Positivity of the Veneziano Amplitude in $D=4$

Abstract

The Veneziano amplitude was put forward as a solution to the axioms of the S-matrix bootstrap. However, unitarity, reflected in the positivity of the coefficients in the Gegenbauer expansion of the amplitude is not obvious. In this note we compute the generating function of these coefficients in terms of the Appell hypergeometric function. We use this to read off an exact form of this coefficient on the leading Regge trajectory in $D=4$. We find that it decays with the spin but always remains positive. Since for large spin these coefficients are expected to be smaller than those on the subleading trajectories, our result indicates the positivity of the full Veneziano amplitude in $D=4$.

References in corpus (3)

• The EFT-Hedron
• Crossing Symmetry in the Planar Limit
• On Unitarity of Tree-Level String Amplitudes

Cited by in corpus (11)

• On Unitarity of Tree-Level String Amplitudes
• On the unitarity and low energy expansion of the Coon amplitude
• Where is M-theory in the space of scattering amplitudes?
• Properties of infinite product amplitudes: Veneziano, Virasoro, and Coon
• On the positivity of Coon amplitude in D=4
• On the positivity of the hypergeometric Veneziano amplitude
• Positivity of the Hypergeometric Coon Amplitude
• Coon unitarity via partial waves or: how I learned to stop worrying and love the harmonic numbers
• On-shell Supersymmetry and higher-spin amplitudes
• Adelic Amplitudes and Intricacies of Infinite Products
• Worldsheet for Generalized Veneziano Amplitudes