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Description
by Chris Wymant
In the Standard Model of particle physics, quantum corrections to the mass of the Higgs boson mean we would naively expect it to be ~1016 times heavier than observed, close to the 'Planck mass' scale for gravitational interactions. This discrepancy is referred to as the hierarchy problem; the Standard Model has no solution other than an enormous amount of fine-tuning. Supersymmetric theories solve the hierarchy problem chiefly by virtue of two spin-less partners for the top quark - the stops - which contribute to the Higgs mass quantum corrections by an equal amount with the opposite sign. The necessary breaking of supersymmetry makes the cancellation incomplete, with unnaturalness returning as the stop becomes heavier. This leads us to consider stops as light as possible, subject to the extra constraint of the now observed Higgs mass of ~126 GeV. However we will show how 'maximal mixing' of the stops, while minimising their masses, contributes a new source of fine-tuning that is in fact dominant. Lagrange constrained maximisation of analytic expressions for the Higgs-stop interactions explicitly shows the optimal scenario to be near-maximal mixing. We explain why the splitting between the two stop mass eigenstates is entirely unconstrained. We introduce the NMSSM and explain its potential utility and limitations for boosting the Higgs mass naturally.
In the Standard Model of particle physics, quantum corrections to the mass of the Higgs boson mean we would naively expect it to be ~1016 times heavier than observed, close to the 'Planck mass' scale for gravitational interactions. This discrepancy is referred to as the hierarchy problem; the Standard Model has no solution other than an enormous amount of fine-tuning. Supersymmetric theories solve the hierarchy problem chiefly by virtue of two spin-less partners for the top quark - the stops - which contribute to the Higgs mass quantum corrections by an equal amount with the opposite sign. The necessary breaking of supersymmetry makes the cancellation incomplete, with unnaturalness returning as the stop becomes heavier. This leads us to consider stops as light as possible, subject to the extra constraint of the now observed Higgs mass of ~126 GeV. However we will show how 'maximal mixing' of the stops, while minimising their masses, contributes a new source of fine-tuning that is in fact dominant. Lagrange constrained maximisation of analytic expressions for the Higgs-stop interactions explicitly shows the optimal scenario to be near-maximal mixing. We explain why the splitting between the two stop mass eigenstates is entirely unconstrained. We introduce the NMSSM and explain its potential utility and limitations for boosting the Higgs mass naturally.
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