Gravitational Wave Background Search by Correlating Multiple Triangular Detectors in the mHz Band

With the recent strong developments of TianQin and Taiji, we now have an increasing chance to make a correlation analysis in the mHz band by operating them together with LISA. Assuming two LISA-like triangular detectors at general geometrical configurations, we develop a simple formulation to evaluate the network sensitivity to an isotropic gravitational wave background. In our formulation, we fully use the symmetry of data channels within each triangular detector and provide tractable expressions without directly employing cumbersome detector tensors. We concretely evaluate the expected network sensitivities for various potential detector combinations, including the LISA-TianQin pair.