Criticality and inflation of the gauged B − L model

aam slamet rusydiana, [et. all];

We consider the multiple point principle (MPP) and the inflation of the gauged B − L (baryon number minus lepton number) extension of the StandardModel (SM) with a classical conformality. We examine whether the scalar couplings and their beta functions can become simultaneously zero at MPP := 1017 GeV by using two-loop renormalization group equations (RGEs).We find that we can actually realize such a situation and that the parameters of the model are uniquely determined by theMPP. However, as discussed by S. Iso and Y. Orikasa [Prog. Theor. Exp. Phys. 2013, 023B08 (2013) [arXiv:1210.2848 [hep-ph]]], if we want to realize electroweak symmetry breaking by radiative B − L symmetry breaking, the self-coupling λ of a newly introduced SM singlet complex scalar  must have a non-zero value at MPP, which means the breaking
of the MPP. We find that O(100) GeV electroweak symmetry breaking can be achieved even if this breaking is very small; λ  MPP 
≤ 10−10. Within this situation, the mass of the B − L gauge boson is predicted to be MB−L = 2 √ 2 × √ λ(vh)/0.10 × vh  696 GeV, where λ is the Higgs self-coupling and vh is the Higgs expectation value. This is a remarkable prediction of the (slightly broken) MPP. Furthermore, such a small λ opens a new possibility:  plays the role of the inflaton [28]. Another purpose of this paper is to investigate the λ4 inflation scenario with non-minimal gravitational coupling ξ2R based on two-loop RGEs.