CC1$\pi^+$ to CCQE cross sections ratio at accelerator energies

MiniBooNE and K2K collaborations have recently reported the ratio for the $\nu_\mu$ induced charge current 1$\pi^+$ production cross section to the charged current induced quasielastic lepton production cross section i.e. $R(E)=\frac{\sigma^{CC1\pi^+}}{\sigma^{CCQE}}$. In this paper we study, theoretically, in a local density approximation the effect of nuclear medium in charged current quasielastic(CCQE) and charged current one pion production(CC1$\pi^+$) processes for the $\nu_\mu$ induced reaction in nuclei. The theoretical results have been compared with the results of experimental observations by the MiniBooNE and K2K collaborations. The ratio R(E) for $\nu_\mu$ induced reaction in water for the proposed T2K experiment is also presented.