Abstract
In this work, we classify all the possible local four-point couplings relevant for tree-level flat space 2 → 2 scattering of external massive particles of spin one and spin two which do not grow faster than s2 at large s and fixed t. This kinematic constraint on local growth of tree-level S-matrices is known as Classical Regge Growth criteria or CRG [1]. We first construct the spin one and spin two tree-level contact S-matrices as modules of polarisation tensors and momenta over the ring of polynomials generated by Mandelstam invariants. We then consider a general scattering process where the external scattering particles are of different masses but of same spin and constrain this space to obtain a finite number of CRG allowed local Lagrangians. Our concrete results are primarily for D ≥ 8 but the process outlined is easily generalised to lower dimensions to include low dimensional parity violating structures. The space of CRG allowed structures reduces when we specialise to identical scattering and restrict to parity even couplings in D = 4. We show that tree-level scattering amplitudes involving exchange diagrams and contact terms in de Rham-Gabadadze-Tolley massive gravity (dRGT) violate CRG unless the parameters of the theory take special values. The CRG allowed S-matrices, in the context of large N conformal field theories (CFTs), can also be interpreted as bulk AdS counterterms consistent with Chaos bound. Our classified structures therefore can be thought of as ambiguities arising in the context of conformal field theory inversion formula for four point functions of unconserved spin one and spin two operators in large N CFTs.
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Acknowledgments
We would like to thank Shiraz Minwalla for collaboration at various stages of the project and very useful discussions throught the duration of the project. We would also like to thank Giulia Isabella and Shiraz Minwalla for very useful comments on the manuscript. This work of SDC is supported by the NSF Grant No. PHY2014195 and Kadanoff fellowship at the University of Chicago. The work of VK and AR was supported by the Infosys Endowment for the study of the Quantum Structure of Spacetime and by the J C Bose Fellowship JCB/2019/000052. The work of SK was supported in part by an ISF, center for excellence grant (grant number 2289/18), Simons Foundation grant 994296, Koshland Fellowship and TIFR for hospitality. VK and AR would also like to acknowledge their debt to the people of India for their steady support to the study of the basic sciences.
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Chowdhury, S.D., Kumar, V., Kundu, S. et al. Regge constraints on local four-point scattering amplitudes of massive particles with spin. J. High Energ. Phys. 2024, 123 (2024). https://doi.org/10.1007/JHEP05(2024)123
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DOI: https://doi.org/10.1007/JHEP05(2024)123