We investigate theoretically strong-coupling and finite-temperature effects on the p-wave contacts, as well as the asymptotic behavior of the momentum distribution in the large-momentum region in a one-component Fermi gas with a tunable p-wave interaction. Including p-wave pairing fluctuations within a strong-coupling theory, we calculate the p-wave contacts above the superfluid transition temperature Tc from the adiabatic energy relations. We show that, while the p-wave contact related to the scattering volume monotonically increases with increasing interaction strength, the one related to the effective range depends nonmonotonically on interaction strength and its sign changes in the intermediate-coupling regime. The nonmonotonic interaction dependence of these quantities is shown to originate from the competition between the increase of the cutoff momentum and the decrease of the coupling constant of the p-wave interaction with increasing effective range. We also analyze the asymptotic form of the momentum distribution in the large-momentum region. In contrast to the conventional s-wave case, we show that the asymptotic behavior cannot be completely described by only the p-wave contacts, and the extra terms, which are not related to the thermodynamic properties, appear. Furthermore, in the high-temperature region, we find that the extra terms dominate the subleading term of the large-momentum distribution. We also directly compare our results with the recent experimental measurement by including the effects of a harmonic trap potential within the local density approximation. We show that, while our model qualitatively explains the dependence on the interaction strength of the p-wave contacts, there are some quantitative disagreements between our theory and recent experiment; for example, the peak position of the p-wave contact related to the effective range. Since the p-wave contacts connect the microscopic properties to the thermodynamic properties of the system, our results would be helpful for further understanding many-body properties of this anisotropic interacting Fermi gas in the normal phase.
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