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Large-momentum distribution of a polarized Fermi gas and p-wave contacts

We present a derivation of the adiabatic energy relations as well as the large momentum distribution of a polarized Fermi gas near p-wave Feshbach resonances. The leading asymptotic behavior ($k^{-2}$) and subleading behavior ($k^{-4}$) of the large momentum distribution have recently been predicted by Yu et al. [Phys. Rev. Lett. 115, 135304 (2015)] and by He et al. [Phys. Rev. Lett. 116, 045301 (2016)] using two different approaches. Here, we show that the subleading asymptotic behavior ($\sim k^{-4}$) can not fully be captured by the contact defined from the adiabatic energy relation related to the p-wave effective range, and there should be an extra term resulted from the center-of-mass motion of the pairs. The omission of this extra term is perhaps a reasonable approximation at zero temperature. However, it should be taken into account at finite temperature and should be of significant importance to understand the recently measured momentum distribution in a resonant p-wave Fermi gas of ultracold $^{40}$K atoms [Luciuk et al., Nature Phys. 12, 599 (2016)].