Weak decays of heavy hadrons into dynamically generated resonances

In this paper, we present a review of recent works on weak decay of heavy mesons and baryons with two mesons, or a meson and a baryon, interacting strongly in the final state. The aim is to learn about the interaction of hadrons and how some particular resonances are produced in the reactions. It is shown that these reactions have peculiar features and act as filters for some quantum numbers which allow to identify easily some resonances and learn about their nature. The combination of basic elements of the weak interaction with the framework of the chiral unitary approach allow for an interpretation of results of many reactions and add a novel information to different aspects of the hadron…

Study of the $\bar K N$ system and coupled channels in a finite volume

We investigate the $\bar KN$ and coupled channels system in a finite volume and study the properties of the $\Lambda(1405)$ resonance. We calculate the energy levels in a finite volume and solve the inverse problem of determining the resonance position in the infinite volume. We devise the best strategy of analysis to obtain the two poles of the $\Lambda(1405)$ in the infinite volume case, with sufficient precision to distinguish them.

Improved fixed center approximation of the Faddeev equations for the (K)over-bar N N system with S=0

We extend the Fixed Center Approximation (FCA) to the Faddeev Equations for the K¯NN system with S=0, including the charge exchange mechanisms in the K¯ rescattering which have been ignored in former works within the FCA. We obtain similar results to those found before, but the binding is reduced by 6 MeV. At the same time we also evaluate the explicit contribution the πNΣ intermediate state in the three body system and find that it produces and additional small decrease in the binding of about 3 MeV. The system appears bound by about 35 MeV and the width omitting two body absorption, is about 50 MeV.

Line shape and D(*)D¯(*) probabilities of ψ(3770) from the e+e−→DD¯ reaction

We have performed a calculation of the DD¯, DD¯*, D*D¯, D*D¯* components in the wave function of the ψ(3770). For this we make use of the P03 model to find the coupling of ψ(3770) to these components, that with an elaborate angular momentum algebra can be obtained with only one parameter. Then we use data for the e+e-→DD¯ reaction, from where we determine a form factor needed in the theoretical framework, as well as other parameters needed to evaluate the meson-meson self-energy of the ψ(3770). Once this is done we determine the Z probability to still have a vector core and the probability to have the different meson components. We find Z about 80%–85%, and the individual meson-meson compon…

NDK, (K)over-barDN, and ND(K)over-bar molecules

We investigate theoretically baryon systems made of three hadrons which contain one nucleon and one D meson, and in addition another meson, (D) over tilde, K, or (K) over tilde. The systems are studied using the fixed center approximation to the Faddeev equations. The study is made assuming scattering of a K or a (K) over tilde on a DN cluster, which is known to generate the Lambda(c)(2595), or the scattering of a nucleon on the D (D) over tilde cluster, which has been shown to generate a hidden charm resonance named X(3700). We also investigate the configuration of scattering of N on the KD cluster, which is known to generate the D*(s0)(2317). In all cases we find bound states, with the ND…

A new perspective on the Faddeev equations and the (K)over-bar N N system from chiral dynamics and unitarity in coupled channels

We review recent work concerning the K¯N interaction and Faddeev equations with chiral dynamics which allow us to look at the K¯NN from a different perspective and pay attention to problems that have been posed in previous studies on the subject. We show results which provide extra experimental evidence on the existence of two Λ(1405) states. We then show the findings of a recent approach to Faddeev equations using chiral unitary dynamics, where an explicit cancellation of the two body off shell amplitude with three body forces stemming from the same chiral Lagrangians takes place. This removal of the unphysical off shell part of the amplitudes is most welcome and renders the approach unamb…

K-bar NN system with chiral dynamics

We have performed a calculation of the scattering amplitude for the three body system K¯NN assuming K¯ scattering against a NN cluster, using the Fixed Center approximation to the Faddeev equations. The K¯N amplitudes, which we take from chiral unitary dynamics, govern the reaction and we find a K¯NN amplitude that peaks around 40 MeV below the K¯NN threshold, with a width in |T|2 of the order of 50 MeV for spin 0 and has another peak around 27 MeV with similar width for spin 1. The results are in line with those obtained using different methods but implementing chiral dynamics. The simplicity of the approach allows one to see the important ingredients responsible for the results. In partic…

Combined theoretical study of the $D^+ \to \pi^+ \eta \eta$ and $D^+ \to \pi^+ \pi^0 \eta $ reactions

