  We study the scaling behavior in the tunneling amplitude when quasiparticles
tunnel along a straight path between the two edges of a fractional quantum Hall
annulus. Such scaling behavior originates from the propagation and tunneling of
charged quasielectrons and quasiholes in an effective field analysis. In the
limit when the annulus deforms continuously into a quasi-one-dimensional ring,
we conjecture the exact functional form of the tunneling amplitude for several
cases, which reproduces the numerical results in finite systems exactly. The
results for Abelian quasiparticle tunneling is consistent with the scaling
anaysis; this allows for the extraction of the conformal dimensions of the
quasiparticles. We analyze the scaling behavior of both Abelian and non-Abelian
quasiparticles in the Read-Rezayi Z_k-parafermion states. Interestingly, the
non-Abelian quasiparticle tunneling amplitudes exhibit nontrivial k-dependent
corrections to the scaling exponent.
