This is not with the Jat history only but confusing situation prevails about the antiquity of history of other indian castes, too, like Rajputs/gurjars/Ahirs/Yadavas and so on.
The confusing position as regards Jats is that serious attempts by pioneer Historians on the Jats to dig out antiquity of the word 'Jat' remained confined to extant Sanskrit literature which in turn proved creation of more confusion than to solve the mystery.
Then historians moved to another field i.e. tracing antiquity of various Jat clans about which latest scholar B S Dahiya did a valuable service to the history of Jats. We may agree or disagree with some of his findings but cannot overlook his research zeal and results arrived at with quotation of references from different language sources of history.
The contribution of Hukam Singh is second to none so far collection/consultation of sources on the antiquity to dna use to find out the roots of the Jats. But, in a nut shell, though he shattered a number of mythical hypotheses yet could not produce one authentic theory of his own.
Therefore, in the quest for finding the root/first word in literature of any language used around the world and original home of the Jats somewhere on the Globe, the discussion continues to progress.
Let us hope some convincing results would emerge one day not in distant future but soon !
P S : Recently Dr. S S Rana has also brought out a monograph on this very theme.