Abstract
We prove a set of sum rules needed for KK-graviton pair production from matter in orbifolded extra-dimensional models. The sum rules can be found in full generality by considering the properties of solutions to the Sturm-Liouville problem, which describes the wave functions and the masses of the KK-gravitons in four dimensions. They ensure cancellations in the amplitudes of the processes mentioned above which considerably reduce their growth with s in the high-energy limit. This protects extra-dimensional theories from the low-scale unitarity problems that plague other theories with massive spin-2 particles. We argue that such relations are valid for a broader category of models thus generalizing our previous results that were limited to the large μ limit of the Randall-Sundrum model.
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Acknowledgments
A.d.G. thanks Alejandro Pérez Rodríguez for useful discussions and especially thanks Carlos A. Argüelles and the group of Palfrey House for their hospitality and the stimulating working environment during which a core part of this work was realised. The work of A.d.G. is supported by the European Union’s Horizon 2020 Marie Skłodowska-Curie grant agreement No 860881-HIDDeN. This work was also available with preprint IFT-UAM/CSIC-23-139.
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de Giorgi, A., Vogl, S. Gravity-matter sum rules in models with a single extra-dimension. J. High Energ. Phys. 2024, 315 (2024). https://doi.org/10.1007/JHEP05(2024)315
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DOI: https://doi.org/10.1007/JHEP05(2024)315