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

• Published in: The journal of high energy physics Vol. 2017; no. 4; pp. 1 - 19
• Main Authors: Veneziano, G., Yankielowicz, S., Onofri, E.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2017; Springer Nature B.V; Springer; SpringerOpen
• Subjects: 1/N Expansion; Bosonic Strings; Classical and Quantum Gravitation; Elementary Particles; High energy physics; High Energy Physics - Theory; Physics; Physics and Astronomy; Pions; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering; Scattering Amplitudes; String Theory; Scattering Amplitudes; 1/N Expansion; Bosonic Strings; expansion 1/N; toy model; pi pi: scattering; quantum chromodynamics: perturbation theory
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP04(2017)151

A bstract 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.