How Irrelevant Operators affect the Determination of Fractional Charge

We show that the inclusion of irrelevant terms in the Hamiltonian describing tunneling between edge states in the fractional quantum Hall effect can lead to a variety of non perturbative behaviors in intermediate energy regimes, and, in particular, affect crucially the determination of charge through shot noise measurements. We show, for instance, that certain combinations of relevant and irrelevant terms can lead to an effective measured charge $\nu e$ in the strong backscattering limit and an effective measured charge $e$ in the weak backscattering limit, in sharp contrast with standard perturbative expectations. This provides a possible scenario to explain the experimental observations by Heiblum and coworkers, which are so far not understood.