  We investigate how entanglement in the mixed state of a quantum field theory
can be described using the cross-computable norm or realignment (CCNR)
criterion, employing a recently introduced negativity. We study its symmetry
resolution for two disjoint intervals in the ground state of the massless Dirac
fermion field theory, extending previous results for the case of adjacent
intervals. By applying the replica trick, this problem boils down to computing
the charged moments of the realignment matrix. We show that, for two disjoint
intervals, they correspond to the partition function of the theory on a torus
with a non-contractible charged loop. This confers a great advantage compared
to the negativity based on the partial transposition, for which the Riemann
surfaces generated by the replica trick have higher genus. This result empowers
us to carry out the replica limit, yielding analytic expressions for the
symmetry-resolved CCNR negativity. Furthermore, these expressions provide also
the symmetry decomposition of other related quantities such as the operator
entanglement of the reduced density matrix or the reflected entropy.
