Effective interaction of vector bosons of the SM expansion of the Chern-Simons type with fermions of the Standard Model

Abstract

We consider the vector extension of the Standard Model (SM) with Chern-Simons (CS) type interaction. This extension contains a new massive vector boson X_μ (Chern-Simons boson). The minimal gauge-invariant Lagrangian of the interaction with SM particles has the form of 6-dimension operators

L_1 = C_Y / Λ_Y^2 * X_μ (D_ν H)^† H B_λρ * ε^μνλρ + h.c.,

L_2 = C_SU(2) / Λ_SU(2)^2 * X_μ (D_ν H)^† F_λρ H * ε^μνλρ + h.c.

After electroweak symmetry breaking, these Lagrangians generate (among other terms of higher dimensions) Lagrangians of three fields interactions of the CS vector boson with vector fields of the SM and the Higgs boson. In unitary gauge, they have forms

L_CS^(4) = c_z ε^μνλρ X_μ Z_ν ∂_λ Z_ρ + c_γ ε^μνλρ X_μ Z_ν ∂_λ A_ρ + { c_w ε^μνλρ X_μ W_ν^- ∂_λ W_ρ^+ + h.c. },

L_CS^(5) = c_γh ε^μνλρ X_μ (∂_ν h / v) ∂_λ A_ρ + c_zh ε^μνλρ X_μ (∂_ν h / v) ∂_λ Z_ρ.

We consider the effective loop interaction of a new vector boson with fermions of the SM and its renormalizability in an arbitrary gauge. Our analysis shows that loop divergences cannot be eliminated in the effective interaction between CS bosons and fermions of the same flavor, whereas the effective loop interaction with fermions of different flavors remains well-defined. The interaction terms between the CS boson and fermions of the same flavor, characterised by divergent prefactors, have been identified. Since the initial interaction of the CS bosons with SM fields is given by dimension-6 operators, we conclude that after the electroweak symmetry breaking the interaction of the CS boson with fermions of the same flavor should be considered within the framework of the effective field theory approach

L_Xff^int = f_bar γ^μ (α_f + β_f γ^5) f X_μ + (m_f / v^2) f_bar σ^μν (γ_f + δ_f γ^5) f X_μν + L'_Xff.

where dimensionless parameters α_f, β_f, γ_f, δ_f should be considered as new parameters of the effective theory and L'_Xff is a well-defined Lagrangian of interaction. The obtained results will help identify the dominant CS-boson production and decay channels, thereby allowing us to determine the sensitivity region of intensity-frontier experiments in the search for the CS boson.