There are many proposals how to extend the Standard Model, designed to deal with its fundamental inconsistencies. Since no new particles have been detected experimentally so far, the models which add only one more scalar particle and possibly right-chiral neutrinos are favoured. One of them is the Conformal Standard Model, which proposes a coherent solution to the Standard Model drawbacks including the hierarchy problem and a dark matter candidate.
On the other hand there are signs that gravity is asymptotically safe. If there are no intermediate scales between electroweak and Planck scale then the Conformal Standard Model supplemented with asymptotically safe gravity can be valid up to arbitrarily high energies and give a complete description of particle physics phenomena. Moreover asymptotic safety hypothesis restricts the mass of the second scalar particle to 300 +/-28 GeV for negative anomalous dimension of lambda 3, while for positive second scalar particle is decoupled. The masses of heavy neutrinos can also be estimated as 342 +/- 41 GeV. These predictions can be explicitly tested in the nearby future.
Talk based on the article: https://arxiv.org/abs/1810.08461 written in collaboration with Frederic Grabowski and Krzysztof A. Meissner.