2023/09/18 by Seyed M. F. Khaki, Khaki, Seyed
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Physics (physics.gen-ph) #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.2309.09762
openalex publication_date 2023/09/18 · openalex created_date 2023/09/20 · openalex updated_date 2026/07/28
As the Higgs field is a weak isospin doublet of the SU(2) symmetry, the Standard Model requires any symmetry solution to the Higgs hierarchy problem to be SU(2) invariant, a constraint on the type of the symmetry. However, the hierarchy problem is about the size. The size of SU(2) for the Higgs boson can be calculated by |SU2(ℓ)|=ℓ3-ℓ, having the Higgs mass MH=1/ℓH≈125 GeV. To find the origin of the relative smallness of the Higgs mass in Planck units, alternatively, we search for the origin of such a large order assuming that it stems from an unknown field theory X beyond the Standard Model. Accordingly, this order, which corresponds to the quantum of the Higgs field, should determine the order of quantum/core of X symmetry, its automorphism group. We calculate |Aut(X)|≈8.2× 1053, close to the order of the Monster sporadic group, |\mathbb M|≈ 8.1× 1053, the automorphism group of the Monster CFT, which we therefore conjecture to be X. To examine this conjecture, we calculate the mass of a scalar boson whose SU(2) order is determined by |\mathbb M|, observing a 125.4 GeV boson mass and a 245.7 GeV VEV. The Monster CFT does not have any spin-1 operators and Kac-Moody symmetry. Therefore, based on the CFT/(A)dS correspondences, it only describes pure gravity without the gauge fields. In search of a gauge theory candidate, we promote SU(2) (double cover of SO(3)), to SO(d), and show that the same \mathbb M-symmetric vacuum configuration reaches the Planck mass of quantum gravity precisely at d=32 (with 99% accuracy). Then, the spin-1 boson mass of the eligible gauge candidates, SO(32) and E8× E8, is calculated to be 80.9 GeV. Further, several pieces of evidence are provided supporting the conjecture.