Phenomenology of quintessino dark matter -- Production of NLSP particles

In the model of quintessino as dark matter particle, the dark matter and dark energy are unified in one superfield, where the dynamics of the Quintessence drives the Universe acceleration and its superpartner, quintessino, makes up the dark matter of the Universe. This scenario predicts the existence of long lived $\tilde{\tau}$ as the next lightest supersymmetric particle. In this paper we study the possibility of detecting $\tilde{\tau}$ produced by the high energy cosmic neutrinos interacting with the earth matter. By a detailed calculation we find that the event rate is one to several hundred per year at a detector with effective area of $1 km^2$. The study in this paper can be also applied for models of gravitino or axino dark matter particles.