We study matter effects which arise in the muon neutrino oscillation and survival probabilities relevant to atmospheric neutrino and very long baseline beam experiments. The inter-relations between the three probabilities P_{ \mu e}, P_{ \mu \tau} and P_{ \mu \mu} are examined. It is shown that large and observable sensitivity to the neutrino mass hierarchy can be present in P_{ \mu \mu} and P_{ \mu \tau}. We emphasize that at baselines of > 7000 Km, matter effects in P_{ \mu \tau} can be large under certain conditions. The muon survival rates in experiments with very long baselines thus depend on matter effects in both P_{ \mu \tau} and P_{ \mu e}. We indicate where these effects are sensitive to \theta_{ 13}, and identify ranges of E and L where the event rates increase with decreasing \theta_{ 13}, providing a handle to probe small \theta_{ 13}. The effect of parameter degeneracies in the three probabilities at these baselines and energies is studied in detail. Realistic event rate calculations are performed for a charge discriminating 100 kT iron calorimeter which demonstrate the possibility of realising the goal of determining the neutrino mass hierarchy using atmospheric neutrinos. It is shown that a careful selection of energy and baseline ranges is necessary in order to obtain a statistically significant signal, and that the effects are largest in bins where matter effects in both P_{ \mu e} and P_{ \mu \tau} combine constructively. Under these conditions, upto a 4\sigma signal for matter effects is possible (for \Delta_{ 31}>0) within a timescale appreciably shorter than the one anticipated for neutrino factories.
Categories: hep-ph