Theta-13 as a Probe of Mu-Tau symmetry for Leptons

Many experiments are being planned to measure the neutrino mixing parameter $\theta_{13}$ using reactor as well as accelerator neutrino beams. In this note, the theoretical significance of a high precision measurement of this parameter is discussed. It is emphasized that it will provide crucial information about different ways to understand the origin of large atmospheric neutrino mixing and move us closer towards determining the neutrino mass matrix. For instance if exact $\mu\leftrightarrow \tau$ symmetry in the neutrino mass matrix is assumed to be the reason for maximal $\nu_\mu-\nu_\tau$ mixing, one gets $\theta_{13}=0$. Whether $\theta_{13}\simeq \sqrt{\Delta m^2_{\odot}/\Delta m^2_A}$ or $\theta_{13}\simeq \Delta m^2_{\odot}/\Delta m^2_A$ can provide information about the way the $\mu\leftrightarrow \tau$ symmetry breaking manifests in the case of normal hierarchy. We also discuss the same question for inverted hierarchy as well as possible gauge theories with this symmetry.