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arXiv · 1701.06315

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

Gabriele Veneziano·Shimon Yankielowicz·Enrico Onofri
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Abstract

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 Pi-Pi 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 (including logarithmic corrections) behavior 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 alpha_0-beta-gamma 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.

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Gabriele Veneziano, Shimon Yankielowicz, Enrico Onofri. 2017-01-30. A model for pion-pion scattering in large-N QCD. https://doi.org/10.1007/jhep04(2017)151

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