Constant in Regge trajectory

Question

The Regge trajectory in QCD is given by

$$m=\sqrt{\frac{J}{\alpha}-\alpha_0},$$

where $m$ is the mass and $J$ is the angular momentum of the hadrons, $\alpha=(4\pi\sigma)^{-1}$ is the inverse QCD string coupling and $\alpha_0$ is a constant.

Is the theoretical origin and an analytical expression for $\alpha_0$ known, or is it just an experimentally obtained input parameter?

Answer 1

I found the answer to my question in this publication: http://arxiv.org/pdf/hep-ph/0309075v2.pdf

The mass formula is given by

\begin{equation} m = \sqrt{\frac{2m_1m_2}{\alpha}J+(m_1^2 + m_2^2)}, \end{equation}

where $m_1$ and $m_2$ are the masses of the partons, $\alpha$ is the fine structure constant and $J$ is the angular momentum of the hadron.