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

G. Veneziano*, S. Yankielowicz, E. Onofri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 α0< 1, and an effective bending of the trajectories in the negative-t region producing a fixed branch point at J = 0 for t < t0< 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)−γF (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 α0-β-γ parameter space, which nicely includes a physically interesting region around α0 = 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.

Original languageEnglish
Article number151
JournalJournal of High Energy Physics
Issue number4
StatePublished - 1 Apr 2017


  • 1/N Expansion
  • Bosonic Strings
  • Scattering Amplitudes


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