Systematic effects induced by half-wave plate differential optical load and TES nonlinearity for LiteBIRD

LiteBIRD, a forthcoming satellite mission, aims to measure the polarization of the Cosmic Microwave Background (CMB) across the entire sky. The experiment will employ three telescopes, Transition-Edge Sensor (TES) bolometers and rotating Half-Wave Plates (HWPs) at cryogenic temperatures to ensure high sensitivity and systematic effects mitigation. This study is focused on the Mid- and High-Frequency Telescopes (MHFT), which will use rotating metal mesh HWPs. We investigate how power variations due to HWP differential emissivity and transmittance combine with TES nonlinear responsivity, resulting in an effective instrumental polarization. We present the results of simulations for the current HWP design, modeling the TES deviation from linearity as a second-order response. We quantify the level of acceptable residual nonlinearity assuming the mission requirement on the tensor-to-scalar ratio, $\delta r < 0.001$. Moreover, we provide an accuracy requirement on the measurement of TES responsivity nonlinearity level for MHFT channels. Lastly, we present possible mitigation methods that will be developed in future studies.