Abstract
Attempts to solve naturalness by having the weak scale as the only breaking of classical scale invariance have to deal with two severe difficulties: gravity and the absence of Landau poles. We show that solutions to the first problem require premature modifications of gravity at scales no larger than 1011 GeV, while the second problem calls for many new particles at the weak scale. To build models that fulfill these properties, we classify 4- dimensional Quantum Field Theories that satisfy Total Asymptotic Freedom (TAF): the theory holds up to infinite energy, where all coupling constants flow to zero. We develop a technique to identify such theories and determine their low-energy predictions. Since the Standard Model turns out to be asymptotically free only under the unphysical conditions g 1 = 0, M t = 186 GeV, M τ = 0, M h = 163 GeV, we explore some of its weak-scale extensions that satisfy the requirements for TAF.
Highlights
The naturalness problem of the Higgs mass is a central issue for the searches in the upcoming high-energy run of the LHC and, more generally, for defining the future strategy of particle physics
We show that solutions to the first problem require premature modifications of gravity at scales no larger than 1011 GeV, while the second problem calls for many new particles at the weak scale
Since the Standard Model turns out to be asymptotically free only under the unphysical conditions g1 = 0, Mt = 186 GeV, Mτ = 0, Mh = 163 GeV, we explore some of its weak-scale extensions that satisfy the requirements for Total Asymptotic Freedom (TAF)
Summary
The naturalness problem of the Higgs mass is a central issue for the searches in the upcoming high-energy run of the LHC and, more generally, for defining the future strategy of particle physics. Even without specifying the model of softened gravity or knowing if any such theory exists, we can reach a general conclusion about them Since such theories must soften the ordinary power-law energy increase starting from a scale smaller or equal to ΛG, the gravitational interactions felt by SM particles remain weak at all energies, with couplings at most ∼ ΛG/MPl ∼ 10−7. We address the question of constructing viable observable sectors for theories with softened gravity Such observable sectors must be extensions of the SM that satisfy the TAF conditions, while restricting all new particles to live near the weak scale. The observation of “odd and unexpected” particles at the weak scale, seemingly unrelated to dynamical explanations of naturalness, but with the appropriate quantum numbers to satisfy the TAF conditions, are indicators for nonanthropic and non-dynamical solutions of naturalness, belonging to the class of theories with softened gravity.
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