Resonance mass spectra of gravity and fermion on Bloch branes

Abstract

In this paper, by presenting the potentials of Kaluza-Klein (KK) modes in the corresponding Schrödinger equations, we investigate the localization and resonances of gravity and fermion on the symmetric and asymmetric Bloch branes. We find that the localization properties of zero modes for gravity and fermion in the symmetric brane case are the same, whereas, for the asymmetric brane case, the fermion zero mode is localized on one of the sub-branes, while the gravity zero mode is localized on another sub-brane. The spectra of the gravity and the left-or right-handed fermion are composed of a bound zero mode and a series of gapless continuous massive KK modes.Among the continuous massive KK modes, we obtain some discrete gravity and fermion resonant (quasilocalized) KK states on the brane, which have a finite probability of escaping into the bulk.The KK states with lower resonant masses have a longer lifetime on the brane. And the number of the resonant KK states increases linearly with the width of the brane and the scalar-fermion coupling constant, but it decreases with the asymmetric factor β. The structure of the resonance spectrum is investigated in detail.

Multiresonance modes in sine–Gordon brane models

“…Moreover, the zero mode of the equation (19) is not bound on the brane, as showed in figure (4). Thus, we cannot exclude the possibility of tachyonic states [33,38].…”

“…The choice of the integration interval z b = 0.1z max does not interfere with the values of the masses to the possible resonance modes [15]. A symmetric brane should result in even and odd solutions ofŪ (z) [38]. Hence we use the initial conditions U (0) = 1 and U (0) = 0 for the even solutions and the conditions U (0) = 0 and U (0) = 1 for the odd solutions [38].…”

“…A symmetric brane should result in even and odd solutions ofŪ (z) [38]. Hence we use the initial conditions U (0) = 1 and U (0) = 0 for the even solutions and the conditions U (0) = 0 and U (0) = 1 for the odd solutions [38].…”

Hybrid Bloch brane

“…3 offer explicit possibilities to implement the hybrid Bloch brane scenario, and the results open up new issues, such as the ones investigated before in the case of the Bloch brane, namely the study of degeneracy and criticality, fermion localization, gauge field localization, and graviton resonances [15][16][17][18][19][20][21][22][23]25,26]. We end our work in Sect.…”

“…[14] the authors suggested a brane scenario described by two real scalar fields coupled with gravity, the second field contributing to propitiate internal arrangement, implementing therefore the so-called Bloch brane model. This framework was then explored by several authors in different situations, such as in the study of criticality and degeneracy, fermion localization, gauge field localization, graviton resonances, and so forth [15][16][17][18][19][20][21][22][23][24][25][26].…”