Upper limits on the Polarized Isotropic Stochastic Gravitational-Wave Background from Advanced LIGO-Virgo's First Three Observing Runs

Parity violation is expected to generate an asymmetry between the amplitude of left and right-handed gravitational-wave modes which leads to a circularly polarized stochastic gravitational-wave background (SGWB). Due to the three independent baselines in the LIGO-Virgo network, we focus on the amplitude difference in strain power characterized by Stokes' parameters and do maximum-likelihood estimation to constrain the polarization degree of SGWB. Our results indicate that there is no evidence for the circularly polarized SGWB in the data. Furthermore, by modeling the SGWB as a power-law spectrum, we place upper limit on the normalized energy density $\Omega_\text{gw}(25\,\text{Hz})<5.3\times10^{-9}$ at $95\%$ confidence level after marginalizing over the polarization degree and spectral index.