Charged Lepton Flavour Violation at Belle and Belle II

Lepton Flavour Violating (LFV) τ lepton decays are strongly suppressed in the Standard Model but several New Physics scenarios bring the branching fractions of decays such as τ→ℓℓℓ and τ→μγ in the experimentally obtainable range of 10−9 to 10−7. Belle has studied 48 different LFV τ lepton modes and set 90% C.L. upper limits of O(10−8) on the branching fractions. In this article, we review these measurements and summarize the Belle results. The experiment is currently undergoing an upgrade aiming at increasing the size of the data sample by a factor of 50. We also discuss this Belle II upgrade and the prospects for LFV searches in τ lepton decays.