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The area of a jet has several applications when associating different objects using ghosts, and when performing calibrations, particularly for subtraction of the average contribution from pile-up to a jet:
https://arxiv.org/abs/2007.02645
https://arxiv.org/pdf/1107.4277
The methods used to calculate the jet are are documented by Cacciari et al., and available in fastjet:
https://arxiv.org/abs/0802.1188
etc.
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