Correlation function and the inverse problem in the BD interaction

We study the correlation functions of the B0D+,B+D0 system,which develops a bound state of approximately 40MeV,using inputs consistent with the Tcc(3875)state.Then,we address the inverse problem starting from these correlation functions to determine the scattering observables related to the system,including the existence of the bound state and its molecular nature.The important output of the approach is the uncertainty with which these observables can be obtained,considering errors in the B0D+,B+D0 correlation functions typical of current values in correlation functions.We find that it is possible to obtain scattering lengths and effective ranges with relatively high precision and the existence of a bound state.Although the pole position is obtained with errors of the order of 50%of the binding energy,the molecular probability of the state is obtained with a very small error of the order of 6%.All these findings serve as motivation to perform such measurements in future runs of high energy hadron collisions.

A non-relativistic model for the[cc]■ tetraquark

We use a non-relativistic model to study the spectroscopy of a tetraquark composed of [cc]■ in a diquark-antidiquark configuration.By numerically solving the Schr?dinger equation with a Cornell-inspired potential,we separate the four-body problem into three two-body problems.Spin-dependent terms(spin-spin,spin-orbit and tensor)are used to describe the splitting structure of the ■ spectrum and are also extended to the interaction between diquarks.Recent experimental data on charmonium states are used to fix the parameters of the model and a satisfactory description of the spectrum is obtained.We find that the spin-dependent interaction is sizable in the diquark-antidiquark system,despite the heavy diquark mass,and also that the diquark has a finite size if treated in the same way as the ■ systems.We find that the lowest S-wave T 4c tetraquarks might be below their thresholds of spontaneous dissociation into low-lying charmonium pairs,while orbital and radial excitations would be mostly above the corresponding charmonium pair thresholds.Finally,we repeat the calculations without the confining part of the potential and obtain bound diquarks and bound tetraquarks.This might be relevant to the study of exotic charmonium in the quark-gluon plasma.The T 4c states could be investigated in the forthcoming experiments at the LHC and BelleⅡ.

Dynamically generated N* resonances from the interaction of two mesons and a baryon

We have studied the ππN system and coupled channels by using of the Faddeev equations and two N＊ and one A states, all of them with jR =1/2＋, have been found in the formalism as dynamically generated states. In addition, signatures for a new N＊ resonance with JR = 1/2＋ are found around an energy of 1920 MeV in the three-body center of mass system.

Dynamically generated resonances from the vector octet-baryon decuplet interaction and their radiative decays into γ-baryon decuplet

The dynarnically generated resonances from vector meson-baryon decuplet are studied using La- grangians of the hidden gauge theory for vector interactions. One shows that some of the generated states can be associated with some known baryon resonances in the PDG data, while others are predictions for new states. Furthermore, we calculate the radiative decay widths of these resonances into a photon and a baryon decuplet.

Repercussion of the a_(0)(1710)[a_(0)(1817)]resonance and future developments

In a recent paper[1],the BESIII Collaboration reported the observation of a scalar meson of spin-parity J^(P)=0^(+)with isospin I¼1,branded as a_(0)(1817).The state is seen as a peak in the K0 SKþmass distribution in the D_(s)^(+)→K_(s)^(0)K^(+)π^(0)decay.Its mass and width are reported as.

The ■_(s)^(0)→J/ψπ^(0)η decay and the a_(0)(980)-f_(0)(980) mixing

We study the ■_(s)^(0)→J/ψf_(0)(980) and ■_(s)^(0)→J/ψa_(0)(980) reactions,and pay attention to the different sources of iso spin violation and mixing of f_(0)(980) and a_(0)(980) resonances where these resonances are dynamically generated from meson-meson interactions.We find that the main cause of isospin violation is isospin breaking in the meson-meson transition T matrices,and the other source is that the loops involving kaons in the production mechanism do not cancel due to the different masses of charged and neutral kaons.We obtain a branching ratio for a_(0)(980)production of the order of 5×10^(-6).Future experiments can address this problem,and the production rate and shape of the π^(0)η mass distribution will definitely help to better understand the nature of scalar resonances.

Triangle singularity enhancing isospin violation in B^0_s→ J/ψπ~0f_0(980)

We perform calculations for the Bs0→ J/ψπ0f0（980） and Bs0 → J/ψπ0a0（980） reactions, showing that the first is isospin-suppressed while the second is isospin-allowed. The reaction proceeds via a triangle mechanism, with Bs0 →J/ψK＊ K ＋c.c., followed by the decay K＊ →Kπ and a further fusion of KK into the f0（980） or a0（980）. We show that the mechanism develops a singularity around the π0 f0（980） or π0a0（980） invariant mass of 1420 MeV, where the π0f0 and π0a0 decay modes are magnified and also the ratio of π0f0 to π0a0 production. Using experimental information for the Bs0 → J/ψK＊K ＋c.c. decay, we are able to obtain absolute values for the reactions studied which fall into the experimentally accessible range. The reactions proposed and the observables evaluated, when contrasted with actual experiments, should be very valuable to obtain information on the nature of the low lying scalar mesons.

