Estimation \({\text {of }^{32}}\) Si \({\text {and}\,^{32}}\) P Background Rate in CDMS II Experiment

The Cryogenic Dark Matter Search experiment II (CDMS II) was a direct dark matter search experiment that operated between the years 2003 to 2012 at Soudan Underground Laboratory, Minnesota, USA. The experiment deployed a total of 19 germanium (Ge) and 11 silicon (Si) cryogenic detectors each having a mass of \(\sim \) 250 g and \(\sim \) 100 g respectively, in a 5 tower configuration, at a temperature of \(\sim \) 50 mK. The detection principle of this experiment involves measuring the recoil energy of the target mass (Ge or Si) after a dark matter particle elastically scatters off it. The detector measured charge and phonon signals from an interaction with the target atom. The dark matter is expected to interact weakly and the expected interaction rate in material like Ge, Si is on the order of few events per kg per year. Hence the identification and rejection of the backgrounds in these experiments are crucial. \(^{32}\!\) Si is an isotope of silicon which is present in the silicon detectors from the time of fabrication. It decays \(\text {to}\,^{32}\) P which further decays to \(\text {stable}\,^{32}\) S with half-lives of 153 years and 14.27 days respectively. These \(\beta \) particles act as a source of backgrounds in CDMS II. The endpoint energies of the \(\beta \) spectrum are 227 keV \(\text {for}\,^{32}\) Si \(\rightarrow \) \({^{32}}\) P and 1710 keV \(\text {for}\,^{32}\) P \(\rightarrow \) \(\,{^{32}}\) S. The \(\beta \) particles create electron recoils in the detector. Our analysis goal is to estimate the activity \(\text {of}\,^{32}\) Si \(\text {and}\,^{32}\) P in the Si detectors using CDMS II data. We will present the recent progress towards using a likelihood method to measure the specific radioactivity \(\text {of}\,^{32}\) Si \(\text {and}\,^{32}\) P in Si detectors. Our analysis is important for the SuperCDMS SNOLAB experiment, the successor of CDMS and other experiments that uses Si detectors to look for rare events.