  We present a theoretical analysis of the expected X-ray and gamma-ray
polarization signatures resulting from synchrotron self-Compton emission in
leptonic models, compared to the polarization signatures from proton
synchrotron and cascade synchrotron emission in hadronic models for blazars.
Source parameters resulting from detailed spectral-energy-distribution modeling
are used to calculate photon-energy-dependent upper limits on the degree of
polarization, assuming a perfectly organized, mono-directional magnetic field.
In low-synchrotron-peaked blazars, hadronic models exhibit substantially higher
maximum degrees of X-ray and gamma-ray polarization than leptonic models, which
may be within reach for existing X-ray and gamma-ray polarimeters. In
high-synchrotron-peaked blazars (with electron-synchrotron-dominated X-ray
emission), leptonic and hadronic models predict the same degree of X-ray
polarization, but substantially higher maximum gamma-ray polarization in
hadronic models than leptonic ones. These predictions are particularly relevant
in view of the new generation of balloon-borne X-ray polarimeters (and possibly
GEMS, if revived), and the ability of Fermi-LAT to measure gamma-ray
polarization at < 200 MeV. We suggest observational strategies combining
optical, X-ray, gamma-ray polarimetry to determine the degree of ordering of
the magnetic field and to distinguish between leptonic and hadronic high-energy
emission.
