The mass spectra of charmonia, bottomonia and B_c mesons are calculated in the framework of the QCD-motivated relativistic quark model based on the quasipotential approach. The dynamics of heavy quarks and antiquarks is treated fully relativistically without application of the nonrelativistic v^2/c^2 expansion. The known one-loop radiative corrections to the heavy quark potential are taken into account perturbatively. The heavy quarkonium masses are calculated up to rather high orbital and radial excitations (L=5, n_r=5). On this basis the Regge trajectories are constructed both in the total angular momentum J and radial quantum number n_r. It is found that the daughter trajectories are almost linear and parallel, while parent trajectories exhibit some nonlinearity in the low mass region. Such nonlinearity is most pronounced for bottomonia and is only marginal for charmonia. The obtained results are compared with the available experimental data, and a possible interpretation of the new charmonium-like states above open charm production threshold is discussed.
The spectra of heavy quarkonia are studied in two approaches: with the use of the Afonin-Pusenkov representation of the Regge trajectory for the squared excitation energy $E^2(nl)$ (ERT), and using the relativistic Hamiltonian with the universal interaction. The parameters of the ERTs are extracted from experimental mass differences and their values in bottomonium: the intercept $a(b\bar b)=0.131\,$GeV$^2$, the slope of the orbital ERT $b_l(b\bar b) =0.50$\,GeV$^2$, and the slope of the radial ERT, $b_n(b\bar b)=0.724$\,GeV$^2$, appear to be smaller than those in charmonium, where $a(c\bar c)=…
The spectrum of the $s\bar s$ mesons is studied performing a phenomenological analysis of the Regge trajectories defined for the excitation energies. For the $ϕ(3 ^3S_1)$ state the mass $M(ϕ(3S))=2100(20)$ MeV and the leptonic width $Γ_{ee}(ϕ(3S))=0.27(2)$ keV are obtained, while the mass of the $2 ^3D_1$ state, $M(ϕ(2 ^3D_3))=2180(5)$ MeV, appears to be in agreement with the mass of the $ϕ(2170)$ resonance, and its leptonic width, $Γ_{ee}(2 ^3D_1)=0.20\pm 0.10$ keV, has a large theoretical uncertainty, depending on the parameters of the flattened confining potential.
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 sp…
I briefly review the Regge approach to the hadron spectrum and advocate a dynamical emergence of principal quantum number in the known spectrum of light non-strange mesons. Further it is shown how the linear radial trajectories with universal slope can be extended to heavy quarkonia and a qualitative string interpretation is given. After that I discuss a recently proposed non-string model leading to a natural appearance of linear Regge trajectories and explaining many mass relations.
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 discuss…
Fine Structure Constant in the Slope of Regge Trajectories
最近的研究表明，介子和重子的Regge轨迹是非线性的，目前所有的模型都被数据排除了。Tang和Norbury已经确定了Regge轨迹的一些性质：线性，发散，平行和相交线的测试区。同样，Inopin重建了介子和重子的Regge轨迹，表明大多数轨迹是严重非线性的。在大多数Regge轨道模型中，没有迹象表明研究人员研究了粒子结合能来解释实验数据与理论的偏差。根据夸克模型，麦克格雷戈研究了组分夸克（CQ）模型中的结合能，我们将求助于这个模型来解释介子雷奇轨道的斜率。PACS编号：12.40.Nn，12.39.- X
We argue that two seemingly different phenomena, namely the well-known saturation of the Hagedorn exponential distribution and the less familiar saturation of Regge trajectories at resonance masses $m\approx$ 2-2.5 GeV are related and have the same origin: quark deconfinement. We show that the slope of the real part of non-linear Regge trajectories determines the prefactor $f(m)$ in Hagedorn's resonance mass density distribution $ρ(m)$. While the Hagedorn distribution comes from statistics, Regge trajectories contain dynamics.
We propose a model-independent ansatz $M={β_x}\left(x+c_0\right)^ν+c_1$ ($x=l,\,n_r$) and then use it to fit the orbital and radial pion Regge trajectories without the preset values. It is shown that nonzero $c_1$ is reasonable and acceptable. Nonzero $c_1$ gives an explanation for the nonlinearity of the pion Regge trajectories in the usually employed $(M^2,\,x)$ plane. As $m_R$ or $c_1$ is chosen appropriately, both the orbital and radial pion Regge trajectories are linear in the $((M-m_R)^2,\,x)$ plane whether the $π^0$ is included or not on the Regge trajectories. The fitted pion Regge tra…
In this paper, masses and radii of $Σ^-_u$ states hybrid charmonium mesons are calculated by numerically solving the Schrödinger equation with non-relativistic potential model. Results for calculated masses of $Σ^-_u$ states charmonium hybrid mesons are found to be close to the results obtained through lattice simulations. Calculated masses are used to construct Regge trajectories. It is found that the trajectories are almost linear and parallel.
The dynamical picture of a quark-antiquark interaction in light mesons, which provides linearity of radial and orbital Regge trajectories (RT), is studied with the use of the relativistic string Hamiltonian with flattened confining potential and taking into account the self-energy and string corrections. Due to the flattening effect both slopes, $β_n$ of the radial and $β_l$ of the orbital RT, decrease by $\sim 30\%$ with the value of $β_n=1.30(5)$~GeV$^2$ being larger than $ β_l=0.95(5)$~GeV. The self-energy correction provides the linearity of RT and remains important up to very high excitat…
