We present the search for the lepton flavour violating decay {tau} {yields} lK{sup 0}{sub s} with the BaBar experiment data. This process and many other lepton flavour violating {tau} decays, like {tau} {yields} {mu}{gamma} and {tau} {yields} lll, are one of the most promising channel to search for evidence of new physics. According to the Standard Model and the neutrino mixing parameters, branching fractions are estimated well below 10{sup -14}, but many models of new physics allow for branching fractions values close to the present experimental sensitivity. This analysis is based on a data sample of 469fb{sup -1} collected by BABAR detector at the PEP-II storage ring from 1999 to 2007, equivalent to 431 millions of {tau} pairs. the BABAR experiment, initially designed for studying CP violation in B mesons, has demonstrated to be one of the most suitable environments for studying {tau} decays. The tracking system, the calorimeter and the particle identification of BABAR, together with the knowledge of the {tau} initial energy, allow an extremely powerful rejection of background events that, for this analysis, is better than 10{sup -9}. Being {tau} {yields} lK{sup 0}{sub s} a decay mode without neutrinos, the signal {tau} decay can be fully reconstructed. Kinematical constraints are used in a fit that provides a decay tree reconstruction with a high resolution. For this analysis MC simulated events play a decisive role for estimating the signal efficiency and study the residual background. High statistics MC sample are produced simulating detector conditions for different periods of data collection, in order to reduce any discrepancies with the data. When discrepancies can not be removed, we perform studies to compute a correction factor or an estimation of systematic errors that need to be included in the final measurement. A significant improvement of the current result can be reached only with a higher statistics and, therefore, with a new collider providing a luminosity from 10 to 100 times more than PEP-II. A new detector, with improved performance and able to collect data in a high background environment, is also requested to fully exploit the capability of such amount of data. In fact, only keeping the efficiency and the background as similar as possible to present ones, we will be able to scale almost linearly the estimated upper limit according to the luminosity. The strong potential of improvement for the search of lepton flavour violation {tau} decays makes the building of such a machine highly desirable.
