abstract

Recently, we have developed a method called “Symmetry Finder” (SF) for hunting the reparametrization symmetry in the three-neutrino system in matter. Here, we apply SF to the Denton et al. (DMP) perturbation theory extended by including unitarity violation (UV), a possible low-energy manifestation of physics beyond the \(\nu \)SM. Implementation of UV into the SF framework yields the additional two very different constraints, which nonetheless allow for remarkably consistent solutions, the eight DMP-UV symmetries. Treatment of one of the constraints, the genuine non-unitary part, leads to the key identity which entails the UV \(\alpha \) parameter transformation only by rephasing, which innovates the invariance proof of the Hamiltonian. The quantum mechanical nature of the symmetry dictates the both \(\nu \)SM and UV variables to transform jointly, through which the response of the two sectors are related to reveal their interplay. Thus, the symmetry can serve as a tool for diagnostics, probing the interrelation between the \(\nu \)SM and a low-energy description of new physics. The problem of SF symmetry in vacuum is revisited to complete eight symmetries akin to DMPs.

abstract

Particle physics models with extra dimensions of space (EDSs) and branes shed new light on electroweak and flavor hierarchies with a rich TeV scale phenomenology. This article highlights new model building issues with EDSs and branes, arising in the framework of weakly nonlocal field theories. It is shown that a brane-localized field is still delocalized in the bulk at a small distance from the brane position: fields localized on such distant fuzzy branes are thus allowed to interact directly with suppressed couplings. Directions for model building are also given: (i) with fuzzy branes, a new realization of split fermions in an EDS is presented, naturally generating flavor hierarchies; (ii) with a warped EDS, the usual warp transmutation of a brane-localized mass term is revisited, where it is shown that the nonlocal scale is also redshifted and provides a smooth UV cutoff for the Higgs boson mass. This framework is expected to have natural UV completions in string theory, but the possibility to embed it in recent UV complete weakly nonlocal quantum field theories is commented.