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A hard TeV $\gamma$-ray component excess over the single-zone leptonic modelprediction (TeV excess) is observed in the spectral energy distributions (SEDs)of some BL Lacs. Its origin is uncertain. We revisit this issue with four BLLacs (1ES 0229+200, 1ES 0347--121, 1ES 1101--232, and H2356--309), in which theTeV excess is detected in their intrinsic SEDs. We represent their SEDs with asingle-zone leptohadronic model, where radiations of the electrons and protonsas well as the cascade electrons produced by the $\gamma\gamma$ and p$\gamma$interactions within their jets are considered. We show that the observed SEDsbelow the GeV gamma-ray band are attributed to the synchrotron radiations andself-Compton process of the primary electrons, and the TeV excess is explainedwith the $\gamma$-ray emission from the p$\gamma$ process via the $\pi^{0}$decay. The cascade emission of the electrons produced via the $\gamma\gamma$and p$\gamma$ interactions results in a keV-MeV excess in the SEDs, illustratedas a bump or plateau. This extra photon field enhances the production of TeVphotons from the $p\gamma$ process, resulting in a reduction of the protonpower by about one order of magnitude. However, the derived powers are still3--4 orders of magnitude larger than the Eddington limit, being challenged bythe current black hole accretion physics. Applying our model to Mrk 421, wepropose that synergic observations with current and upcoming TeV and keV-MeVtelescopes for its tentative TeV and MeV excesses can give insights to thehadronic process in its jet.

TeV and keV-MeV Excesses as Probes for Hadronic Process in BL Lacertaes