Abstract
Much of the discussion regarding future measurements of the Higgs boson mass and self-coupling is focused on how well various collider options can do. In this article we ask a physics-based question of how well do we need colliders to measure these quantities to have an impact on discovery of new physics or an impact in how we understand the role of the Higgs boson in nature. We address the question within the framework of the Standard Model and various beyond the Standard Model scenarios, including supersymmetry and theories of composite Higgs bosons. We conclude that the LHC's stated ability to measure the Higgs boson to better than 150 MeV will be as good as we will ever need to know the Higgs boson mass in the foreseeable future. On the other hand, we estimate that the self-coupling will likely need to be measured to better than 20% to see a deviation from the Standard Model expectation. This is a challenging target for future collider and upgrade scenarios.
Highlights
How well do we need to measure the Higgs boson mass?Measuring the mass of any newly discovered elementary particle is an important scientific endeavor
Much of the discussion regarding future measurements of the Higgs boson mass and self-coupling is focussed on how well various collider options can do
In the subsequent sections we compute the Higgs self-coupling measurement precision needed according to the criterion explained in the previous paragraph in theories with mixed-in singlets, composite Higgs models, theories with first-order electroweak phase transition, the Minimal Supersymmetric Standard Model (MSSM) and the Next to Minimal Supersymmetric Standard Model (NMSSM)
Summary
Measuring the mass of any newly discovered elementary particle is an important scientific endeavor. The difference between the Higgs mass value when both mt and ∆S are at their central values to both being 1σ lower than their central values, under these optimistic assumptions, is δmh = 149 MeV, and for 2σ shifts in mt and ∆S the value is δmh = 297 MeV This is right near and above the uncertainty in the Higgs mass measurement already anticipated at the LHC, and we can conclude that there is no need to measure the Higgs mass to better accuracy for this test within supersymmetry. The three examples provided here illustrate our general conjecture that the inherent uncertainties in experimental measurements of observables and higher-order computations of theory imply that there is no obvious physics justification for pursuing a Higgs boson mass measurement better than what the LHC can provide
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