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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.D. Coon, Uniqueness of the veneziano representation, Phys. Lett. B 29 (1969) 669 [INSPIRE].
M. Baker and D.D. Coon, Dual resonance theory with nonlinear trajectories, Phys. Rev. D 2 (1970) 2349 [INSPIRE].
D.D. Coon, U.P. Sukhatme and J. Tran Thanh Van, Duality and proton-proton scattering at all angles, Phys. Lett. B 45 (1973) 287.
I. Ridkokasha, Confronting Dual Models of the Strong Interaction, Mod. Phys. Lett. A 36 (2021) 2150031 [arXiv:2008.11418] [INSPIRE].
F. Figueroa and P. Tourkine, Unitarity and Low Energy Expansion of the Coon Amplitude, Phys. Rev. Lett. 129 (2022) 121602 [arXiv:2201.12331] [INSPIRE].
N. Geiser and L.W. Lindwasser, Properties of infinite product amplitudes: Veneziano, Virasoro, and Coon, arXiv:2207.08855 [INSPIRE].
J. Maldacena and G.N. Remmen, Accumulation-point amplitudes in string theory, JHEP 08 (2022) 152 [arXiv:2207.06426] [INSPIRE].
S. Caron-Huot, Z. Komargodski, A. Sever and A. Zhiboedov, Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude, JHEP 10 (2017) 026 [arXiv:1607.04253] [INSPIRE].
Z. Bern, D. Kosmopoulos and A. Zhiboedov, Gravitational effective field theory islands, low-spin dominance, and the four-graviton amplitude, J. Phys. A 54 (2021) 344002 [arXiv:2103.12728] [INSPIRE].
Y.-t. Huang and G.N. Remmen, UV-complete gravity amplitudes and the triple product, Phys. Rev. D 106 (2022) L021902 [arXiv:2203.00696] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, The EFT-Hedron, JHEP 05 (2021) 259 [arXiv:2012.15849] [INSPIRE].
L.-Y. Chiang, Y.-t. Huang, W. Li, L. Rodina and H.-C. Weng, (Non)-projective bounds on gravitational EFT, arXiv:2201.07177 [INSPIRE].
M. Chaichian, J.F. Gomes and P. Kulish, Operator formalism of q deformed dual string model, Phys. Lett. B 311 (1993) 93 [hep-th/9211029] [INSPIRE].
L.L. Jenkovszky, M. Kibler and A. Mishchenko, Two parametric quantum deformed dual amplitude, Mod. Phys. Lett. A 10 (1995) 51 [hep-th/9407071] [INSPIRE].
D.D. Coon and S. Yu, Dual Four Point Functions with No Negative Residues, Phys. Rev. D 10 (1974) 3780 [INSPIRE].
D.B. Fairlie and J. Nuyts, A fresh look at generalized Veneziano amplitudes, Nucl. Phys. B 433 (1995) 26 [hep-th/9406043] [INSPIRE].
P. Maity, Positivity of the Veneziano amplitude in D = 4, JHEP 04 (2022) 064 [arXiv:2110.01578] [INSPIRE].
N. Arkani-Hamed, L. Eberhardt, Y.-t. Huang and S. Mizera, On unitarity of tree-level string amplitudes, JHEP 02 (2022) 197 [arXiv:2201.11575] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2208.02735
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Chakravarty, J., Maity, P. & Mishra, A. On the positivity of Coon amplitude in D = 4. J. High Energ. Phys. 2022, 43 (2022). https://doi.org/10.1007/JHEP10(2022)043
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2022)043