Low energy atmospheric muon neutrinos in MACRO

We present the measurement of two event samples induced by atmospheric $\nu_\mu$ of average energy $ \bar {E}_\nu \sim 4 GeV$. In the first sample, the neutrino interacts inside the MACRO detector producing an upward-going muon leaving the apparatus. The ratio of the number of observed to expected events is $ 0.57 \pm0.05_{stat} \pm0.06_{syst} \pm0.14_{theor}$ with an angular distribution similar to that expected from the Bartol atmospheric neutrino flux. The second is a mixed sample of internally produced downward-going muons and externally produced upward-going muons stopping inside the detector. These two subsamples are selected by topological criteria; the lack of timing information makes it impossible to distinguish stopping from downgoing muons. The ratio of the number of observed to expected events is $0.71 \pm 0.05_{stat} \pm0.07_{syst} \pm0.18_{theor}$ . Using the ratio of the two subsamples (for which most theoretical uncertainties cancel) we can test the pathlength dependence of the oscillation hypothesis. The probability of agreement with the no-oscillation hypothesis is 5% . The deviations of our observations from the expectations has a preferred interpretation in terms of $\nu_\mu$ oscillations with maximal mixing and $\Delta m^2 \sim 10^{-3} \div 10^{-2} eV^2$. These parameters are in agreement with our results from upward throughgoing muons, induced by $\nu_\mu$ of much higher energies.