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

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${}^{\prime }$ + ${\beta }_x$$\sqrt{x+c_{0x}}$, (x = l, n${}_r$). Another reads M = m${}_1$ + C${}^{\prime }$ + $\sqrt{{\beta }_x^2(x+c_{0x})+\frac{4}{3}\sqrt{\pi {\beta }_x}{m}_2^{3/2}(x+c_{0x}{)}^{1/4}}$. 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${}^{\prime }$ 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${}_{f{n}_r}$ (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${}_{f{n}_r}$ (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.