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We perform a diagrammatic analysis of the energy of a mobile impurityimmersed in a strongly interacting two component Fermi gas to second order inthe impurity-bath interaction. These corrections demonstrate divergent behaviorin the limit of large impurity momentum. We show the fundamental processesresponsible for these logarithmically divergent terms.  We study the problem in the general case without any assumptions regardingthe fermion-fermion interactions in the bath. We show that the divergent termcan be summed up to all orders in the Fermi-Fermi interaction and that theresulting expression is equivalent to the one obtained in the few bodycalculation.  Finally, we provide a perturbative calculation to the second order in theFermi-Fermi interaction in the annex, and we show the diagrams responsible forthese terms.

Exploring beyond-mean-field logarithmic divergences in Fermi-polaron energy