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

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 ${\alpha }_0<1$, 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: $A(s,t)s^{-\beta }\log (s{)}^{-\gamma }F(\theta )$. 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 ${\alpha }_0=0.5$, $\beta =2$ and $\gamma =3$. The full consistency of the model would require an extension to multi-pion processes, a program we do not undertake in this paper.

17 pages, 6 figures

References in corpus (4)

• The Pomeron and Gauge/String Duality
• Corrections to Nambu-Goto energy levels from the effective string action
• Closed flux tubes and their string description in D=3+1 SU(N) gauge theories
• The large-N Yang-Mills S-matrix is ultraviolet finite, but the large-N QCD S-matrix is only renormalizable

Cited by in corpus (11)

• Bootstrapping Pions at Large $N$
• The Stringy S-matrix Bootstrap: Maximal Spin and Superpolynomial Softness
• Selection rules for the S-Matrix bootstrap
• On Fine Structure of Strings: The Universal Correction to the Veneziano Amplitude
• On the N-pion extension of the Lovelace-Shapiro model
• The decay width of stringy hadrons
• Partonic behavior of string scattering amplitudes from holographic QCD models
• Unitarity constraint on the Kähler curvature
• Hadronic Strings -- A Revisit in the Shade of Moonshine
• High-Energy Fixed-Angle Meson Scattering and the Constituent Counting Rule in Holographic QCD
• High-Energy Pion Scattering in Holographic QCD: A Comparison with Experimental Data