TY - JOUR

T1 - A model for pion-pion scattering in large-N QCD

AU - Veneziano, G.

AU - Yankielowicz, S.

AU - Onofri, E.

N1 - Publisher Copyright:
© 2017, The Author(s).

PY - 2017/4/1

Y1 - 2017/4/1

N2 - 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.

AB - 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.

KW - 1/N Expansion

KW - Bosonic Strings

KW - Scattering Amplitudes

UR - http://www.scopus.com/inward/record.url?scp=85018320358&partnerID=8YFLogxK

U2 - 10.1007/JHEP04(2017)151

DO - 10.1007/JHEP04(2017)151

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AN - SCOPUS:85018320358

SN - 1126-6708

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 4

M1 - 151

ER -