Revisiting High-Energy Polarization from Leptonic and Hadronic Blazar Scenarios

X-ray and MeV polarization can be powerful diagnostics for leptonic and hadronic blazar models. Previous predictions are mostly based on a one-zone framework. However, recent IXPE observations of Mrk~421 and 501 strongly favor a multi-zone framework. Thus, the leptonic and hadronic polarization predictions need to be revisited. Here we identify two generic radiation transfer effects, namely, double depolarization and energy stratification, that can have an impact on the leptonic and hadronic polarization. We show how they are generalized from previously known multi-zone effects of the primary electron synchrotron radiation. Under our generic multi-zone model, the leptonic polarization degree is expected to be much lower than the one-zone prediction, unlikely detectable in most cases. The hadronic polarization degree can reach a value as high as the primary electron synchrotron polarization during simultaneous multi-wavelength flares, consistent with the one-zone prediction. Therefore, IXPE and future X-ray and MeV polarimeters such as eXTP, COSI, and AMEGO-X, have good chances to detect hadronic polarization during flares. However, the hadronic polarization cannot be well constrained during the quiescent state. Nonetheless, if some blazar jets possess relatively stable large-scale magnetic structures, as suggested by radio observations, a non-trivial polarization degree may show up for the hadronic model after a very long exposure time ($\gtrsim 1$ year).