  Experiments on tunneling into fractional quantum Hall droplets systematically
found tunneling exponents smaller than those predicted by the ordinary chiral
Luttinger liquid theory. In this note, by considering the effects of a smooth
boundary, we propose a modification of the theory that predicts a reduced
exponent, in qualitative agreement with experiments. Such modification consists
on a self-interaction cubic term, containing higher derivatives of the chiral
boson field, that provides a non-universal one loop correction to the
propagator.
