New origin for approximate symmetries from distant breaking in extra dimensions

The recently proposed theories with TeV-scale quantum gravity do not have the usual ultraviolet desert between ∼ 103 −1019 GeV where effective field theory ideas apply. Consequently, the success of the desert in explaining approximate symmetries is lost, and theories of flavor, neutrino masses, proton longevity or supersymmetry breaking, lose their usual habitat. In this paper we show that these ideas can find a new home in an infrared desert: the large space in the extra dimensions. The main idea is that symmetries are primordially exact on our brane, but are broken at O(1) on distant branes. This breaking is communicated to us in a distance-suppressed way by bulk messengers. We illustrate these ideas in a number of settings: 1) We construct theories for the fermion mass hierarchy which avoid problems with large flavor-changing neutral currents. 2) We re-iterate that proton stability can arise if baryon number is gauged in the bulk. 3) We study limits on light gauge fields and scalars in the bulk coming from rare decays, astrophysics and cosmology. 4) We remark that the same ideas can be used to explain small neutrino masses, as well as hierarchical supersymmetry breaking. 5) We construct a theory with bulk technicolor, avoiding the difficulties with extended technicolor. There are also a number of interesting experimental signals of these ideas: 1) Attractive or repulsive, isotope dependent sub-millimeter forces ∼ 106 times gravitational strength, from the exchange of light bulk particles. 2) Novel Higgs decays to light generation fermions plus bulk scalars. 3) Collider production of bulk vector and scalar fields, leading to γ or jet+ missing energy signals as in the case of bulk graviton production, with comparable or larger rates. 1 Life without the desert The standard paradigm of particle physics dates back to the advent of grand unified theories [1] or perhaps even further back to Fermi’s theory of beta decay. Its premise is that there are two fundamental scales –the weak and Planck masses– separated by a large “desert”. The existence of the desert plays a fundamental role in formulating and solving problems in particle physics. Examples include the physics of flavor, neutrino masses and of unification. Much of the physics of the early universe takes place when the temperature of the universe is in the desert. The very hierarchy problem is simply the statement of the large size of the desert. This suggested a new proposal for solving the hierarchy problem simply postulating that the desert does not exist: namely that the fundamental scale of gravity is in fact identical to the weak interaction scale ∼ TeV [2, 3, 4]. In this new paradigm, the observed weakness of gravity at long distances is due the existence of new sub-millimeter spatial dimensions into which gravity spreads. The standard model fields are localized to a (3 + 1)-dimensional wall or “3-brane”. The hierarchy problem becomes isomorphic to the problem of the large size of the extra dimensions. Some ideas for stabilizing large dimensions have been explored in [5, 6]. Whereas the absence of a desert may allow for a novel approach to the hierarchy problem, it also deprives us from all mechanisms whose existence relied on the desert. This includes baryon stability, naturalness of approximate lepton number conservation and neutrino masses, as well as approximate neutral flavor conservation which are some of the successes of the nonsupersymmetric standard model . In addition there are phenomena and mechanisms in extensions of the standard model such as the supersymmetric gauge coupling constant unification, electroweak breaking in technicolor or susy, supersymmetry breaking as well as models of flavor which largely relies on the existence of the desert. It is the purpose of this paper to find new and natural mechanisms to account for some of these phenomena within the new framework of theories without a desert. While we have been deprived of the desert in short-distance scales between the weak and Planck scales, we have gained the large space in the extra Note that the naturallness of these successes of the standard model is lost in any ∼ TeV extension of the standard model, including low energy supersymmetry