On measuring the double longitudinal spin asymmetry $A_{LL}$ for non-photonic electrons in polarized $\vec{p}+\vec{p}$ collisions at STAR

The measurement of the gluon's spin structure function $\Delta g(x)$ in the proton is one of the main focuses of the STAR spin program. In polarized proton-proton collisions at RHIC, one of the processes sensitive to $\Delta g(x)$ is heavy flavor quark production through gluon fusion $gg \rightarrow q\bar{q}$. A way to access these heavy quarks is through the non-photonic electrons resulting from their semi-leptonic decays. This contribution will describe an analysis to obtain the first measurement of $A_{LL}$ for non-photonic electrons produced in $\sqrt{s} = 200 GeV$ $\vec{p}\vec{p}$ collisions at RHIC in 2005.