  When a constriction is realized in a 2D quantum spin Hall system, electron
tunneling between helical edge states occurs via two types of channels allowed
by time-reversal symmetry, namely spin-preserving ({p}) and spin-flipping ({f})
tunneling processes. Determining and controlling the effects of these two
channels is crucial to the application of helical edge states in spintronics.
We show that, despite the Hamiltonian terms describing these two processes do
not commute, the scattering matrix entries of the related 4-terminal setup
always factorize into products of p-terms and f-terms contributions. Such
factorization provides an operative way to determine the transmission
coefficient $T_p$ and $T_f$ related to each of the two processes, via
transconductance measurements. Furthermore, these transmission coefficients are
also found to be controlled independently by a suitable combination of two gate
voltages applied across the junction. This result holds for an arbitrary
profile of the tunneling amplitudes, including disorder in the tunnel region,
enabling us to discuss the effect of the finite length of the tunnel junction,
and the space modulation of both magnitude and phase of the tunneling
amplitudes.
