Revisiting the pion Regge trajectories

TL;DR

This paper introduces a model-independent ansatz for pion Regge trajectories, demonstrating that nonzero intercepts explain nonlinearity and that appropriate parameter choices yield linear trajectories, providing insights into the confining potential.

Contribution

It proposes a new flexible ansatz for fitting pion Regge trajectories without preset parameters, revealing the role of nonzero intercepts and potential implications for confinement models.

Findings

Nonzero intercepts explain trajectory nonlinearity.

Linear trajectories achieved with appropriate parameters.

Fitted trajectories suggest a confining potential with power between 9/11 and 1.

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 $0.45\le\nu\le0.5$, which indicates the confining potential $r^a$ with $9/11{\le}a\le1$. 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.