Properties of infinite product amplitudes: Veneziano, Virasoro, and Coon

Geiser, Nicholas; Lindwasser, Lukas

doi:10.48550/arxiv.2207.08855

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2022

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“…In particular, this mysterious amplitude is the unique solution to duality constraints having an infinity of exchanges with logarithmic trajectories. Recently, it has been brought forward as an interesting case study on its own [4][5][6][7][8] while also serving as a useful reference to the study of accumulation point amplitudes with similar infinite towers of states [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

On the positivity of Coon amplitude in D=4

Chakravarty¹,

Maity²,

Mishra³

2022

Preprint

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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.

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