Probing Magnetic Moment Operators in $H gamma$ Production and $H to tau^+ tau^- gamma$ Rare Decay

The magnetic moment ($a_gamma$) and weak magnetic moment ($a_W$) of charged leptons and quarks are sensitive to quantum effects of new physics heavy resonances. In effective field theory $a_gamma$ and $a_W$ are induced by two independent operators, therefore, one has to measure both the $a_gamma$ and $a_W$ to shed lights on new physics. The $a_W$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 $ppto H gamma$ and $ggto H to tau^+ tau^- gamma$ at the High-Luminosity Large Hadron Collider. We demonstrate that the two processes could cover most of the parameter space that cannot be probed at the LEP.