Regge trajectories for the heavy-light diquarks
Abstract: We attempt to apply the Regge trajectory approach to the heavy-light diquarks composed of one heavy quark and one light quark. However, we find that the direct application of the usual Regge trajectory formula for the heavy-light mesons and baryons fails. In order to correctly estimate the masses of the heavy-light diquarks, it is needed to consider the light quark mass correction and the parameter C in the Cornell potential within the Regge trajectory formula. By using the modified Regge trajectory formulas, … Show more
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Cited by 2 publications
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Regge trajectories for the light diquarks
We attempt to present an unified description of the light meson spectra and the light diquark spectra by applying the Regge trajectory approach. However, we find that the direct application of the linear Regge trajectory formula for the light mesons and baryons fails. To address this issue, we fit the experimental data of light meson spectra and the light diquark spectra obtained by other theoretical approaches. By considering the light quark mass and the parameter C in the Cornell potential, we provide a provisional Regge trajectory formula. We also crudely estimate the masses of the light diquarks (ud), (us), and (ss), and find that they agree with other theoretical results. The diquark Regge trajectory not only becomes a new and very simple approach for estimating the spectra of the light diquarks, but also can explicitly show the behavior of the masses with respect to l or $$n_r$$ n r . Moreover, it is expected that the diquark Regge trajectory can provide a simple method for investigating the $$\rho $$ ρ -mode excitations of baryons, tetraquarks and pentaquarks containing diquarks.
Regge trajectories for the light diquarks
We attempt to present an unified description of the light meson spectra and the light diquark spectra by applying the Regge trajectory approach. However, we find that the direct application of the linear Regge trajectory formula for the light mesons and baryons fails. To address this issue, we fit the experimental data of light meson spectra and the light diquark spectra obtained by other theoretical approaches. By considering the light quark mass and the parameter C in the Cornell potential, we provide a provisional Regge trajectory formula. We also crudely estimate the masses of the light diquarks (ud), (us), and (ss), and find that they agree with other theoretical results. The diquark Regge trajectory not only becomes a new and very simple approach for estimating the spectra of the light diquarks, but also can explicitly show the behavior of the masses with respect to l or $$n_r$$ n r . Moreover, it is expected that the diquark Regge trajectory can provide a simple method for investigating the $$\rho $$ ρ -mode excitations of baryons, tetraquarks and pentaquarks containing diquarks.
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 $$M=m_1+m_2+C'+\beta _x\sqrt{x+c_{0x}}$$ 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.
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