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.

arXiv comment14 pages, 9 figures, 4 tables. V3: Nucl. Phys. B

References in corpus (36)

• The hidden-charm pentaquark and tetraquark states
• A review of the open charm and open bottom systems
• Systematics of q anti-q states in the (n,M^2) and (J,M^2) planes
• Mass spectra and Regge trajectories of light mesons in the relativistic quark model
• Light Meson Spectroscopy
• The pion: an enigma within the Standard 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
• Effective Functional Form of Regge Trajectories
• Charmed Baryonium
• Systematics of radial and angular-momentum Regge trajectories of light non-strange q\bar{q}-states
• 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
• Universal Effective Hadron Dynamics from Superconformal Algebra
• QCD coupling below 1 GeV from quarkonium spectrum
• Universal description of radially excited heavy and light vector mesons
• Towards understanding broad degeneracy in non-strange mesons
• Generalizing the Noether theorem for Hopf-algebra spacetime symmetries
• Properties of Regge Trajectories
• The 2^-+ assignment for the X(3872)
• Experimental indication on chiral symmetry restoration in meson spectrum
• Hadronic Regge Trajectories: Problems and Approaches
• Hadronic Spectra from Deformed AdS Backgrounds
• Excited mesons, baryons, glueballs and tetraquarks: Predictions of the Holography Inspired Stringy Hadron model
• Regge behaviors in orbitally excited spectroscopy of charmed and bottom baryons
• Observations On the Potential Confinement of a Light Fermion
• Concavity of the meson Regge trajectories
• Regge-like relation and a universal description of heavy-light systems
• Bethe--Salpeter equation in QCD
• Sum rules, Regge trajectories, and relativistic quark models
• Note on universal description of heavy and light mesons
• Lattice QCD investigation of the structure of the $a_0(980)$ meson
• Structure of the meson Regge trajectories
• Regge trajectories and quarkonium spectrum from a first principle Salpeter equation
• Relativistic Three-Dimensional Two- and Three-Body Equations on a Null Plane and Applications to Meson and Baryon Regge Trtajectories

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