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=m₁+m₂+C'+β ₓ√x+c₀ₓ M = m 1 + m 2 + C ′ + β x x + c 0 x , (x=l,\,nᵣ) ( x = l , n r ) . Another reads M=m₁+C'+√β ₓ²(x+c₀ₓ)+4/3√π β ₓm3/2₂(x+c₀ₓ)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. m₁ m 1 and m₂ m 2 are the masses of the heavy constituent and the light constituent, respectively. l is the orbital angular momentum and nᵣ n r is the radial quantum number. β ₓ β x and c₀ₓ c 0 x are fitted. m₁ m 1 , m₂ 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 cfnᵣ c f n r ( cfl 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 cfnᵣ c f n r ( cfl 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 (M²,\,nᵣ) ( M 2 , n r ) and (M²,\,l) ( M 2 , l ) planes.