Measurment of the Charged Current Inclusive Anti-Neutrino to Neutrino Cross Section Ratio Using the $\pi^0$ Detector at T2K

Recent anti-neutrino data taken by the T2K experiment is used to measure the ratio of the cross sections for charged current interactions of muon type neutrinos relative to anti-neutrinos, $\frac{\sigma ( \overline{\nu}_\mu+nucleons \rightarrow \mu^+ + X)}{\sigma ( \nu_\mu+nucleons \rightarrow \mu^- + X )}$. Theoretical estimates for charged current quasi-elastic neutrino-quark scattering predict this ratio should be approximately $\frac{1}{3}$. This measurement used the $\pi^0$ detector (P$\emptyset$D) and a time projection chamber (TPC1) directly downstream at the off axis near detector (ND280) complex of the T2K experiment. Neutrino interactions occurring in the P$\emptyset$D with an exiting muon whose momentum is measured by TPC1 were selected. Preliminary results and studies of the event selection and relevant systematic uncertainties are presented.