Is the Standard Model saved asymptotically by conformal symmetry?

TL;DR

The paper suggests that the Standard Model may be asymptotically safe due to conformal symmetry at the Planck scale, with specific mass relations and RG flow indicating a special conformal fixed point.

Contribution

It proposes a novel scenario where the Standard Model's parameters and RG evolution imply an underlying conformal symmetry at high energies, potentially resolving hierarchy and Landau pole issues.

Findings

Mass relations consistent with conformal symmetry near the Planck scale

RG flow leads to a stable fixed point at the Planck scale

Higgs as a Goldstone boson of broken conformal symmetry

Abstract

It is pointed out that the top-quark and Higgs masses and the Higgs VEV satisfy with great accuracy the relations 4m_H^2=2m_T^2=v^2, which are very special and reminiscent of analogous ones at Argyres - Douglas points with enhanced conformal symmetry. Furthermore, the RG evolution of the corresponding Higgs self-interaction and Yukawa couplings \lambda(0)=1/8 and y(0)=1 leads to the free-field stable point \lambda(M_Pl)= \dot \lambda(M_Pl)=0 in the pure scalar sector at the Planck scale, also suggesting enhanced conformal symmetry. Thus, it is conceivable that the Standard Model is the low-energy limit of a distinct special theory with (super?) conformal symmetry at the Planck scale. In the context of such a "scenario" one may further speculate that the Higgs particle is the Goldstone boson of (partly) spontaneously broken conformal symmetry. This would simultaneously resolve the hierarchy and Landau pole problems in the scalar sector and would provide a nearly flat potential with two almost degenerate minima at the electroweak and Planck scales.