Regge trajectories for heavy quarkonia from the quadratic form of the spinless Salpeter-type equation

Abstract

In this paper, we present one new form of the Regge trajectories for heavy quarkonia which is obtained from the quadratic form of the spinless Salpeter-type equation (QSSE) by employing the Bohr-Sommerfeld quantization approach. The obtained Regge trajectories take the parameterized form M 2 = β(c l l + π n r + c 0 ) 2/3 + c 1 , which are different from the present Regge trajectories. Then we apply the obtained Regge trajectories to fit the spectra of charmonia and bottomonia. The fitted Regge trajectories are in good agreement with the experimental data and the theoretical predictions.

Nonlinear Regge trajectories with AdS/QCD

“…Linear Regge trajectories are a good description of the mesonic mass spectra in the light sector, and this has been used traditionally as a guideline in order to catch hadron properties in the AdS side of AdS/QCD models. But if hadrons contain s or heavy quarks, linearity in trajectory is lost [16][17][18][19][20]. Moreover, starting from the quadratic form of Bethe Salpeter equation [19,21], it is possible to infer that mesons consisting of heavier quarks have Regge trajectories deviated from the linearity.…”

“…But if hadrons contain s or heavy quarks, linearity in trajectory is lost [16][17][18][19][20]. Moreover, starting from the quadratic form of Bethe Salpeter equation [19,21], it is possible to infer that mesons consisting of heavier quarks have Regge trajectories deviated from the linearity. In this sort of analysis, heavy quarkonium is expected to have radial trajectories scaling the excitation number as n 2=3 .…”

Bound state inequality from the spinless Salpeter equation with the Yukawa potential

“…The conditions for the existence of a bound state within the spinless Salpeter equation with the Yukawa potential are Eqs. (22) and (23) which give the constraints on the interaction strength α, the screening parameter μ and the mass of the particle m. The numerical results show that α has a maximum which is independent of μ and m, α max = 8/(3π). As α > α max , the particle in the Yukawa potential will lose its mass due to the binding energy and has negative energy which is in connection with the collapse of the vacuum [11].…”

“…The spinless Salpeter equation (SSE) [19][20][21][22][23] is a relativistic extension of the nonrelativistic Schrödinger equation and a well-defined standard approximation to the Bethe-Salpeter equation [24,25] which is the appropriate tool to describe the bound states within the relativistic quantum field theory. The spinless Salpeter equation is written in the configuration space as…”

Error Estimates for the Nearly Singular Momentum-Space Bound-State Equations

“…When the near singularities are treated and then the eigenvalue integral Equation 3becomes less nearly singular or free of near singularities [5][6][7][8][16][17][18], the obtained matrix equation corresponding to Equation (32) reads…”