Relativistic Borromean states

In this work,the existence of Borromean states is discussed for bosonic and fermionic cases in both the relativistic and non-relativistic limits from the 3-momentum shell renormalization.With the linear bosonic model,we check the existence of Efimov-like states in the bosonic system.In both limits a geometric series of singularities is found in the 3-boson interaction vertex,while the energy ratio is reduced by around 70% in the relativistic limit because of the anti-particle contribution.Motivated by the quark-diquark model in heavy baryon studies,we have carefully examined the p-wave quark-diquark interaction and found an isolated Borromean pole at finite energy scale.This may indicate a special baryonic state of light quarks in high energy quark matter.In other cases,trivial results are obtained as expected.In the relativistic limit,for both bosonic and fermionic cases,potential Borromean states are independent of the mass,which means the results would also be valid even in the zero-mass limit.