Prediction of ultra-narrow Higgs resonance in magnon Bose-condensates

Higgs resonance modes in condensed matter systems are generally broad; meaning large decay widths or short relaxation times. This common feature has obscured and limited their observation to a select few systems. Contrary to this, the present work predicts that Higgs resonances in magnetic field induced, three-dimensional magnon Bose-condensates have vanishingly small decay widths. Specifically for parameters relating to TlCuCl$_3$, we find an energy ($\Delta_H$) to width ($\Gamma_H$) ratio $\Delta_H/\Gamma_H\sim500$, making this the narrowest predicted Higgs mode in a condensed matter system, some two orders of magnitude `narrower' than the sharpest condensed matter Higgs observed so far.