We study the $D^+ \to \pi^+ \eta \eta $ and $D^+ \to \pi^+ \pi^0 \eta$ reactions, which are single Cabibbo suppressed and can proceed both through internal and external emission. The primary mechanisms at quark level are considered, followed by hadronization to produce three mesons in the $D^+$ decay, and after that the final state interaction of these mesons leads to the production of the $a_0(980)$ resonance, seen in the $\pi^+ \eta$, $\pi^0 \eta$ mass distributions. The theory has three unknown parameters to determine the shape of the distributions and the ratio between the $D^+ \to \pi^+ \eta \eta$ and $D^+ \to \pi^+ \pi^0 \eta$ rates. This ratio restricts much the sets of parameters bu…

States Of Rho D*(D)Over-Bar* With J=3 Within The Fixed Center Approximation To The Faddeev Equations

We study the interaction of ρ, D * and $$\bar D^*$$ with spins aligned using the fixed center approximation to the Faddeev equations. We select a cluster of $$D^* \bar D^*$$ , which is found to be bound in I = 0 and can be associated to the X(3915), and let the ρ meson orbit around the D * and $$\bar D^*$$ . In this case we find an I = 1 state with mass around 4340 MeV and narrow width of about 50 MeV. We also investigate the case with a cluster of ρD * and let the $$\bar D^*$$ orbit around the system of the two states. The ρD * cluster is also found to bind and leads to the D 2 * state. The addition of the extra $$\bar D^*$$ produces further binding and we find, with admitted uncertainties…

A narrow quasi-bound state of the DNN system

Abstract We have investigated a charmed system of DNN (composed of two nucleons and a D meson) by a complementary study with a variational calculation and a Faddeev calculation with fixed-center approximation (Faddeev-FCA). In the present study, we employ a DN potential based on a vector–meson exchange picture in which a resonant Λ c ( 2595 ) is dynamically generated as a DN quasi-bound state, similarly to the Λ ( 1405 ) as a K ¯ N one in the strange sector. As a result of the study of variational calculation with an effective DN potential and three kinds of NN potentials, the D N N ( J π = 0 − , I = 1 / 2 ) is found to be a narrow quasi-bound state below Λ c ( 2595 ) N threshold: total bin…

Discussion on triangle singularities in the Λb→J/ψK−p reaction

We have analyzed the singularities of a triangle loop integral in detail and derived a formula for an easy evaluation of the triangle singularity on the physical boundary. It is applied to the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{\ensuremath{-}}p$ process via ${\mathrm{\ensuremath{\Lambda}}}^{*}$-charmonium-proton intermediate states. Although the evaluation of absolute rates is not possible, we identify the ${\ensuremath{\chi}}_{c1}$ and the $\ensuremath{\psi}(2S)$ as the relatively most relevant states among all possible charmonia up to the $\ensuremath{\psi}(2S)$. The $\mathrm{\ensuremath{\Lambda}}(1890){\ensuremath{\chi}}_{c1}p$ loop is ver…

Prediction of a $Z_c(4000)$ $D^* \bar D^*$ state and relationship to the claimed $Z_c(4025)$

After discussing the OZI suppression of one light meson exchange in the interaction of $D^* \bar D^*$ with isospin I=1, we study the contribution of two pion exchange to the interaction and the exchange of a heavy vector $J/\psi$. We find this latter mechanism weak but enough to barely bind the system in J=2 with a mass around 4000 MeV, while the effect of the two pion exchange is a net attraction but weaker than that from $J/\psi$ exchange. We discuss this state and try to relate it to the $Z_c(4025)$ state, above the $D^* \bar D^*$ threshold, claimed in an experiment at BES from and enhancement of the $D^* \bar D^*$ distribution close to threshold. Together with the results from a recent …

Two-, Three-, Many-body Systems Involving Mesons. Multimeson Condensates

In this talk we review results from studies with unconventional many hadron systems containing mesons: systems with two mesons and one baryon, three mesons, some novel systems with two baryons and one meson, and finally systems with many vector mesons, up to six, with their spins aligned forming states of increasing spin. We show that in many cases one has experimental counterparts for the states found, while in some other cases they remain as predictions, which we suggest to be searched in BESIII, Belle, LHCb, FAIR and other facilities.

