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We explore the prospects for bounding the weak scale using the weak gravity conjecture (WGC), addressing the hierarchy problem by violating the expectations of effective field theory. Building on earlier work by Cheung and Remmen, we construct models in which a super-extremal particle satisfying the electric WGC for a new Abelian gauge group obtains some of its mass from the Higgs, setting an upper bound on the weak scale as other UV-insensitive parameters are held fixed. Avoiding undue sensitivity of the weak scale to the parameters entering the bound implies that the super-extremal particle must lie at or below the weak scale. While the magnetic version of the conjecture implies additional physics entering around the same scale, we demonstrate that this need not correspond to a cutoff for the Higgs potential or otherwise trivialize the bound. We stress that linking the WGC to the weak scale necessarily involves new light particles coupled to the Higgs, implying a variety of experimentally accessible signatures including invisible Higgs decays and radiative corrections in the electroweak sector. These models also give rise to natural dark matter candidates, providing additional paths to discovery. In particular, collective effects in the dark matter plasma may provide a telltale sign of the Abelian gauge group responsible for bounding the weak scale.
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We present a new solution to the hierarchy problem, where the Higgs mass is at its observed electroweak value because such a patch inflates the most in the early universe. If the Higgs mass depends on a field undergoing quantum fluctuations during inflation, then inflation will fill the universe with the Higgs mass that corresponds to the largest vacuum energy. The hierarchy problem is solved if the maximum vacuum energy occurs for the observed Higgs mass. We demonstrate this notion with a proof-of-principle model containing an axion, a modulus field and the Higgs, and show that inflation can be responsible for the weak scale.
We propose a framework in which Weinbergs anthropic explanation of the cosmological constant problem also solves the hierarchy problem. The weak scale is selected by chiral dynamics that controls the stabilization of an extra dimension. When the Higgs vacuum expectation value is close to a fermion mass scale, the radius of an extra dimension becomes large, and develops an enhanced number of vacua available to scan the cosmological constant down to its observed value. At low energies, the radion necessarily appears as an unnaturally light scalar, in a range of masses and couplings accessible to fifth-force searches as well as scalar dark matter searches with atomic clocks and gravitational-wave detectors. The fermion sector that controls the size of the extra dimension consists of a pair of electroweak doublets and several singlets. These leptons satisfy approximate mass relations related to the weak scale and are accessible to the LHC and future colliders.
In this letter we show that for observables which involve the measurement of weak charge in final states in hadronic collisions, the standard parton model picture breaks down at scales well above the weak scale due to nonfactorizable electroweak corrections at leading order in the power expansion. This implies that the resummation of these factorization-violating logarithms, which start at order $alpha_s^2, alpha_W^2 log^4(Q^2/M_W^2)$, cannot be accomplished solely by following standard DGLAP evolution equations; other techniques will be needed to systematically sum large logarithms.
The weak bosons, leptons and quarks are considered as composite particles. The interaction of the constituents is a confining gauge interaction. The standard electroweak model is a low energy approximation. The mixing of the neutral weak boson with the photon is a dynamical mechanism, similar to the mixing between the photon and the rho-meson in QCD. This mixing provides information about the energy scale of the confining gauge force. It must be less than 1 TeV. At and above this energy many narrow resonances should exist, which decay into weak bosons and into lepton and quark pairs. Above 1 TeV excited leptons should exist, which decay into leptons under emission of a weak boson or a photon. These new states can be observed with the detectors at the Large Hadron Collider in CERN.
Strong (sublattice or tower) formulations of the Weak Gravity Conjecture (WGC) imply that, if a weakly coupled gauge theory exists, a tower of charged particles drives the theory to strong coupling at an ultraviolet scale well below the Planck scale. This tower can consist of low-spin states, as in Kaluza-Klein theory, or high-spin states, as with weakly-coupled strings. We provide a suggestive bottom-up argument based on the mild $p$-form WGC that, for any gauge theory coupled to a fundamental axion through a $theta F wedge F$ term, the tower is a stringy one. The charge-carrying string states at or below the WGC scale $g M_mathrm{Pl}$ are simply axion strings for $theta$, with charged modes arising from anomaly inflow. Kaluza-Klein theories evade this conclusion and postpone the appearance of high-spin states to higher energies because they lack a $theta F wedge F$ term. For abelian Kaluza-Klein theories, modified arguments based on additional abelian groups that interact with the Kaluza-Klein gauge group sometimes pinpoint a mass scale for charged strings. These arguments reinforce the Emergent String and Distant Axionic String Conjectures. We emphasize the unproven assumptions and weak points of the arguments, which provide interesting targets for further work. In particular, a sharp characterization of when gauge fields admit $theta F wedge F$ couplings and when they do not would be immensely useful for particle phenomenology and for clarifying the implications of the Weak Gravity Conjecture.
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