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Motivated by the experimental realization of single-component degenerateFermi gases of polar ground state KRb molecules with intrinsic two-body losses[L. De Marco, G. Valtolina, K. Matsuda, W. G. Tobias, J. P. Covey, and J. Ye, Adegenerate Fermi gas of polar molecules, Science 363, 853 (2019)], this workstudies the finite-temperature loss rate of single-component Fermi gases withweak interactions. First, we establish a relationship between the two-body lossrate and the $p$-wave contact. Second, we evaluate the contact of thehomogeneous system in the low-temperature regime using $p$-wave Fermi liquidtheory and in the high-temperature regime using the second-order virialexpansion. Third, conjecturing that there are no phase transitions between thetwo temperature regimes, we smoothly interpolate the results to intermediatetemperatures. It is found that the contact is constant at temperatures close tozero and increases first quadratically with increasing temperature and finally-- in agreement with the Bethe-Wigner threshold law -- linearly at hightemperatures. Fourth, applying the local-density approximation, we obtain theloss-rate coefficient for the harmonically trapped system, reproducing theexperimental KRb loss measurements within a unified theoretical framework overa wide temperature regime without fitting parameters. Our results for thecontact are not only applicable to molecular $p$-wave gases but also to atomicsingle-component Fermi gases, such as 40K and 6Li.

Temperature-Dependent Contact of Weakly Interacting Single-Component Fermi Gases and Loss Rate of Degenerate Polar Molecules