  We study the behavior of entanglement between different degrees of freedom of
scattering fermions, based on an exemplary QED scattering process
$e^+e^-\longrightarrow\mu^+\mu^-$. The variation of entanglement entropy
between two fermions from an initial state to the final state was computed,
with respect to different entanglement between the ingoing particles. This
variation of entanglement entropy is found to be proportional to an area
quantity, the total cross section. We also study the spin-momentum and
helicity-momentum entanglements within one particle in the aforementioned
scattering process. The calculations of the relevant variations of mutual
information in the same inertial frame reveals that, for a maximally entangled
initial state, the scattering between the particles does not affect the degree
of both of these entanglements of one particle in the final state. It is also
found that the increasing degree of entanglement between two ingoing particles
would restrict the generation of entanglement between spin (helicity) and
momentum of one outgoing particle. And the entanglement between spin and
momentum within one particle in the final state is shown to always be stronger
than that for helicity-momentum for a general initial entanglement state,
implying significantly distinct properties of entanglement for the helicity and
spin perceived by an inertial observer.
