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We first review the decade-old, broad collider physics research programdubbed energy-peaks. We consider the energy distribution of a massless particlein the lab frame arising from the two-body decay of a heavy particle producedunpolarized, whose boost distribution is arbitrary. Remarkably, the location ofthe peak of this child particle's energy distribution is identical to itssingle-valued energy in the rest frame of the parent, which is a function ofthe parent's mass and that of the other decay product. We summarizegeneralizations to other types of decay and a variety of applications to BSM.The energy-peak idea can also furnish a measurement of the top quark via theenergy of the bottom quark from its decay, which, based on the"parent-boost-invariance," is less sensitive to details of the productionmechanism of the top quark (cf.~most other methods assume purely SM productionof the top quarks, hence are subject to uncertainties therein, including apossible BSM contribution). The original proposal along this line was to simplyuse the $b$-jet energy as a very good approximation to the bottom quark energy.This method has been successfully implemented by the CMS collaboration.However, the $b$-jet energy-peak method is afflicted by the jet-energy scale(JES) uncertainty. Fortunately, this drawback can be circumvented by using thedecay length of a $B$-hadron contained in the $b$-jet as a proxy for the bottomquark energy. An interesting proposal is to then appropriately dovetail theabove two ideas resulting in a "best of both worlds" determination of the topquark mass, i.e., based on a measurement of the $B$-hadron decay length, butimproved by the energy-peak concept: this would be free of JES uncertainty andlargely independent of the top quark production model. We summarize here theresults of such an analysis which is to appear in a forthcoming paper.

Snowmass2021 - White Paper, Implications of Energy Peak for Collider Phenomenology: Top Quark Mass Determination and Beyond