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

Abstract

AbstractTwo newly proposed Regge trajectory relations are employed to analyze the heavy-light systems. One of the relations is $$M=m_1+m_2+C'+\beta _x\sqrt{x+c_{0x}}$$ M = m 1 + m 2 + C ′ + β x x + c 0 x , $$(x=l,\,n_r)$$ ( 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 = m 1 + C ′ + β x 2 ( x + c 0 x ) + 4 3 π β x m 2 3 / 2 ( x + c 0 x ) 1 / 4 . M is the bound state mass. $$m_1$$ m 1 and $$m_2$$ m 2 are the masses of the heavy constituent and the light constituent, respectively. l is the orbital angular momentum and $$n_r$$ n r is the radial quantum number. $$\beta _x$$ β x and $$c_{0x}$$ c 0 x are fitted. $$m_1$$ m 1 , $$m_2$$ m 2 and $$C'$$ 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 f n r ($$c_{fl}$$ 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 f n r ($$c_{fl}$$ 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 $$(M^2,\,n_r)$$ ( M 2 , n r ) and $$(M^2,\,l)$$ ( M 2 , l ) planes.