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In 1997, two scholars at the University of Illinois at Chicago — John T. Ramsey (a classicist) and A. Lewis Licht (a physicist) — published a book  comparing astronomical/astrological evidence from both Han China and Rome. Their analysis, based on historical eye-witness accounts, Chinese astronomical records, astrological literature from later antiquity and ice cores from Greenland glaciers, yielded a range of orbital parameters for the hypothetical object. They settled on a 0.224 A.U. orbit for the object which was apparently visible with a tail from the Chinese capital (in late May) and as a star-like object from Rome (in late July).
A few scholars, such as Robert Gurval of UCLA and Brian G. Marsden of the Harvard-Smithsonian Center for Astrophysics, leave the comet's very existence as an open question. Marsden notes in his forward to Ramsey and Licht's book, "Given the circumstance of a single reporter two decades after the event, I should be remiss if I were not to consider this [i.e., the comet's non-existence] as a serious possibility." 
May 18, 44 BC (China)
July 23–25, 44 BC (Rome)
Absolute magnitude: −4.0
There is one within,
Besides the things that we have heard and seen,
Recounts most horrid sights seen by the watch.
A lioness hath whelped in the streets;
And graves have yawn'd, and yielded up their dead;
Fierce fiery warriors fought upon the clouds,
In ranks and squadrons and right form of war,
Which drizzled blood upon the Capitol;
The noise of battle hurtled in the air,
Horses did neigh, and dying men did groan,
And ghosts did shriek and squeal about the streets.
O Caesar! these things are beyond all use,
And I do fear them.