Conformal Extensions of the Standard Model with Veltman Conditions

TL;DR

The paper addresses the naturalness problem by proposing Perturbative Natural Conformal (PNC) theories that combine classical conformality with Veltman-type cancellations of quadratic divergences via renormalisation-group analysis. By applying Coleman–Weinberg dynamics along renormalisation-scale flat directions and enforcing one-loop Veltman conditions, the authors derive highly constrained parameter spaces and make concrete Higgs-sector predictions across several SM extensions. Among the models studied, a minimal scenario with a real scalar and a Weyl fermion yields a Higgs mass compatible with the observed value ($m_h \\approx 126$ GeV) and predicts a heavy scalar around $m_S \\approx 541$ GeV, illustrating the potential of PNC to guide realistic extensions of the SM with fundamental scalars. Overall, the work demonstrates that PNC can yield highly predictive, testable spectra and offers a framework to construct natural extensions that are falsifiable at collider experiments.

Abstract

Using the renormalisation group framework we classify different extensions of the standard model according to their degree of naturality. A new relevant class of perturbative models involving elementary scalars is the one in which the theory simultaneously satisfies the Veltman conditions and is conformal at the classical level. We term these extensions perturbative natural conformal (PNC) theories. We show that PNC models are very constrained and thus highly predictive. Among the several PNC examples that we exhibit, we discover a remarkably simple PNC extension of the standard model in which the Higgs is predicted to have the experimental value of the mass equal to 126 GeV. This model also predicts the existence of one more standard model singlet scalar boson with a mass of 541 GeV and the Higgs self-coupling to emerge radiatively. We study several other PNC examples that generally predict a somewhat smaller mass of the Higgs to the perturbative order we have investigated them. Our results can be a useful guide when building extensions of the standard model featuring fundamental scalars.