Neutrino dipole moments and charge radii in non-commutative space-time

In this paper we obtain a bound \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Lambda_{\mathrm {NC}}\stackrel{ < }{\sim} 150 $\end{document} TeV on the scale of space-time non-commutativity considering photon-neutrino interactions. We compute “*-dipole moments” and “*-charge radii” originating from space-time non-commutativity and compare them with the dipole moments calculated in the neutrino-mass extended standard model (SM). The computation depends on the nature of the neutrinos, Dirac versus Majorana, their mass and the energy scale. We focus on Majorana neutrinos. The “*-charge radius” is found to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $r^* = \sqrt{|\langle r^2_{\nu}\rangle_{\mathrm {NC}}|}=\left|3\sum_{i=1}^3 ({\theta}^{0i})^2\right|^{1/4} \stackrel{<}{\sim} 1.6 \times 10^{-19}\, {\mathrm {cm}}$\end{document} at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Lambda_{\mathrm {NC}} = 150$\end{document} TeV.