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We study correlation analysis for monopole components of stochasticgravitational wave backgrounds, including the maximally allowed polarizationdegrees. We show that, for typical detector networks, the correlation analysiscan probe virtually five spectra: three for the intensities of the tensor,vector, and scalar modes and two for the chiral asymmetries of the tensor andvector modes. The chiral asymmetric signal for the vector modes has been leftuntouched so far. In this paper, we derive the overlap reduction function forthis signal and thus complete the basic ingredients required for widely dealingwith polarization degrees. We comprehensively analyze the geometricalproperties of all the five overlap reduction functions. In particular, we pointout the importance of reflection transformations for configuring preferablenetworks in the future.

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