  Despite advances in observational data, theoretical models, and computational
techniques to simulate key physical processes in the formation and evolution of
galaxies, the stellar mass assembly of galaxies still remains an unsolved
problem today. Optical spectroscopic measurements appear to show that the
gas-phase metallicities of local ultra-luminous infrared galaxies (ULIRGs) are
significantly lower than those of normal star-forming galaxies. This difference
has resulted in the claim that ULIRGs are fueled by metal-poor gas accretion
from the outskirts\cite{Mannucci10}. Here we report on a new set of gas-phase
metallicity measurements making use of the far-infrared spectral lines of
[O{\sc iii}]52 $\mu$m, [O{\sc iii}]88 $\mu$m, and [N{\sc iii}]57 $\mu$m instead
of the usual optical lines. Photoionization models have resulted in a
metallicity diagnostic based on these three lines that break the electron
density degeneracy and reduce the scatter of the correlation significantly.
Using new data from SOFIA and archival data from Herschel Space Observatory, we
find that local ULIRGs lie on the mass-metallicity relation of star-forming
galaxies and have metallicities comparable to other galaxies with similar
stellar masses and star formation rates. The lack of a departure suggests that
ULIRGs follow the same mass assembly mechanism as luminous star-forming
galaxies and $\sim 0.3$ dex under-abundance in metallicities derived from
optical lines is a result of heavily obscured metal-rich gas which has a
negligible effect when using the FIR line diagnostics.
