  Tunneling of electrons into a two-dimensional electron system is known to
exhibit an anomaly at low bias, in which the tunneling conductance vanishes due
to a many-body interaction effect. Recent experiments have measured this
anomaly between two copies of the half-filled Landau level as a function of
in-plane magnetic field, and they suggest that increasing spin polarization
drives a deeper suppression of tunneling. Here we present a theory of the
tunneling anomaly between two copies of the partially spin-polarized
Halperin-Lee-Read state, and we show that the conventional description of the
tunneling anomaly, based on the Coulomb self-energy of the injected charge
packet, is inconsistent with the experimental observation. We propose that the
experiment is operating in a different regime, not previously considered, in
which the charge-spreading action is determined by the compressibility of the
composite fermions.
