2024/11/12 by André LeClair, LeClair, André
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2411.07476
openalex publication_date 2024/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider 2 coupled Higgs doublets which transform in the usual way under SU(2). By constructing marginal operators which satisfy an operator product expansion based on the SU(2) Lie algebra, we can obtain a rich pattern of renormalization group (RG) flows which includes lines of fixed points and more interestingly, cyclic RG flows which are unavoidable in this model. The hamiltonian is pseudo-hermitian, H^† = \cal K H \cal K^† with \cal K unitary satisfying \cal K2 =1, thus the model is non-unitary. The hamiltonian still has real eigenvalues, but the non-unitarity is manifested in negative norm states. Based on a generalized optical theorem for pseudo-hermitian hamiltonians, we show that our model is in fact unitary below the threshold for particle/anti-particle pair production. It is thus unitary in the non-relativistic limit, which opens up some potential applications to condensed matter physics. We argue that our model breaks \cal C\cal P symmetry. Upon spontaneous symmetry breaking, the Higgs-like fields have an infinite number of vacuum expectation values vn which satisfy ``Russian Doll" scaling vn ∼ e2 n λ where n=1,2,3,… and λ is the period of one RG cycle which is an RG invariant. We speculate that this Russian Doll RG flow can perhaps resolve the so-called hierarchy problem and may shed light on the origin of ``families" in the Standard Model of particle physics. If after spontaneous symmetry breaking of the SU(2) to U(1) a cyclic RG with period λ is operative up to the electro-weak scale, then this admits 3 RG cycles, i.e. 3 families of quarks and leptons. The strongest constraints on the RG period λ comes from the phenomenological Koide formula, wherein λ≈ π/2.