Are the Dirac particles of the Standard Model dynamically confined states in a higher dimensional flat space?

Abstract

Some time ago Rubakov and Shaposhnikov suggested that elementary particles might be excitations trapped on a soliton in a flat higher dimensional space. They gave as an example φ 4 theory in five dimensions with a bosonic excitation on a domain wall φ cl in the fifth dimension. They also trapped a chiral Dirac particle on the domain wall with the interaction lagrangian gψφψ. The field equation for the Dirac field was −i 4 µ=0 γ µ ∂ µ ψ−gφψ = 0. We show that a Dirac equation in eight flat dimensions with −gφ replaced by a harmonic-oscillator "potential" in the four higher dimensions (plus a large constant M 0 ) generates bound states in approximate SU (4) × SU (2) representations. These representations have corresponding "orbital" times "spin" quantum numbers and bear some resemblance to the quarks and leptons of the Standard Model. Soliton-theory suggests that the harmonic-oscillator potential should rise only a finite amount. This will then limit the number of generations in a natural way. It will also mean that particles with sufficient energy might escape the well altogether and propagate freely in the higher dimensions. It may be worthwhile to search for a soliton (instanton?) which can confine Dirac particles in the manner of the harmonic-oscillator potential.1

Matter Localization and Resonant Deconfinement in a Two-Sheeted Space–time

“…Since, the potential is in fact the sum of all external influences acting on the particle, it becomes obvious that the confinement arises mainly from environmental interactions. Such an explanation of the matter confinement in a multidimensional spacetime is elegant in several aspects: first, it does not require any ad-hoc bulk field nor any extradimensional gravitational trapping mechanism [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Secondly, it is quite remarkable that the model suggests that the confinement of fermions may arise from usual 4D interactions (particle scattering, EM interactions, gravitational fields...).…”

“…For a neutron, the Eq. (12) indicates that the maximum amplitude of the oscillations of probability is 2.5 · 10 −16 . This value is so tiny that it is hard to believe that any particle oscillations might be observed in the physical world.…”

“…Since the existence of such fields is still the subject of debate [24], the credibility of these scenarios can be reasonably questioned. In parallel, some attempts have tried to extend the hypothetical graviton capability of moving through the bulk [1,6,7,8] to the case of massive particles as well [12,15,16]. As a result, there could be a possibility for highly massive or energetic particles to acquire a non zero extradimensional momentum and escape from the branes to propagate into the bulk.…”

“…In some string theory inspired models, the confinement arises as a natural consequence of the fact that particles are open strings whose endpoints are attached on Dp-branes [1,2]. Other approaches postulate the existence of domain walls in which standard model particles could be entrapped [9][10][11][12][13][14][15][16][17][18][19][20]. Among earlier works [9,10,11], Rubakov and Shaposhnikov [10] suggested long time ago that the wave function of fermion zero modes could concentrate near domain walls, generating 4D massless chiral fermions attached to them.…”

“…Such conservative point of view adopts the idea that no interaction (except gravitation) can propagate into the bulk or between adjacent branes [6,7,8]. The problem is then to find a physically reasonable mechanism that could effectively constrain the particles to stay confined in a lower dimensional spacetime sheet [1,2,[9][10][11][12][13][14][15][16][17][18][19][20]. In some string theory inspired models, the confinement arises as a natural consequence of the fact that particles are open strings whose endpoints are attached on Dp-branes [1,2].…”