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The Crab nebula is a prominent pulsar wind nebula (PWN) detected in multibandobservations ranging from radio to very high-energy (VHE) $\gamma$-rays.Recently, $\gamma$-rays with energies above $1 \mathrm{PeV}$ had been detectedby the Large High Altitude Air Shower Observatory (LHAASO), and the energy ofthe most energetic particles in the nebula can be constrained. In this paper,we investigate the broadest spectral energy distribution of the Crab nebula andthe energy distribution of the electrons emitting the multiwavelengthnonthermal emission based on a one-zone time-dependent model. The nebula ispowered by the pulsar, and high-energy electrons/positrons with a brokenpower-law spectrum are continually injected in the nebula as the pulsar spinsdown. Multiwavelength nonthermal emission is generated by the leptons throughsynchrotron radiation and inverse Compton scattering. Using appropriateparameters, the detected fluxes for the nebula can be well reproduced,especially for the $\gamma$-rays from $10^2\,\mathrm{MeV}$ to$1\,\mathrm{PeV}$. The results show that the detected $\gamma$-rays can beproduced by the leptons via the inverse Compton scattering, and the lower limitof the Lorentz factor of the most energetic leptons is $\sim 8.5\times10^{9}$.It can be concluded that there are electrons/positrons with energies higherthan $4.3$\,PeV in the Crab nebula.

Investigating the energy distribution of the high-energy particles in the Crab nebula