  For the precision study at the ILC 250, measurement of $A_{LR}$ is important
as it can constrain SMEFT parameters. The current best measured $A_{LR}$ value
is $A_{LR} = 0.1514 \pm 0.0019\,(stat) \pm 0.0011\,(syst)$ which was measured
at the SLC, and a more precise value is required for the global fit for the new
physics search in TeV-scale. At the ILC, we can use the $e^+ e^- \to \gamma Z$
process to evaluate the $A_{LR}$. We performed a full simulation study of the
$e^+ e^- \to \gamma Z$ process at the center-of-mass energy of 250 GeV and
evaluated how much we can improve the precision of this observable. The
statistical error on $A_{LR}$ at the ILC 250 turned out to be $1.8 \times
10^{-4}$. Major source of the systematic error was error from the beam
polarization. As other sources of the systematic error, the uncorrelated parts
of error on the product of luminosity and selection efficiency for each
polarization combination contribute. Including those systematic errors, total
absolute error on $A_{LR}$ was estimated to be 0.00025, 8.8 times better
precision than that from the SLC (0.00219).

High Energy Physics - Experiment