Prediction of anI=1DD¯*state and relationship to the claimedZc(3900),Zc(3885)

We study here the interaction of $D{\overline{D}}^{*}$ in the isospin $I=1$ channel in light of recent theoretical advances that allow us to combine elements of the local hidden gauge approach with heavy quark spin symmetry. We find that the exchange of light $q\overline{q}$ is Okubo-Zweig-Iizuka (OZI) suppressed and thus we concentrate on the exchange of heavy vectors and of two pion exchange. The latter is found to be small compared to the exchange of heavy vectors, which then determines the strength of the interaction. A barely $D{\overline{D}}^{*}$ bound state decaying into ${\ensuremath{\eta}}_{c}\ensuremath{\rho}$ and $\ensuremath{\pi}J/\ensuremath{\psi}$ is found. At the same time we…

States of $ \rho$ B* $ \bar{{B}}^{{*}}_{}$ with J = 3 within the fixed center approximation to Faddeev equations

We study the interaction of the a $\rho$ and $D^*$, $\bar D^*$ with spins aligned using the Fixed Center Approximation to the Faddeev equations. We select a cluster of $D^* \bar D^*$, which is found to be bound in $I=0$ and can be associated to the X(3915), and let the $\rho$ meson orbit around the $D^*$ and $\bar D^*$. In this case we find an $I=1$ state with mass around 4340 MeV and narrow width of about 50 MeV. We also investigate the case with a cluster of $\rho D^*$ and let the $\bar D^*$ orbit around the system of the two states. The $\rho D^*$ cluster is also found to bind and leads to the $D^*_2(2460)$ state. The addition of the extra $\bar D^*$ produces further binding and we find,…

Production of X resonances in Bc− decays

A three body state with J=3 in the ρB*B̅N* interaction

We study the ρB * BN * system solving the Faddeev equations in the fixed center approximation. The B * BN * system will be considered forming a cluster, and using the two-body ρB * unitarized scattering amplitudes in the local Hidden Gauge approach we find a new I ( J PC ) = 1(3 −− ) state. The mass of the new state corresponds to a two particle invariant mass of the ρB * system close to the resonant energy of the B * 2 (5747), indicating that the role of this J = 2 resonance is important in the dynamical generation of the new state.

Prediction of a Z(c)(4000) state and relationship with the claimed Z(c)(4025)

After discussing the OZI suppression of one light meson exchange in the interaction of with isospin I = 1 , we study the contribution of the two-pion exchange to the interaction and the exchange of heavy vectors, J/psi for diagonal transitions and D-* for transitions of to J/psi rho. We find these latter mechanisms to be weak, but enough to barely bind the system in J = 2 with a mass around 4000 MeV, while the effect of the two-pion exchange is a net attraction, though weaker than that from heavy-vector exchange. We discuss this state and try to relate it to the Z (c) (4025) state, above the threshold, claimed in an experiment at BES from an enhancement of the distribution close to threshol…

(K)over-bar N N absorption within the framework of the fixed-center approximation to Faddeev equations

We present a method to evaluate the (K) over bar absorption width in the bound (K) over bar N N system. Most calculations of this system ignore this channel and only consider the (K) over bar N -> pi Sigma conversion. Other works make a qualitative calculation using perturbative methods. Since the (1405) resonance is playing a role in the process, the same resonance is changed by the presence of the absorption channels andwe find that a full nonperturbative calculation is called for, which we present here. We employ the fixed center approximation to Faddeev equations to account for (K) over bar rescattering on the (NN) cluster and we find that the width of the states found previously for S …

Prediction of an I=1 D(D)over-bar* state and relationship to the claimed Z(c)(3900), Z(c)(3885)

We study here the interaction of D (D) over bar* in the isospin I = 1 channel in light of recent theoretical advances that allow us to combine elements of the local hidden gauge approach with heavy quark spin symmetry. We find that the exchange of light q (q) over bar is Okubo-Zweig-Iizuka (OZI) suppressed and thus we concentrate on the exchange of heavy vectors and of two pion exchange. The latter is found to be small compared to the exchange of heavy vectors, which then determines the strength of the interaction. A barely D (D) over bar* bound state decaying into eta(c)rho and pi J/psi is found. At the same time we reanalyze the data of the BESIII experiment on e(+)e(-) -> pi(+/-)(D (D) o…

Ds0*(2317)+in the decay ofBcintoJ/ψDK

In this paper we study the relationship between the ${D}_{s0}^{*}(2317{)}^{+}$ resonance and the decay of the ${B}_{c}$ meson into $J/\ensuremath{\psi}DK$. In this process, the ${B}_{c}$ meson decays first into $J/\ensuremath{\psi}$ and the quark pair $c\overline{s}$, and then the quark pair hadronizes into $DK$ or ${D}_{s}\ensuremath{\eta}$ components, which undergo final state interaction. This final state interaction, generating the ${D}_{s0}^{*}(2317{)}^{+}$ resonance, is described by the chiral unitary approach. With the parameters which allow us to match the pole position of the ${D}_{s0}^{*}(2317{)}^{+}$, we obtain the $DK$ invariant mass distribution of the decay ${B}_{c}\ensuremath…

Energy And Width Of A Narrow I=1/2 Dnn Quasibound State

The energies and widths of DNN quasibound states with isospin I = 1/2 are evaluated in two methods, the fixed center approximation to the Faddeev equation and the variational method approach to the effective one-channel Hamiltonian. The DN interactions are constructed so they dynamically generate the Lambda(c)(2595) (I = 0, J(pi) = 1/2(-)) resonance state. We find that the system is bound by about 250 MeV from the DNN threshold, root s similar to 3500 MeV. Its width, including both the mesonic decay and the D absorption, is estimated to be about 20-40 MeV. The I = 0 DN pair in the DNN system is found to form a cluster that is similar to the Lambda(c)(2595).

