Correlation analysis for isotropic stochastic gravitational wave backgrounds with maximally allowed polarization degrees

We study correlation analysis for monopole components of stochastic gravitational wave backgrounds, including the maximally allowed polarization degrees. We show that, for typical detector networks, the correlation analysis can probe virtually five spectra: three for the intensities of the tensor, vector, and scalar modes and two for the chiral asymmetries of the tensor and vector modes. The chiral asymmetric signal for the vector modes has been left untouched so far. In this paper, we derive the overlap reduction function for this signal and thus complete the basic ingredients required for widely dealing with polarization degrees. We comprehensively analyze the geometrical properties of all the five overlap reduction functions. In particular, we point out the importance of reflection transformations for configuring preferable networks in the future.