Test of the exponential decay law at short decay times using tau leptons

Quantum mechanics predicts an exponential distribution for the decay time of massive particles. However, deviations are expected for decay times shorter than about 10−13 s in models conjecturing the existence of hidden variables. Following a recent proposal, the decay length distribution of 5843 τ leptons decaying into 3 charged particles was analyzed in search of such a deviation. The deviation from an exponential distribution with respect to the number of decays present within the exponential form, expressed as the relative weight of an excess at zero decay length, was measured to be 1.1%±1.4%±3.5%. This result is consistent with zero deviation and leads to an upper limit of 8.5% and a lower limit of −6.3% at the 95% confidence level.