Revisiting the pion Regge trajectories

Abstract

We propose a model-independent ansatz M = βx (x + c0) ν + c1 (x = l, nr) and then use it to fit the orbital and radial pion Regge trajectories without the preset values. It is shown that nonzero c1 is reasonable and acceptable. Nonzero c1 gives an explanation for the nonlinearity of the pion Regge trajectories in the usually employed (M 2 , x) plane. As mR or c1 is chosen appropriately, both the orbital and radial pion Regge trajectories are linear in the ((M − mR) 2 , x) plane whether the π 0 is included or not on the Regge trajectories. The fitted pion Regge trajectories suggest 0.45 ≤ ν ≤ 0.5, which indicates the confining potential r a with 9/11≤a ≤ 1. Moreover, it is illustrated in appendix B that mR can be nonzero for the light mesons and the fitted Regge trajectories are also linear when they are plotted in the ((M − mR) 2 , x) plane. 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 − mR) 2 , x) plane based on the potential models and the string models.

Revisiting the assignment of $$1^{3}D_{1}$$ meson nonet

“…Regge theory originated from the analysis of scattering amplitudes in complex angular momentum space in 1959 [17], and it is applied to the study of high energy particles physics. Regge theory involves almost all aspects of strong interactions, including hadron spectrum, the forces of particles, and the high energy behavior of scattering amplitudes [18][19][20][21][22][23][24][25][26][27].In Regge theory, the pole of split wave amplitude in the plane of the complex angular momentum is called Regge pole, and the curve depended by it moving in the plane when energy changes is called Regge trajectory. The plots of Regge trajectories of hadrons in the (J, M 2 ) plane are usually called Chew-Frautschi plots (where J and M are respectively the total spins and the masses of the hadrons).…”