information about the $\mathrm{\ensuremath{\Xi}}N$ interaction.

Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction

The K-matrix formalism is offering a very realistic approach to arrive at a description of meson-nucleon scattering that obeys unitarity since it takes into account the full coupled channels dynamics. Some examples of the importance of coupled channels effects are presented for photo-induced reactions as well as the results of a simultaneous chi(2) fit to a number of observables in a variety of reactions. A short reflection on the importance of causality is also presented.

Dynamics of strong and radiative decays of Ds-mesons in the hadrogenesis conjecture

The positive parity scalar D*s0(2317) and axial-vector D*s1(2460) charmed strange mesons are generated by coupled-channel dynamics through the s-wave scattering of Goldstone bosons off the pseudoscalar and vector D(Ds)-meson ground states. The specific masses of these states are obtained as a consequence of the attraction arising from the Weinberg–Tomozawa interaction in the chiral Lagrangian. Chiral corrections to order Q2χ are calculated and found to be small. The D*s0(2317) and D*s1(2460) mesons decay either strongly into the isospin-violating π0Ds and π0D*s channels or electromagnetically. We show that the π0-η and (K0D+-K+D0) mixings act constructively to generate strong widths of the order of 140 keV and emphasize the sensitivity of this value to the KD component of the states. The one-loop contribution to the radiative decay amplitudes of scalar and axial-vector states is calculated using the electromagnetic Lagrangian to chiral order Q2χ. We show the importance of taking into account processes involving light vector mesons explicitly in the dynamics of electromagnetic decays. The radiative width are sensitive to both ηDs and KD components, hence providing information complementary to the strong widths on the positive parity Ds-meson structure.

Kaonic production of $ \Lambda$ (1405) off deuteron target in chiral dynamics

The K--induced production of \( \Lambda\)(1405) is investigated in K - d \( \rightarrow\) \( \pi\) \( \Sigma\) n reactions based on coupled-channels chiral dynamics, in order to discuss the resonance position of the \( \Lambda\)(1405) in the \( \bar{{K}}\) N channel. We find that the K - d \( \rightarrow\) \( \Lambda\)(1405)n process favors the production of \( \Lambda\)(1405) initiated by the \( \bar{{K}}\) N channel. The present approach indicates that the \( \Lambda\)(1405) -resonance position is 1420MeV rather than 1405MeV in the \( \pi\) \( \Sigma\) invariant-mass spectra of K - d \( \rightarrow\) \( \pi\) \( \Sigma\) n reactions. This is consistent with an observed spectrum of the K - d \( \rightarrow\) \( \pi^{{+}}_{}\) \( \Sigma^{{-}}_{}\) n with 686-844MeV/c incident K- by bubble chamber experiments done in the 70s. Our model also reproduces the measured \( \Lambda\)(1405) production cross-section.

Born–Oppenheimer quantum dynamics of the C(D1)+H2 reaction on the CH2 ã A11 and b̃ B11 surfaces

We present the Born-Oppenheimer coupled-channel dynamics of the reaction (12)C((1)D)+(1)H(2)(X (1)Sigma(g) (+))-->CH(X (2)Pi)+H((2)S), considering the uncoupled CH(2) states ã (1)A(1) and b (1)B(1), the permutation-inversion symmetry, and Coriolis interactions. Using accurate MRCI potential energy surfaces (PESs), we obtain initial-state-resolved reaction probabilities, cross sections, and rate constants through the time-dependent, real wavepacket (WP) and flux methods, taking into account the proton-spin statistics for both electronic species. Comparing results on both PESs, we point out the role of the b (1)B(1) upper state on the initial-state-resolved dynamics and on the thermal kinetic rate. WP probabilities at J=0 and cross sections at E(col)=0.080 eV agree quite well with quantum-mechanical time-independent findings. Probabilities and WP snapshots show the different reaction mechanisms on the PESs, i.e., an ã (1)A(1) indirect perpendicular insertion and a b (1)B(1) direct sideways collision, associated with many and few sharp resonances, respectively. All cross sections are very large at low E(col), decrease at high energies, and that of the lowest reactant state presents some weak resonances. As the temperature increases from 100 to 400 K, the ã (1)A(1) rate constant increases slightly from 1.37x10(-10) to 1.43x10(-10) cm(3) s(-1), whereas the b (1)B(1) one decreases from 1.30x10(-10) to 0.98x10(-10) cm(3) s(-1). In this temperature range, the b (1)B(1) contribution to the total rate constant thus decreases from 49% to 41%. At 300 K, the WP and experimental rates are equal to (2.45+/-0.08)x10(-10) and (2.0+/-0.6)x10(-10) cm(3) s(-1), respectively.

Effective $\boldsymbol{\bar{K}\!N}$ interaction with strong πΣ dynamics constrained by chiral SU(3) symmetry

We derive a single-channel effective \(\bar{K}\!N\) interaction from chiral SU(3) coupled-channel dynamics, emphasizing the important role of the πΣ channel and the structure of the Λ(1405) resonance. The chiral low energy theorem requires strongly attractive interaction not only in the \(\bar{K}\!N\) channel but also in the πΣ channel. As a consequence of the strong πΣ dynamics, the equivalent potential in single \(\bar{K}\!N\) channel turns out to be less attractive than the one used in a purely phenomenological approach.

Born–Oppenheimer and Renner–Teller coupled-channel quantum dynamics of the N(D2)+HD reactions

We present the Born-Oppenheimer (BO) and Renner-Teller (RT) coupled-channel dynamics of the N((2)D) + HD --> NH + D and N((2)D) + HD --> ND + H reactions, considering the X (2)A(") and A (2)A(') states and RT and Coriolis couplings. We use the best available potential energy surfaces and obtain initial-state-resolved probabilities, cross sections, and rate constants via the real wave packet and flux methods for both electronic states. In contrast with the RT results of BO-X (2)A(") ones, we point out the role of RT and Coriolis interactions for both reactions and discuss the importance of the excited state on the initial-state-resolved dynamics and on the thermal kinetic rate. Moreover the competition for the formation of two products is discussed, showing some snapshots of the RT wave-packet density on the ground state. However, the BO approximation gives thermal rates that are smaller than those obtained via full RT calculation, especially at 300 K. Our calculated RT rate constants at room temperature are in good agreement with the experimental ones. The branching ratio is also calculated at T = 150-300 K at BO and RT levels. At 300 K the calculated value overestimates slightly the experimental data.

DYNAMICS OF STRONG AND RADIATIVE DECAYS OF Ds MESONS

The positive parity scalar [Formula: see text] and axial-vector [Formula: see text] charmed strange mesons are generated by coupled-channel dynamics through the s-wave scattering of Goldstone bosons off the pseudoscalar and vector D ( D s)-meson ground states. The attraction leading to the specific masses of these states reflects the chiral symmetry breaking scale which characterizes the Weinberg-Tomozawa interaction in the chiral Lagrangian. Chiral corrections to order [Formula: see text] are calculated and found to be small. The [Formula: see text] and [Formula: see text] mesons decay either strongly into the isospin-violating π0 D s and [Formula: see text] channels or electromagnetically. We show that the π0-η and ( K 0 D +- K + D 0) mixings act constructively to generate strong widths of the order of 140 keV. The one-loop contribution to the radiative decay amplitudes of scalar and axial-vector states is calculated using the electromagnetic Lagrangian to chiral order [Formula: see text]. We show the importance of taking into account processes involving light vector mesons explicitly in the dynamics of electromagnetic decays to obtain a satisfactory description of the available data.