The addition of gravitons to the standard model of particle physics does not introduce new kinds of infinities per se. However, it is worth noting that the combination of quantum field theory, which describes particle interactions, and general relativity, which governs gravity, leads to theoretical challenges involving infinities.
In the context of quantum field theory, interactions between particles are described by mathematical entities called Feynman diagrams. These diagrams involve virtual particles, including virtual gravitons, which represent the exchange of forces between particles. When calculating the probability amplitudes of these processes, infinities may arise in certain calculations.
These infinities are known as divergences and occur due to the intrinsic properties of the mathematical framework used in these calculations. In the standard model, these divergences are encountered in processes involving particles such as electrons, photons, and the weak force carriers (W and Z bosons). However, the standard model does not include gravity, so gravitons are not present in its formulation.
When attempts are made to combine gravity with the standard model, such as in theories of quantum gravity, the divergences become more complicated. In particular, combining general relativity and quantum mechanics leads to difficulties in perturbative calculations, resulting in infinities that are harder to manage than in the standard model alone.
To address these infinities, various techniques have been developed, such as renormalization, which allows physicists to remove the divergences and obtain meaningful results. However, the precise treatment of gravitons within the context of a complete theory of quantum gravity remains an active area of research and is one of the major challenges in theoretical physics today.