Looking into the details, one can observe from the bottom panels of Fig. that both the UP and the LP linewidth exhibit a convex distribution against the exciton fraction, which is more pronounced as N increases. The analytic expression in Eq. 34 agrees nearly perfectly with the numerical exact results when |C ex | → 0, but becomes less accurate as |C ex | → 1 and as N increases, which overestimates the LP linewidth. Similarly, Eq. 35 describes the UP linewidth better for |C ex | → 1 than |C ex | → 0. Further, regarding the linewidth differences between the UP and the LP, this effect is well captured by FGR which includes only UP to dark states (as well as to LP) scattering processes. We expect that polariton multiple scatterings (which correspond to higher order processes that are beyond FGR) play a less important role for the model parameters we considered, agreeing with the conclusion by Whittaker . Going beyond, we anticipate that under larger electron-phonon coupling strengths where the FGR theory starts to fail and it becomes necessary to perform nonperturbative treatments to get the correct linewidths, then polariton multiple scatterings shall become important. It is also worth mentioning that the FGR expressions in Eq. 37 work better for the negative detuned cases than the positive detuned cases . . The silver dashed line denotes the result of Eq. 21 which does not exhibit motional narrowing.