Novel Machine Learning Methods to Improve Z Pole Integrated Luminosity at Future Colliders

Future $e^+e^-$ colliders at the Z pole place strong demands of $\frac{\delta L}{L}<10^{-4}$ on the integrated luminosity measurement. Small angle Bhabha scattering (SABS) remains the standard channel, while diphoton ($\gamma\gamma$) events provide a complementary measurement. This contribution summarizes recent work on two dominant uncertainties. First, we investigate backgrounds to the diphoton channel and find that SABS and low-invariant-mass neutral hadrons are the most significant backgrounds. A gradient boosted decision tree (BDTG) is used to classify events by particle ID. The classification results show the existing and upgraded forward tracker and luminosity calorimeter (LumiCal) designs reject neutral hadrons but only the LumiCal upgrade can reject SABS at $\frac{\delta L}{L}<10^{-4}$. Second, we solve the beam deflection bias problem on an event-by-event basis using two machine learning algorithms. A BDTG and the newly written Adaptive Symbolic Memetic Regression (ASMR) are trained on beam deflection data. ASMR outperforms BDTG and provides a reduced uncertainty of $5\times10^{-6}$ for beam deflection.