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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Z. Komargodski, The S-matrix Bootstrap program revived, https://www.youtube.com/watch?v=JZGLD7emxp4.
G. Veneziano, Construction of a crossing-symmetric, Regge behaved amplitude for linearly rising trajectories, Nuovo Cim. A 57 (1968) 190 [INSPIRE].
R. Dolen, D. Horn and C. Schmid, Finite energy sum rules and their application to pi N charge exchange, Phys. Rev. 166 (1968) 1768 [INSPIRE].
M. B. Green, J. H. Schwarz and E. Witten, Superstring Theory. Vol. 1: Introduction, Cambridge University Press, Cambridge, U.K. (2012) [DOI].
H. B. Meyer and M. J. Teper, Glueball Regge trajectories and the Pomeron: A Lattice study, Phys. Lett. B 605 (2005) 344 [hep-ph/0409183] [INSPIRE].
X. O. Camanho, J. D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [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].
M. F. Paulos, J. Penedones, J. Toledo, B. C. van Rees and P. Vieira, The S-matrix bootstrap. Part I: QFT in AdS, JHEP 11 (2017) 133 [arXiv:1607.06109] [INSPIRE].
M. Correia, A. Sever and A. Zhiboedov, An analytical toolkit for the S-matrix bootstrap, JHEP 03 (2021) 013 [arXiv:2006.08221] [INSPIRE].
S. Mizera, Crossing symmetry in the planar limit, Phys. Rev. D 104 (2021) 045003 [arXiv:2104.12776] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, The EFT-Hedron, JHEP 05 (2021) 259 [arXiv:2012.15849] [INSPIRE].
D. D. Coon, Uniqueness of the veneziano representation, Phys. Lett. B 29 (1969) 669 [INSPIRE].
D. B. Fairlie and J. Nuyts, A fresh look at generalized Veneziano amplitudes, Nucl. Phys. B 433 (1995) 26 [hep-th/9406043] [INSPIRE].
J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 2nd edition, Cambridge University Press, Cambridge, U.K. (2017) [DOI].
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: 2110.01578
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
Maity, P. Positivity of the Veneziano amplitude in D = 4. J. High Energ. Phys. 2022, 64 (2022). https://doi.org/10.1007/JHEP04(2022)064
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2022)064