The Hierarchy Problem and New Dimensions at a Millimeter

The Hierarchy Problem and New Dimensions at a Millimeter

November 26, 2024 | Nima Arkani-Hamed*, Savas Dimopoulos** and Gia Dvali†
This paper proposes a new framework to solve the hierarchy problem without relying on supersymmetry or technicolor. The framework unites gravitational and gauge interactions at the weak scale, which is considered the only fundamental short-distance scale in nature. The observed weakness of gravity at distances greater than 1 mm is due to the existence of n ≥ 2 new compact spatial dimensions much larger than the weak scale. The Planck scale is not fundamental; its large value is a consequence of the size of the new dimensions. Gravitons can propagate freely in the new dimensions, but Standard Model (SM) fields must be localized to a 4-dimensional manifold of weak scale thickness in the extra dimensions. This leads to observable signals in accelerator and laboratory experiments. For n=2, sub-millimeter gravity measurements may observe a transition from 1/r² to 1/r⁴ Newtonian gravity. The LHC and NLC could observe strong quantum gravitational interactions. SM particles may escape into the new dimensions, carrying away energy and reducing events with high transverse momentum. For certain compact manifolds, these particles may circle in the extra dimensions, periodically returning and depositing energy. The paper constructs a model with SM fields localized on the 4-dimensional throat of a vortex in 6 dimensions with a Pati-Salam gauge symmetry SU(4)×SU(2)×SU(2). The framework suggests that the weak scale is the only fundamental short-distance scale, and the hierarchy problem is trivially resolved. Gravity becomes comparable to gauge interactions at the weak scale. The Planck scale is not fundamental, and the effective 4-dimensional gravity is weakly coupled due to the large size of the extra dimensions. The SM fields are localized on a 4-dimensional submanifold, and the only fields propagating in the (4+n)-dimensional bulk are the graviton. The framework has dramatic experimental consequences, including the possibility of observing deviations in gravity at sub-millimeter distances and the potential for high-energy collisions to produce particles that escape into the extra dimensions. The framework is also consistent with astrophysical constraints and does not conflict with current data. The paper presents a realistic model with SM fields localized on the four-dimensional throat of a vortex in 6 dimensions, incorporating the ideas of the paper. The model includes a Pati-Salam gauge symmetry and a singlet scalar field that forms a vortex. The gauge group is spontaneously broken inside the vortex, and the SM fermions are localized as chiral zero modes. The model predicts a rich phenomenology, including the possibility of observing new particles and interactions at high energies. The framework offers a new perspective on fundamental issues in particle physics and cosmology, including the hierarchy problem and the need for supersymmetry. The framework is consistent with early universe cosmology, including primordial nucleosynthesis, and may accommodate weak-scale inflation and baryogenesis. The paper concludes that the framework provides a new and exciting approachThis paper proposes a new framework to solve the hierarchy problem without relying on supersymmetry or technicolor. The framework unites gravitational and gauge interactions at the weak scale, which is considered the only fundamental short-distance scale in nature. The observed weakness of gravity at distances greater than 1 mm is due to the existence of n ≥ 2 new compact spatial dimensions much larger than the weak scale. The Planck scale is not fundamental; its large value is a consequence of the size of the new dimensions. Gravitons can propagate freely in the new dimensions, but Standard Model (SM) fields must be localized to a 4-dimensional manifold of weak scale thickness in the extra dimensions. This leads to observable signals in accelerator and laboratory experiments. For n=2, sub-millimeter gravity measurements may observe a transition from 1/r² to 1/r⁴ Newtonian gravity. The LHC and NLC could observe strong quantum gravitational interactions. SM particles may escape into the new dimensions, carrying away energy and reducing events with high transverse momentum. For certain compact manifolds, these particles may circle in the extra dimensions, periodically returning and depositing energy. The paper constructs a model with SM fields localized on the 4-dimensional throat of a vortex in 6 dimensions with a Pati-Salam gauge symmetry SU(4)×SU(2)×SU(2). The framework suggests that the weak scale is the only fundamental short-distance scale, and the hierarchy problem is trivially resolved. Gravity becomes comparable to gauge interactions at the weak scale. The Planck scale is not fundamental, and the effective 4-dimensional gravity is weakly coupled due to the large size of the extra dimensions. The SM fields are localized on a 4-dimensional submanifold, and the only fields propagating in the (4+n)-dimensional bulk are the graviton. The framework has dramatic experimental consequences, including the possibility of observing deviations in gravity at sub-millimeter distances and the potential for high-energy collisions to produce particles that escape into the extra dimensions. The framework is also consistent with astrophysical constraints and does not conflict with current data. The paper presents a realistic model with SM fields localized on the four-dimensional throat of a vortex in 6 dimensions, incorporating the ideas of the paper. The model includes a Pati-Salam gauge symmetry and a singlet scalar field that forms a vortex. The gauge group is spontaneously broken inside the vortex, and the SM fermions are localized as chiral zero modes. The model predicts a rich phenomenology, including the possibility of observing new particles and interactions at high energies. The framework offers a new perspective on fundamental issues in particle physics and cosmology, including the hierarchy problem and the need for supersymmetry. The framework is consistent with early universe cosmology, including primordial nucleosynthesis, and may accommodate weak-scale inflation and baryogenesis. The paper concludes that the framework provides a new and exciting approach
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