Concavity of the meson Regge trajectories

It is illustrated by the fitted Regge trajectories for a large majority of mesons that both the radial and orbital Regge trajectories for mesons prefer being concave. The concavity of the meson Regge trajectories is model-independent. If the convex Regge trajectories or the Regge trajectories having the inflection points do not exist, the concavity can act as a criterion to choose a newly observed meson or to assign a particle to the unwell-established state. The curvature of the meson Regge trajectories can be taken as a guide in constructing models. The appropriate models should yield the spectra which can produce the concave Regge trajectories according to the concavity of the meson Regge trajectories. If the large majority of the meson Regge trajectories are concave while a few meson Regge trajectories are convex which neither have been confirmed nor have been completely excluded at present, many existing models should be corrected or even be reconstructed, which will lead to the further understanding of the meson dynamics.Comment: 12 pages, 2 figures, 3 tables. Matches the published version in PL

Structure of the meson Regge trajectories

We investigate the structure of the meson Regge trajectories based on the quadratic form of the spinless Salpeter-type equation. It is found that the forms of the Regge trajectories depend on the energy region. As the employed Regge trajectory formula does not match the energy region, the fitted parameters neither have explicit physical meanings nor obey the constraints although the fitted Regge trajectory can give the satisfactory predictions if the employed formula is appropriate mathematically. Moreover, the consistency of the Regge trajectories obtained from different approaches is discussed. And the Regge trajectories for different mesons are presented. Finally, we show that the masses of the constituents will come into the slope and explain why the slopes of the fitted linear Regge trajectories vary with different kinds of mesons.Comment: 14 pages, 4 figures, 6 tables. Matches the published version in the European Physical Journal

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

The Regge trajectory relation $M=m_R+c_{fx}c_xc_c\sqrt{x+c_{0x}}\,(x=l,\,n_r)$ is employed to give an universal description of the heavy-light systems. The universality is illustrated by fitting the Regge trajectories for the heavy-light mesons, the heavy baryons composed of one heavy quark and one light diquark and the tetraquarks consisting of one heavy diquark and one light antidiquark. The universality leads to the meson-baryon-tetraquark partners in case of the heavy-light systems inspired by the hadron superpartners from superconformal and supersymmetric algebra discussed in [22]. As the slope is universal and the parameters $c_{fl}=c_{fn_r}=1$, we find the relative errors of the estimated values are about $2\%$. The values estimated by the universal relation agree well with the experimental and theoretical data. Moreover, we estimate crudely the masses of the orbitally and radially excited states of $D^{\ast}(2010)^{\pm}$, $B^{\ast}$, $\Lambda_c^{+}$, $\Lambda_b^0$ and the $2^{++}$ state of tetraquark $T_{bb\bar{u}\bar{d}}$.Comment: 9 pages, 5 figures and 9 tables. arXiv admin note: substantial text overlap with arXiv:2302.0592

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

By employing the nonlinear Regge trajectory relation $M=m_R+\beta_x(x+c_{0x})^{2/3}\,\,(x=l,\,n_r)$, we investigate the heavy-heavy systems, such as the doubly heavy diquarks, the doubly heavy mesons, the heavy-heavy baryons, and the heavy-heavy tetraquarks. The fitted Regge trajectories illustrate that these heavy-heavy systems satisfy the above formula and show the existence of a universal description of the heavy-heavy systems. The universality embodies not only the universal behavior $M{\sim}x^{2/3}$ but also the universal parameters. The values of $c_{fn_r}$ and $c_{fl}$ vary with different heavy-heavy systems, but they are close to one. There is an inequality $\beta_{n_r}>\beta_{l}$, and it holds for all the heavy-heavy systems. Moreover, the expression of $\beta_x$ [Eq. (11)] explains its variation with the change of the constituents' masses.Comment: 8 pages, 5 figures and 6 tables. The manuscript is rewritten. The main results remain unchange