Title: Prediction of ultra-narrow Higgs resonance in magnon Bose-condensates,
Abstract: 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.