Regge trajectory relations for the universal description of the heavy-light systems: diquarks, mesons, baryons and tetraquarks

Abstract

Two newly proposed Regge trajectory relations are employed to analyze the heavy-light systems. One of the relations is $M=m_1+m_2+C'+\beta_x\sqrt{x+c_{0x}}$, $(x=l,\,n_r)$. Another reads $M=m_1+C'+\sqrt{\beta_x^2(x+c_{0x})+\frac{4}{3}\sqrt{{\pi}{\beta_x}}m^{3/2}_2(x+c_{0x})^{1/4}}$. $M$ is the bound state mass. $m_1$ and $m_2$ are the masses of the heavy constituent and the light constituent, respectively. $l$ is the orbital angular momentum and $n_r$ is the radial quantum number. $\beta_x$ and $c_{0x}$ are fitted. $m_1$, $m_2$ and $C'$ are input parameters. These two formulas consider both of the masses of heavy constituent and light constituent. We find that the heavy-light diquarks, the heavy-light mesons, the heavy-light baryons and the heavy-light tetraquarks satisfy these two formulas. When applying the first formula, the heavy-light systems satisfy the universal description irrespective of both of the masses of the light constituents and the heavy constituent. When using the second relation, the heavy-light systems satisfy the universal description irrespective of the mass of the heavy constituent. The fitted slopes differ distinctively for the heavy-light mesons, baryons and tetraquarks, respectively. When employing the first relation, the average values of $c_{fn_r}$ ($c_{fl}$) are $1.026$, $0.794$ and $0.553$ ($1.026$, $0.749$ and $0.579$) for the heavy-light mesons, the heavy-light baryons and the heavy-light tetraquarks, respectively. Upon application of the second relation, the mean values of $c_{fn_r}$ ($c_{fl}$) are $1.108$, $0.896$ and $0.647$ ($1.114$, $0.855$ and $0.676$) for the heavy-light mesons, the heavy-light baryons and the heavy-light tetraquarks, respectively. Moreover, the fitted results show that the Regge trajectories for the heavy-light systems are concave downwards in the $(M^2,\,n_r)$ and $(M^2,\,l)$ planes.