On the N-pion extension of the Lovelace-Shapiro model

Abstract

We reconsider a modification of the N-point amplitude of the Neveu-Schwarz (NS) model in which the tachyon becomes a pion by shifting its mass to zero and keeping the super-projective invariance of the integrand of the amplitude. For the scattering of four particles it reduces to the amplitude written by Lovelace and Shapiro that has Adler zeroes. We confirm that also the N-pion amplitude has Adler zeroes and show that it reduces to that of the non-linear $\sigma$-model for ${\alpha }^{\prime }\to 0$ keeping $F_{\pi }$ fixed. The four- and six-point flavour-ordered amplitudes satisfy tree-level unitarity since they can be derived from the correspondent amplitudes of the NS model in ten dimensions by suitably choosing the components of the momenta of the external mesons in the six extra dimensions. Negative norm states (ghosts) are shown to appear instead in higher-point amplitudes. We also discuss several amplitudes involving different external mesons.

21 pages plus appendices and 1 figure

References in corpus (4)

• The Pomeron and Gauge/String Duality
• A holographic model of deconfinement and chiral symmetry restoration
• Multi-Gluon Scattering in Open Superstring Theory
• Theta dependence in Holographic QCD

Cited by in corpus (9)

• Carving out the Space of Open-String S-matrix
• Bootstrapping Pions at Large $N$
• Cornering Large-$N_c$ QCD with Positivity Bounds
• Positivity and Geometric Function Theory Constraints on Pion Scattering
• The Stringy S-matrix Bootstrap: Maximal Spin and Superpolynomial Softness
• On the unitarity and low energy expansion of the Coon amplitude
• Selection rules for the S-Matrix bootstrap
• Partonic behavior of string scattering amplitudes from holographic QCD models
• High-Energy Fixed-Angle Meson Scattering and the Constituent Counting Rule in Holographic QCD