Z⁰-boson decays in a strong electromagnetic field

Abstract

The probability of Z ⁰-boson decay to a pair of charged fermions in a strong electromagnetic field, Z ⁰ → $\bar f$ f, is calculated. On the basis of a method that employs exact solutions to relativistic wave equations for charged particles, an analytic expression for the partial decay width Γ(ϰ) = Γ(Z ⁰ → $\bar f$ f) is obtained at an arbitrary value of the parameter ϰ = $eM_Z^{ - 3} \sqrt { - (F_{\mu \nu } q^\nu )^2 }$, which characterizes the external-field strength. The total Z ⁰-boson decay width in an intense electromagnetic field, Γ _Z (ϰ), is calculated by summing these results over all known generations of charged leptons and quarks. It is found that, in the region of relatively weak fields (ϰ < 0.06), the field-induced corrections to the standard Z ⁰-boson decay width in a vacuum do not exceed 2%. As ϰ increases, the total decay width Γ _Z (ϰ) develops oscillations against the background of its gradual decrease to the absolute-minimum point. At ϰ_min = 0.445, the total Z ⁰-boson decay width reaches the minimum value of Γ _Z (ϰ_min) = 2.164 GeV, which is smaller than the Z ⁰-boson decay width in a vacuum by more than 10%. In the region of superstrong fields (ϰ > 1), Γ _Z (ϰ) grows monotonically with increasing external-field strength. In the region ϰ > 5, the t-quark-production process Z ⁰ → $\bar t$ t, which is forbidden in the absence of an external field, begins contributing significantly to the total decay width of the Z ⁰ boson.