Pileup mitigation at the LHC: a theorist's view

To maximise the potential for new measurements and discoveries at the LHC, the machine delivers as high as possible collision rates. As a consequence, multiple proton-proton collisions occur whenever two bunches cross. Interesting high-energy (hard) collisions are therefore contaminated by several soft, zero-bias, ones. This effect known as pileup pollutes the final state of the collision. It complicates the reconstruction of the objects in this final state, resulting in increased experimental uncertainties. To reduce these uncertainties, and improve the quality and precision of LHC measurements, techniques are devised to correct for the effects of pileup. This document provides a theoretical review of the main methods used during Run I and II of the LHC to mitigate pileup effects. I start with an in-depth presentation of the area--median used for the majority of applications, including several refinements of the original idea, their practical implementation and an assessment of their efficiency and robustness. I then focus on several theoretical calculations that can provide both quantitative and qualitative information on the area--median approach. In the case of boosted jets, a field that has seen a wide interest recently, a set of methods, known as grooming techniques has also been used. I describe these techniques, address their performance and briefly show that they are amenable to a theoretical, analytic, understanding. The last part of this review focuses on ideas oriented towards future pileup mitigation techniques. This includes new methods that have recently been proposed as well as a large series of alternative ideas. The latter are yet unpublished and have not received the same amount of investigation than the former but they have the potential to bring new developments and further improvement over existing techniques in a future where pileup mitigation will be crucial.