Using Support Vector Machines for $D^0$ Reconstruction in STAR Simulations

The STAR Collaboration proposes to construct a microvertex detector, called the Heavy Flavor Tracker (HFT), using components made up of active pixel sensors and silicon strips to study the quark-gluon plasma (QGP). The HFT is designed to measure heavy mesons containing $c$ and $b$ quarks, such as the $D^0$ meson. These heavy quarks are an ideal probe to study the QGP. Support Vector Machines (SVMs), which are a set of kernel- based learning methods used for classification and regression, provide one candidate method for $D^0$ reconstruction in the HFT. Given two sets of training data, viewed as vectors in an $n$-dimensional space, the SVM will construct an $(n-1)$- dimensional hyperplane which maximizes the separation between the data, while minimizing misclassification error. Using the hadronic decay channel, $D^0 \rightarrow K^- + \pi^+$, our preliminary results show that with a Radial Basis Function (RBF) kernel, $K(x,z)=\exp{(-\gamma\|x-z\|^2)}$, SVMs can correctly classify pion-kaon pairs with a very high success rate. We compare the performance of SVM reconstruction with the currently implemeted reconstruction method, and determine which yields a greater signal significance, $\frac{S}{\sqrt{S+B}}$, per $p_T$ bin.