Hidden BPS states of electroweak monopoles and a new bound estimate

Abstract

Using the BPS Lagrangian method, we obtain a distinct set of Bogomolny equations for the Cho–Maison monopoles from the bosonic sector of a regularized electroweak theory. In the limit of n→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\rightarrow \\infty $$\\end{document} of the permittivity regulator, ϵρn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon \\left( \\rho ^n\\right) $$\\end{document}, the mass of the monopole can be estimated as MW∼3.56\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_W\\sim 3.56$$\\end{document} TeV. This value is within the latest theoretical window, 2.98–3.75 TeV. We also discuss some possible regularization mechanisms of the electroweak monopole in the Yang–Mills sector and the existence of its BPS state.