B-0 And B-S(0) Decays Into J/Psi Plus A Scalar Or Vector Meson

We extend a recent approach to describe the B-0 and B-s(0) decays into J/psi f(0)(500) and J/psi f(0)(980), relating it to the B-0 and B-s(0) decays into J/psi and a vector meson, phi, rho, K*. In addition, the B-0 and B-s(0) decays into J/psi and kappa(800) are evaluated and compared to the K* vector production. The rates obtained are in agreement with the available experiment while predictions are made for the J/psi plus kappa(800) decay.

The Bc → J/ΨKD weak decay and its relation with the D*s0(2317) resonance

We study the influence of the D * s 0 (2317) + resonance in the decay B c → J/ψKD . In this process, we consider that the B c meson decays first into J/ψ and the quark pair cs , and then the quark pair hadronizes into DK or D s η components. The final state interaction, generating the D * s 0 (2317) + resonance, is described by the chiral heavy meson unitary approach. With the parameters chosen in order to match the pole position of the D * s 0 (2317) + , we obtain the DK invariant mass distribution of the decay B c → J/ψDK , and also the rate for B c → J/ψD * s 0 (2317). We predict the ratio of these two magnitudes. This decay mechanism has not been measured yet, and it would provide insig…

a 0 (980)− f 0 (980) mixing in χ c1 → π 0 f 0 (980)→ π 0 π + π − and χ c1 → π 0 a 0 (980)→ π 0 π 0 η

Abstract We study the isospin breaking in the reactions χ c 1 → π 0 π + π − and χ c 1 → π 0 π 0 η and its relation to the a 0 ( 980 ) − f 0 ( 980 ) mixing, which was measured by the BESIII Collaboration. We show that the same theoretical model previously developed to study the χ c 1 → η π + π − reaction (also measured by BESIII), and further explored in the predictions to the η c → η π + π − , can be successfully employed in the present study. We assume that the χ c 1 behaves as an S U ( 3 ) singlet to find the weight in which trios of pseudoscalars are created, followed by the final state interaction of pairs of mesons to describe how the a 0 ( 980 ) and f 0 ( 980 ) are dynamically generat…

Energy and width of a narrowI=1/2DNNquasibound state

The energies and widths of $DNN$ quasi-bound states with isospin I=1/2 are evaluated in two methods, the fixed center approximation to the Faddeev equation and the variational method approach to the effective one-channel Hamiltonian. The $DN$ interactions are constructed so that they dynamically generate the $\Lambda_c(2595)$ (I=0, $J^{\pi} =1/2^-$) resonance state. We find that the system is bound by about 250 MeV from the $DNN$ threshold, $\sqrt{s} \sim 3500$ MeV. Its width including both the mesonic decay and the $D$ absorption, is estimated to be about 20-40 MeV. The I=0 $DN$ pair in the $DNN$ system is found to form a cluster that is similar to the $\Lambda_c(2595)$.

Narrow Bound States of the DNN System

We report on a recent calculation of the properties of the $DNN$ system, a charmed meson with two nucleons. The system is analogous to the $\bar K NN$ system substituting a strange quark by a charm quark. Two different methods are used to evaluate the binding and width, the Fixed Center approximation to the Faddeev equations and a variational calculation. In both methods we find that the system is bound by about 200 MeV and the width is smaller than 40 MeV, a situation opposite to the one of the $\bar K NN$ system and which makes this state well suited for experimental observation.

Strategy to find the two $\Lambda(1405)$ states from lattice QCD simulations

Theoretical studies within the chiral unitary approach, and recent experiments, have provided evidence of the existence of two isoscalar states in the region of the $\Lambda(1405)$. In this paper we use the same chiral approach to generate energy levels in a finite box. In a second step, assuming that these energies correspond to lattice QCD results, we devise the best strategy of analysis to obtain the two states in the infinite volume case, with sufficient precision to distinguish them. We find out that using energy levels obtained with asymmetric boxes and/or with a moving frame, with reasonable errors in the energies, one has a successful scheme to get the two $\Lambda(1405)$ poles.