To commemorate this Roman triumph and to honor the victorious general (and later emperor), Titus, Emperor Domitian built an honorific monument—the Arch of Titus, which stands on the main processional street of ancient Rome (Via Sacra) to this day. The relief panels of the Arch of Titus in Rome chronicle the triumphal episodes following the fall of Jerusalem, capturing prominently the triumphal procession. One of the scenes confirms that the Temple Menorah was carried on litters in the parade that took place in the summer of 71 C.E. But what happened to the seven-branched candelabrum after that? The possibilities are explored in detail in the article “Did the Temple Menorah Come Back to Jerusalem?” in the September/October 2017 issue of Biblical Archaeology Review, where Fredric Brandfon unravels the Menorah’s intricate story.The BAR article is behind the subscription wall, but this BHD piece gives some idea of what is in it.
As for the question, PaleoJudaica has been exploring answers for a long time. So far, none of them are particularly convincing. Start here and here and follow the links. And for the Arch of Titus, and for ancient menorahs and representations of menorahs in general, see here and follow the many links.
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