Leptonic decays of the W boson in a strong electromagnetic field

The probability of W-boson decay into a lepton and a neutrino, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$W^ \pm \to \ell ^ \pm \bar \nu _\ell $$ \end{document}, in a strong electromagnetic field is calculated. On the basis of the method for deriving exact solutions to relativistic wave equations for charged particles, an exact analytic expression is obtained for the partial decay width \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\Gamma () = \Gamma (W^ + \to \ell ^ + \bar \upsilon _\ell )$$ \end{document} at an arbitrary value of the external-field-strength parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ = eM_W^{ - 3} \sqrt { - (F_{\mu \upsilon } q^\upsilon )^2 } $$ \end{document}. It is found that, in the region of comparatively weak fields (ϰ≪1), field-induced corrections to the standard decay width of theW boson in a vacuum are about a few percent. As the external-field-strength parameter is increased, the partial width with respect to W-boson decay through the channel in question, Γ(ϰ), first decreases, the absolute minimum of Γmin=0.926Γ(0) being reached at ϰ=0.6116. A further increase in the external-field strength leads to a monotonic growth of the decay width of the W boson. In superstrong fields (ϰ≫1), the partial width with respect to W boson decay is greater than the corresponding partial width \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\Gamma ^{(0)} (W^ \pm \to \ell ^ \pm \bar \upsilon _\ell )$$ \end{document} in a vacuum by a factor of a few tens.