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Although it is widely accepted that the electromagnetic spectrum from radioto very-high-energy $\gamma$-rays of pulsar wind nebulae (PWNe) originates fromleptons, there is still an open question that protons (or more generally, ions)may exist in pulsar wind and are further accelerated in PWN. The broadbandspectrum of the prototype PWN Crab, extended recently by the detection of theTibet AS$\gamma$ and HAWC experiments above 100 TeV, may be helpful inconstraining the acceleration efficiency of ions. Here, we model the broadestenergy spectrum of Crab and find that the broadband spectrum can be explainedby the one-zone leptonic model in which the electrons/positrons produce theemission from radio to soft $\gamma$-rays via the synchrotron process, andsimultaneously generate the GeV-TeV $\gamma$-rays through inverse Comptonscattering including the synchrotron self-Compton process. In the framework ofthis leptonic model, the fraction of energy converted into the energeticprotons is constrained to be below $0.5\ (n_{\rm t}/10\ {\rm cm}^{-3})^{-1}$per cent, where $n_{\rm t}$ is the target gas density in the Crab. However,this fraction can be up to $7\ (n_{\rm t}/10\ {\rm cm}^{-3})^{-1}$ per cent ifonly the $\gamma$-rays are used.

Modeling the broadest spectral band of the Crab nebula and constraining the ions acceleration efficiency