  We theoretically analyse photonic-plasmonic coupling between a high Q
whispering gallery mode (WGM) resonator and a core-shell nanoparticle. Blue and
red shifts of WGM resonances are shown to arise from crossing of the photonic
and plasmonic modes. Level repulsion in the hybrid system is further seen to
enable sensitivity enhancements in WGM sensors: maximal when the two resonators
are detuned by half the plasmon linewidth. Approximate bounds are given to
quantify possible enhancements. Criteria for reactive vs. resistive coupling
are also established.
