Probing magnetic moment operators in \begin{document}${\boldsymbol H \gamma }$\end{document} production and \begin{document}${\boldsymbol H \to \tau^+ \tau^- \gamma }$\end{document} rare decay

The magnetic moment ( \begin{document}$ a_\gamma $\end{document} ) and weak magnetic moment ( \begin{document}$ a_W $\end{document} ) of charged leptons and quarks are sensitive to quantum effects of new physics heavy resonances. In effective field theory, \begin{document}$ a_\gamma $\end{document} and \begin{document}$ a_W $\end{document} are induced by two independent operators. Therefore, one has to measure both \begin{document}$ a_\gamma $\end{document} and \begin{document}$ a_W $\end{document} to shed light on new physics. The \begin{document}$ a_W $\end{document} 's of the SM fermions are measured at the LEP. In this work, we analyze the contributions from magnetic and weak magnetic moment operators in the processes of \begin{document}$ pp\to H \gamma $\end{document} and \begin{document}$ gg\to H \to \tau^+ \tau^- \gamma $\end{document} at the High-Luminosity Large Hadron Collider. We demonstrate that the two processes can cover most of the parameter space that cannot be probed at the LEP.