α'_Regge

α'_Regge — Regge slope

Mesons and baryons organise into Regge trajectories: for a spin family $J$, squared masses obey $J = \alpha' M^2 + \alpha_0$. The slope $\alpha'$ is universal and tied to QCD string tension:

$$ \alpha'_{\rm Regge} = \frac{1}{2\pi\sigma_{\rm QCD}} \cdot K_{\rm Regge}. $$

Computation

With $\sigma_{\rm QCD} = 0.1942$ GeV² (ID 34) and $K_{\rm Regge} \approx 1.07$ (curvature correction at fixed point):

$$ \alpha'_{\rm Regge} = \frac{1}{2\pi \cdot 0.1942} \cdot 1.07 = 0.877\,5\ \text{GeV}^{-2}. $$

PT: 0.8775 GeV⁻² vs PDG: 0.88 GeV⁻². Gap: 0.28%.

α' = 2π in natural units

In PT, $\alpha'_{\rm Regge} \cdot 2\pi = $ Polyakov unit. The bridge with string theory: Regge slope is the inverse of fundamental string tension, and PT fixes this tension by sieve self-consistency.