2 Gravitons minimally coupled to Standard Model

Author

Tran Quang Loc

• Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge
• loctranq@…

Description of the model & references

Gravitons minimally coupled to Standard Model (SM) is described by the theory of SM with weak gravitational perturbations of Minkowski space, in which graviton is suppressed by a factor of two over Planck scale (denoted as kappa).

In this implementation, we start from the generic Lagrangian and expand the metric in linearised theory up to second-order expansion. The bosonic sector is trivially expanded while the spinor sector makes use of newly introduced vielbein fields and torsion-free spin connections to construct the covariant derivative.

At first-order, the model can be used to produce the interactions including 1 graviton minimally coupled to SM, i.e. light-by-light scattering in ​Phys.Rev.Lett. 127 (2021) 9, 091602: Katsuki Aoki, Tran Quang Loc, Toshifumi Noumi, Junsei Tokuda, Is the Standard Model in the Swampland? Consistency Requirements from Gravitational Scattering

At second-order, the model is useful for processes with 2 gravitons minimally coupled to SM vertices.

Model files & extensions

• Main FeynRules file for the 2 gravitons coupled to full SM: ​2Gravitons.fr.
• Example of a Mathematica® notebook loading the model and the parameters: ​2Gravitons.nb.
• A model for fourth-order formalism is being developed.

Validation

At first order, the model has reproduced the results from:

​Phys.Rev.Lett. 127 (2021) 9, 091602: Katsuki Aoki, Tran Quang Loc, Toshifumi Noumi, Junsei Tokuda, Is the Standard Model in the Swampland? Consistency Requirements from Gravitational Scattering

​Phys. Rev. D 103, 125020 (2021): Lasma Alberte, Claudia de Rham, Sumer Jaitly, Andrew J. Tolley, QED positivity bounds

The model has also been cross-checked with Spin 2 simplified model. We found complete agreement.

At second order, the model has been checked with Graviton + Photon -> Graviton + Photon process. Its amplitudes satisfy crossing symmetric properties and find complete agreement to ones generated by manual inputs of Feynman rules.