On the positivity of Coon amplitude in D=4

Abstract

The Coon amplitude is the unique solution to duality constraints with logarithmic Regge trajectories. A striking feature of this solution is that it interpolates between the Veneziano amplitude and a scalar particle amplitude. However, an analytic proof of unitarity of the amplitude is not yet known. In this short note, we explicitly compute the partial wave coefficients on the leading Regge trajectory in D=4. We find that these coefficients always remain positive, even though their magnitude decreases with spin. Since the coefficients on the subleading trajectories are observed to be larger than those on the leading ones, our result indicates the positivity of the full Coon amplitude in D=4.

12 pages including appendices. Comments and suggestions are welcome

References in corpus (5)

• On Unitarity of Tree-Level String Amplitudes
• On the unitarity and low energy expansion of the Coon amplitude
• UV-Complete Gravity Amplitudes and the Triple Product
• Accumulation-Point Amplitudes in String Theory
• Positivity of the Veneziano Amplitude in $D=4$

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• Cutting the Coon Amplitude
• On (Scalar QED) Gravitational Positivity Bounds
• On the positivity of the hypergeometric Veneziano amplitude
• Uniqueness Criteria for the Virasoro-Shapiro Amplitude
• Positivity of the Hypergeometric Coon Amplitude
• Coon unitarity via partial waves or: how I learned to stop worrying and love the harmonic numbers
• Worldsheet for Generalized Veneziano Amplitudes
• A glimpse into the Ultrametric spectrum