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

MiniBooNE and K2K collaborations have recently reported the ratio for the $ν_μ$ induced charge current 1$π^+$ production cross section to the charged current induced quasielastic lepton production cross section i.e. $R(E)=\frac{σ^{CC1π^+}}{σ^{CCQE}}$. 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$π^+$) processes for the $ν_μ$ 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 $ν_μ$ induced reaction in water for the proposed T2K experiment is also presented.