Extracting physics asymmetry from raw data

$$A_{phy} = \frac{\Delta}{P_bP_tf}$$

Then the target asymmetry $A_1^{^3\rm {He}}$ can be extracted from the measured asymmetries $A_\perp$ and $A_\parallel$ as:

$$A_1 = \frac{1}{D(1+\eta\xi)}A_{\parallel}-\frac{\eta}{d(1+\eta\xi)}A_{\perp}$$ (15)

$$A_2 = \gamma \Big\{\frac{1-\frac{y}{2}}{D^\prime}A_\parallel + \frac{1}... ...theta/2)+\frac{y}{2\sin\theta}\frac{1+(1-y)\cos\theta}{1-y}}\Big]A_\perp \Big\}$$ (16)

where $A_\parallel$ is the asymmetry when the beam polarization is parallel and antiparallel to the target polarization: $A_\parallel=\frac{\sigma^{\uparrow\downarrow} -\sigma^{\uparrow\uparrow}}{\sigma^{\uparrow\downarrow} +\sigma^{\uparrow\uparrow}}$. And $A_\perp$ is the asymmetry when the beam polarization is transverse to the target polarization: $A_\perp=\frac{\sigma^{\downarrow\leftarrow} -\sigma^{\uparrow\leftarrow}}{\sigma^{\downarrow\leftarrow} +\sigma^{\uparrow\leftarrow}}$.