The stability and the lifetime of the scalar boson star.

In this paper, we introduce the formalism to examine the impact of the dark scalar sector to the conformal and the electroweak symmetries breaking in the sense of formation of the scalar boson star (BS). The BS is presented by the local scalar field containing the Higgs boson field and the scalar dilaton field in the conformal field theory. We study in detail the modification of the Higgs quartic coupling away from its Standard Model (SM) value within the influence of the dark sector. We show that the repulsive self-interactions and the flatness degree in the dark scalar sector can prevent an instability and the destruction of the BS. We have estimated the rate of the deviation from the SM with production of leptonic pairs due to decays of dilatons and dark photons emerged because of the BS instability. The lifetime, the maximal mass and the density of the BS, the average minimal distance between the stars are estimated. The effects of new physics should be visible at the HL-LHC, FCC-hh accompanied by the current LHC and the cosmological data. [ABSTRACT FROM AUTHOR]