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 thisnote, the theoretical significance of a high precision measurement of thisparameter is discussed. It is emphasized that it will provide crucialinformation about different ways to understand the origin of large atmosphericneutrino mixing and move us closer towards determining the neutrino massmatrix. For instance if exact $\mu\leftrightarrow \tau$ symmetry in theneutrino mass matrix is assumed to be the reason for maximal $\nu_\mu-\nu_\tau$mixing, one gets $\theta_{13}=0$. Whether $\theta_{13}\simeq \sqrt{\Deltam^2_{\odot}/\Delta m^2_A}$ or $\theta_{13}\simeq \Delta m^2_{\odot}/\Deltam^2_A$ can provide information about the way the $\mu\leftrightarrow \tau$symmetry breaking manifests in the case of normal hierarchy. We also discussthe same question for inverted hierarchy as well as possible gauge theorieswith this symmetry.Comment: 12 pages; no figures; latex; more exact expressions given for some parameters and minor typos corrected; paper accepted for publication in JHE