Softened Gravity and the Extension of the Standard Model up to Infinite Energy

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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 fulfil 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 g₁ = 0, Mₜ = 186 GeV, Mτ= 0, Mₕ = 163 GeV, we explore some of its weak-scale extensions that satisfy the requirements for TAF.