Measuring the Higgsplosion Yield: Counting Large Higgs Multiplicities at Colliders

Recent work has brought renewed attention to the possibility that the cross section for producing $n$ Higgs bosons grows large with $n$ at a sufficiently energetic hadron collider. In particular, this "Higgsplosion'" mechanism has been suggested as a solution to the hierarchy problem. We investigate the phenomenology of this scenario. Discovery is trivial, so we consider several variables for use in measuring large Higgs multiplicities and evaluate their effectiveness. We find that a $10$% level measurement of the number of Higgs bosons is possible with a handful of events, using the scalar sum of jet transverse momenta, but determining the exact multiplicity may take a few thousand events, depending on the degree of statistical significance desired for the measurement. While this situation may be acceptable given the potentially large cross sections in this scenario, future research to improve the measurement is warranted.