Formation of Asymmetrical Two-Brane Structure and its Possible Manifestation

TL;DR

The paper investigates a six-dimensional thick two-brane world derived from $f(R)$ gravity, predicting brane-localized field profiles with brane-1 hosting Standard Model-like physics and brane-2 containing superheavy partners. It shows that fields distributed across both branes split into two independent effective 4D fields with brane-specific parameters, while gauge fields remain in the bulk to preserve charge universality. The Higgs vacuum expectation value and fermion masses become brane-dependent, with brane-2 lacking observers, leading to potential dark matter candidates and inter-brane interactions that could generate ultra-high-energy phenomena. Stability analyses indicate robust brane structures against perturbations, and the framework suggests observable consequences in dark matter phenomenology and high-energy astrophysics, warranting further constraints on brane geometry and couplings.

Abstract

In this paper, we consider the class of extra-dimensional models with two branes and show that each field of the Standard Model must be localized on both neighboring branes, whose asymmetry is of great importance. The discussion is conducted in the framework of a previously developed model. Here we show that the Higgs vacuum average is brane-dependent. As the result, fermion masses on the two branes are also different. The second brane (brane-2) lacks observers, eliminating the need for fine-tuning; consequently the particle masses remains of the order of the initial energy scale of the universe formation. Such superheavy charged leptons may serve as a small component of dark matter. Additionally, we show that inter-brane interactions mediated by photons enable massive fermions in brane-2 to act as sources of ultra-high-energy particles. The gauge fields are uniformly distributed in the bulk, ensuring charge universality.

Figures (3)

• Figure 1: The typical metric functions, $\gamma(u)$ - solid line, $r(u)$ - dashed line. The interval is normalized so that the endpoints are $u_1=0,\quad u_2=\pi$ in the units $m_D=1$. Their shapes depends on additional conditions and are characterized by zeros at the endpoints. The parameter values are $p= 1/3 , q=1/5 , A=2$. As was shown in Popov:2024nax, test particles move toward the endpoints ($u=0$ or $u=\pi$ in this case) along the geodesics derived from the metric containing function $\gamma(u)$.
• Figure 2: Fermion distribution over the extra dimensions. The metric functions are represented in Fig.\ref{['metricfig']}. The localizations near $u_1=0$ and $u_2=\pi$ are evident.
• Figure 3: The Higgs field distribution over the internal coordinate $u$ is specific to each brane. The background metric functions are represented in Fig.\ref{['metricfig']}. Additional conditions are $Y_H(1.5)=0,\, Y_H'(1.5)=10^{-2}$. The sharp peaks which define the branes are the result of numerical solutions to equation \ref{['boxUU']} in wide range of parameters. The Higgs field is approximately zero in the interval between two black points. The fermion fields are also concentrated near the branes, see Fig.\ref{['fermifig']}.