A model for pion-pion scattering in large-N QCD

Following up on recent work by Caron-Huot et al. we consider a generalization of the old Lovelace-Shapiro model as a toy model for ππ scattering satisfying (most of) the properties expected to hold in (’t Hooft’s) large-N limit of massless QCD. In particular, the model has asymptotically linear and parallel Regge trajectories at positive t, a positive leading Regge intercept α$_{0}$ < 1, and an effective bending of the trajectories in the negative-t region producing a fixed branch point at J = 0 for t < t$_{0}$ < 0. Fixed (physical) angle scattering can be tuned to match the power-like behavior (including logarithmic corrections) predicted by perturbative QCD: A(s, t) ∼ s$^{−}^{β}$ log(s)$^{−γ}$ F (θ). Tree-level unitarity (i.e. positivity of residues for all values of s and J ) imposes strong constraints on the allowed region in the α$_{0}$-β-γ parameter space, which nicely includes a physically interesting region around α$_{0}$ = 0.5, β = 2 and γ = 3. The full consistency of the model would require an extension to multi-pion processes, a program we do not undertake in this paper.