Hadron Molecular States Were Studied By The Quasipotential Bethe-Salpeter Equation

In recent years,a large number of exotic hadronic states were found in experiment,such as XYZ particles,hidden-charm pentaquarks,and dibaryon d*(2380).These newly observed particles are beyond the conventional quark model.Up to now,physicists proposed many different interpretations of these exotic states,among which the popular physical pictures include compact multiquark state,hadronic molecular state,threshold effect.An obvious observation is that many exotic states locate close to the threshold of two hadrons,which suggests that such states are very likely to be deuteron-like hadron molecular states composed of two hadrons.The hadronic molecular state is a new form of material structure,and also important for understanding the origin and internal structure of exotic hadronic states as well as hadron-hadron interaction.We performed following works in the field of the hadronic molecular state.1.Recently,a new structure Y(4626)was observed in the process e+e-→Ds+Ds1(2536)-at Belle.Since the mass of Y(4626)is very close to the Ds*Ds1(2536)threshold,we study the S-wave interactions Ds*Ds1(2536)and Ds(?)s1(2536)in the quasipotential Bethe-Salpeter approach.With the help of the Lagrangians in the heavy quark effective theory,the potential is constructed within the one-boson-exchange model,and inserted into the quasipotential Bethe-Salpeter equation.The poles of obtained scattering amplitudes are searched for at the real axis,which correspond to molecular states from the interactions Ds*Ds1(2536)and Ds(?)s1(2536).The results suggest that the Y(4626)can be assigned as a Ds*Ds1(2536)molecular state with JPC=1--.In the same model,a Ds*Ds1(2536)molecular state with 1-+ and two Ds(?)s1(2536)states with 1-± are also predicted,which can be searched for in future experiments.2.We study possible hidden-bottom molecular pentaquarks Pb from the ∑b(*)B(*)interaction.With the help of the heavy quark symmetry,the theoretical model which successfully interpreted the LHCb hidden-charm pentaquarks is extended to study the hidden-bottom pentaquarks.In isodoublet sector with I=1/2,with the same reasonable parameter seven molecular states are produced:a state near ∑bB threshold with spin parity JP=1/2-,a state near ∑b*B threshold with 3/2-,two states near ∑bB*threshold with 1/2-and 3/2-,and three states near∑b*B*threshold with 1/2-,3/2-and 5/2-.The results suggest that three states near∑b*B*threshold and two states near ∑bB*threshold are very close,respectively,which may be difficult to distinguish in experiment without partial wave analysis.These states can be studied in future high-energy photoproduction experiments,such as the proposed EicC in China.In the case with the isospin I=3/2,a very large cutoff is required to produce bound states from these interactions,which makes the existence of these states unreliable.Hence,our model does not support the existence of the hidden bottom pentaquark states with I=3/2.We also calculate states with different quantum numbers from the ΛbB*interaction,but the values of cutoff αrequired to produce bound states are beyond the limit of reasonable value needed.The calculation does not support existence of S wave ΛbB*molecular states.3.We propose an assignment of the newly observed X(2239),as well as the η(2225),as a molecular state from the interaction of a baryon Λ and an antibaryon (?).With the help of effective Lagrangians,the Λ(?) interaction is described by η,η’,ω,Φ,and σ exchanges.After inserting the potential kernel into the quasipotential Bethe-Salpeter equation,the bound states from the AA interaction can be studied by searching for the poles of the scattering amplitude.Two loosely bound states with quantum numbers IG(JPC)=0+(0-+)and 0-(1--)appear near the threshold almost with the same parameter.Our results support the X(2239)can be interpreted as a 0-(1--)state from the Λ(?) interaction,and the scalar meson η(2225)can be interpreted as a Λ(?) molecular state with 0+(0-+).