This is not one investigation but a long argument, and it has never been concluded. The Rig Veda gives its entire ninth book to soma and describes the plant's mountain habitat, its pressing between stones, the straining of the juice through a woollen filter and the effect of drinking it. It does not describe the plant in the terms a botanist needs, and the living tradition had already lost the identification by the late Vedic period, when the ritual texts prescribe substitutes.
R. Gordon Wasson made the fullest single case in 1968, for the fly agaric, resting on the pressing and straining imagery and on the absence of leaf, root and seed from the hymns. John Brough replied in 1971 that the hymns do mention parts a mushroom does not have, and that the argument depended on selective reading. David Flattery and Martin Schwartz argued in 1989 for Syrian rue, working from the Iranian haoma rather than from the Indian material. Ephedra has been urged for over a century on the strength of Iranian ritual use and of the substitutes later prescribed in India.
Each candidate accounts for some verses and fails on others. None has carried the field, and the atlas records the question as open rather than choosing among them.