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We study theoretically the lifetimes of attractive and repulsive Fermipolarons, as well as the molecule at finite momentum in three dimensions. Tothis end, we develop a new technique that allows for the computation of Green'sfunctions in the whole complex frequency plane using exact analyticalcontinuation within the functional renormalization group. The improvednumerical stability and reduced computational cost of this method yield accessto previously inaccessible momentum-dependent quasiparticle properties oflow-lying excited states. While conventional approaches like thenon-selfconsistent $T$-matrix approximation method cannot determine theselifetimes, we are able to find the momentum-dependent lifetime at differentinteraction strengths of both the attractive and repulsive polaron as well asthe molecule. At weak coupling our results confirm predictions made fromeffective Fermi liquid theory regarding the decay of the attractive polaron,and we demonstrate that Fermi liquid-like behavior extends far into thestrong-coupling regime where attractive polaron and molecule exhibit a $p^4$momentum scaling in their decay widths. Our results offer an intriguing insightinto the momentum-dependent quasiparticle properties of the Fermi polaronproblem, which can be measured using techniques such as Raman transfer andRamsey interferometry.

Momentum-dependent quasiparticle properties of the Fermi polaron from the functional renormalization group