  We investigate trions, paired states and quantum phase transitions in
one-dimensional SU(3) attractive fermions in external fields by means of the
Bethe ansatz and the dressed energy formalism. Analytical results for the
ground state energy, critical fields and complete phase diagrams are presented
for weak and strong regimes. Numerical solutions of the dressed energy
equations allow us to examine how the different phase boundaries modify by
varying the inter-component coupling throughout the whole attractive regimes.
The pure trionic phase reduces smoothly by decreasing this coupling until the
weak limit is reached. In this weak regime, a pure BCS-paired phase can be
sustained under certain nonlinear Zeeman splittings. Finally we confirm that
the analytic expressions for the physical quantities and resulting phase
diagrams are highly accurate in the weak and strong coupling regimes.
