The lepton flavor violating process $J/psito ll (l eq l)$ serves as an ideal place to probe the unparticle theory. Such process can only occur at loop level in the Standard model (SM), so that should be very suppressed, by contrast in unparticle scenario, it happens at tree level and its contribution may be sizable for practical measurement. Moreover, the BESIII will offer the largest database on $J/psi$ which makes more accurate measurements possible. Furthermore, for such purely leptonic decays background is relatively low and signal would be cleaner. Our work carefully investigates the possibility of observing such processes from both theoretical and experimental aspects.
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