Revisiting the pion Regge trajectories

Abstract

We propose a model-independent ansatz $M={\beta }_x{\left(x+c_0\right)}^{\nu }+c_1$ ($x=l,n_r$) 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 ${\pi }^0$ is included or not on the Regge trajectories. The fitted pion Regge trajectories suggest $0.45\le \nu \le 0.5$, which indicates the confining potential $r^a$ with $9/11\le a\le 1$. Moreover, it is illustrated in the appendix B that $m_R$ can be nonzero for the light nonstrange mesons. We present discussions in the appendix A on the structure of the Regge trajectories plotted in the $(M,x)$ plane and on the structure of the Regge trajectories in the $((M-m_R{)}^2,x)$ plane based on the potential models and the string models.

14 pages, 9 figures, 4 tables. V3: Nucl. Phys. B

References in corpus (12)

• Mass spectra and Regge trajectories of light mesons in the relativistic quark model
• Gravitational decoupling for axially symmetric systems and rotating black holes
• Assignments of ${\Lambda }_Q$ and ${\Xi }_Q$ baryons in the heavy quark-light diquark picture
• Properties of $Q\bar{Q}$ mesons in non-relativistic QCD formalism
• Revealing the structure of light pseudoscalar mesons at the Electron-Ion Collider
• Bound state approach to the QCD coupling at low energy scales
• QCD coupling below 1 GeV from quarkonium spectrum
• Generalizing the Noether theorem for Hopf-algebra spacetime symmetries
• Towards understanding broad degeneracy in non-strange mesons
• Experimental indication on chiral symmetry restoration in meson spectrum
• Regge-like relation and a universal description of heavy-light systems
• Structure of the meson Regge trajectories

Cited by in corpus (10)

• Regge trajectories for the heavy-light diquarks
• Regge trajectory relations for the universal description of the heavy-light systems: diquarks, mesons, baryons and tetraquarks
• Regge trajectories for the triply heavy bottom-charm baryons in the diquark picture
• Regge trajectories for the light diquarks
• Regge trajectory relation for the universal description of the heavy-heavy systems: diquarks, mesons, baryons and tetraquarks
• $\lambda$ and $\rho$ Regge trajectories for hidden bottom and charm tetraquarks $(Qq)(\bar{Q}{\bar{q}}^{\prime })$
• Regge trajectories for the triply heavy triquarks
• $\lambda$ and $\rho$ Regge trajectories for bottom-charm tetraquarks $(bq)(\bar{c}{\bar{q}}^{\prime })$ and $(cq)(\bar{b}{\bar{q}}^{\prime })$
• $\lambda$ and $\rho$ Regge trajectories for the pentaquark $P_{cc\bar{c}bb}$ in the diquark-triquark picture
• Vector mesons from a holographic QCD model in $f(R)$-dilaton gravity