  The optical response of doped monolayer semiconductors is governed by trions,
i.e. photoexcited electron-hole pairs bound to doping charges. While their
photoluminescence (PL) signatures have been identified in experiments, a
microscopic model consistently capturing bright and dark trion peaks is still
lacking. In this work, we derive a generalized trion PL formula on a
quantum-mechanical footing, considering direct and phonon-assisted
recombination mechanisms. We show the trion energy landscape in WSe$_2$ by
solving the trion Schr\"odinger equation. We reveal that the mass imbalance
between equal charges results in less stable trions exhibiting a small binding
energy and, interestingly, a large energetic offset from exciton peaks in PL
spectra. Furthermore, we compute the temperature-dependent PL spectra for n-
and p-doped monolayers and predict yet unobserved signatures originating from
trions with an electron at the $\Lambda$ point. Our work presents an important
step towards a microscopic understanding of the internal structure of trions
determining their stability and optical fingerprint.
