The leptonic di-flavor and di-number violation processes at high energy $\mu^\pm\mu^\pm $ colliders

The leptonic di-flavor violation (LFV) processes $\mu^\pm \mu^\pm \rightarrow e^\pm e^\pm $, $\mu^\pm \mu^\pm \rightarrow \tau^\pm \tau^\pm $ and the leptonic di-number violation (LNV) processes $\mu^\pm \mu^\pm \rightarrow W^\pm _iW^\pm _j$ ($i,\;j=1,\;2$) at the same-sign high energy $\mu^\pm \mu^\pm $ colliders are studied. The new physics (NP) factors that may play roles in these processes are highlighted by cataloging them into three types. Taking into account the experimental constraints, the processes at $\mu^\pm\mu^\pm$ colliders are computed and the results are presented properly. The results lead to the conclusion that observing the NP factors through the LFV and LNV processes at TeV-energy $\mu^\pm\mu^\pm$ colliders has significant advantages that cannot be achieved elsewhere. Therefore, in developing the techniques of muon acceleration and collisions, the option of building the same-sign muon high-energy colliders should be considered seriously too.