On the chiral covariant approach to ρρ scattering

We examine in detail a recent work（D. Gülmez, U. G. Mei？ner and J. A. Oller, Eur. Phys. J. C,77： 460（2017））, where improvements to make ρρ scattering relativistically covariant are made. The paper has the remarkable conclusion that the J =2 state disappears with a potential which is much more attractive than for J =0,where a bound state is found. We trace this abnormal conclusion to the fact that an ＂on-shell＂ factorization of the potential is done in a region where this potential is singular and develops a large discontinuous and unphysical imaginary part. A method is developed, evaluating the loops with full ρ propagators, and we show that they do not develop singularities and do not have an imaginary part below threshold. With this result for the loops we define an effective potential, which when used with the Bethe-Salpeter equation provides a state with J =2 around the energy of the f2（1270）. In addition, the coupling of the state to ρρ is evaluated and we find that this coupling and the T matrix around the energy of the bound state are remarkably similar to those obtained with a drastic approximation used previously, in which the q2 terms of the propagators of the exchanged ρ mesons are dropped, once the cut-off in the ρρ loop function is tuned to reproduce the bound state at the same energy.

Dynamically generated resonances

In this talk I report on recent work related to the dynamical generation of baryonic resonances, some made up from pseudoscalar meson-baryon, others from vector meson-baryon and a third type from two meson-one baryon systems. We can establish a correspondence with known baryonic resonances, reinforcing conclusions previously drawn and bringing new light on the nature of some baryonic resonances of higher mass.

Ξbb and Ωbbb molecular states

Using the vector exchange interaction in the local hidden gauge approach,which in the light quark sector generates the chiral Lagrangians and has produced realistic results for Ωc,Ξc,Ξb and the hidden charm pentaquark states,we study the meson-baryon interactions in the coupled channels that lead to the Ξbb and Ωbbb excited states of the molecular type.We obtain seven states of the Ξbb type with energies between 10408 and 10869 MeV,and one Ωbbb state at 15212 MeV.

The X(4140) and X(4160) resonances in the e^(+)e^(-)→γJ/ψΦ reaction

We investigate the J/Ψ? invariant mass distribution in the e^+e^-→γJ/Ψ? reaction at a center-of-mass energy of ■=4.6 GeV measured by the BESⅢ collaboration,which concluded that no significant signals were observed for e^+e^-→γX(4140) because of the low statistics.We show,however,that the J/Ψ? invariant mass distribution is compatible with the existence of the X(4140) state,appearing as a peak,and a strong cusp structure at the D_s~*■threshold,resulting from the molecular nature of the X(4160) state,which provides a substantial contribution to the reaction.This is consistent with our previous analysis of the B^+→J/Ψ?K^+decay measured by the LHCb collaboration.We strongly suggest further measurements of this process with more statistics to clarify the nature of the X(4140) and X(4160) resonances.

Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory

We review some recent progress in our understanding of the lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments （MMs） in terms of Chiral Perturbation Theory （ChPT）.In particular,we show that at next-to-leading-order ChPT can describe the MMs of the octet baryons quite well.We also make predictions for the decuplet MMs at the same chiral order.Among them,the MMs of the Δ＋＋ and Δ ＋ are found to agree well with data within the experimental uncertainties.

Sequential single pion production explaining the dibaryon"d^(*)(2380)"peak

In this study,we investigate the two step sequential one pion production mechanism,that is,np(I=0)→π^(-)pp followed by the fusion reaction pp→π^(+)d,to describe the np→π^(+)π^(-)d reaction withπ^(+)π^(-)in state I=0.In this reaction,a narrow peak identified with a"d(2380)"dibaryon has been previously observed.We discover that the second reaction step pp→π^(+)d is driven by a triangle singularity that determines the position of the peak of the reaction and the high strength of the cross section.The combined cross section of these two mechanisms produces a narrow peak with a position,width,and strength,that are compatible with experimental observations within the applied approximations made.This novel interpretation of the peak accomplished without invoking a dibaryon explains why this peak has remained undetected in other reactions.

The radiative decay D^(0)→ K^(*0)γ with vector meson dominance

Motivated by the experimental measurements of D0 radiative decay modes, we have proposed a model to study the D0→ K＊0γ decay, by establishing a link with D0→ K＊0V （V=ρ0, ω） decays through the vector meson dominance hypothesis. In order to do this properly, we have used the Lagrangians from the local hidden gauge symmetry approach to account for Vγ conversion. As a result, we have found the branching ratio B[D0→ K＊0γ]=（1.55-3.44）×10-4, which is in fair agreement with the experimental values reported by the Belle and BaBar collaborations.

Three-body hadronic molecules

In this talk,I discuss our recent studies of three-hadron systems and the resonances found therein.The studies consist of solving Faddeev equations with the input two body interactions obtained from the chiral Lagrangians.The systems which we study are either made of two mesons and a baryon or of three mesons.The motivation for these studies comes from the data on many baryon resonances,especially the ones with J ^π = 1/2 ^＋,which show a large branching ratio to the two meson-one baryon decay channels.In addition to this,several new studies at BES,BELLE,BABAR etc.,claim the existence of new meson resonances which seem to couple strongly to three-meson systems,where mostly two out of the three mesons appear as a known resonance.Hitherto,we have studied two meson-one baryon systems with strangeness =-1,0 and 1 and three-meson systems made of two-pseudoscalars and a vector meson.As we will show in this manuscript,we find many resonances which couple to three-hadrons.