Large Matter Effects in ${\nu }_{\mu }\to {\nu }_{\tau }$ Oscillations

We show that matter effects change the ${\nu }_{\mu }\to {\nu }_{\tau }$ oscillation probability by as much as 70% for certain ranges of energies and path lengths. Consequently, the ${\nu }_{\mu }\to {\nu }_{\mu }$ survival probability also undergoes large changes. A proper understanding of ${\nu }_{\mu }$ survival rates must consider matter effects in $P_{\mu \tau }$ as well as $P_{\mu e}$. We comment on (a) how these matter effects may be observed and the sign of ${\Delta }_{31}$ determined in atmospheric neutrino measurements and at neutrino factories, and (b) how they lead to heightened sensitivity for small ${\theta }_{13}$.

Figure 1

$P_{\mu e}$, $P_{\mu \tau }$, and $P_{\mu \mu }$ plotted vs neutrino energy, $E$ (in GeV) in matter and in vacuum for both signs of ${\Delta }_{31}$ for two different baseline lengths: (a) for $L=9700\mathrm{k}\mathrm{m}$ and (b) for $L=7000\mathrm{k}\mathrm{m}$. These plots use ${\Delta }_{31}=0.002{\mathrm{e}\mathrm{V}}^2$ and ${sin}^{2}2{\theta }_{13}=0.1$.

Figure 2

$P_{\mu \tau }$ plotted against the neutrino energy, $E$ (in GeV) for different values of ${\theta }_{13}$. We have used ${\Delta }_{31}=0.002{\mathrm{e}\mathrm{V}}^2$.