Speaker
Description
We study the neutrino sector of an eight-dimensional two-brane model based on $f(R)$ gravity. The metric is warped:
$ds^{2} = e^{2\gamma(u)}\eta_{\mu\nu}dx^{\mu}dx^{\nu} - du^{2} - r^{2}(u)\,d\Omega^{2}_{n-1}.$
Here $u$ is the radial extra coordinate, and the remaining three coordinates parametrise a compact internal manifold. The classical field equations admit a countable family of solutions in which $\gamma(u)$ and $r(u)$ vanish at two endpoints $u_{1}$ and $u_{2}$. Matter fields accumulate near these endpoints. A pair of four-dimensional branes therefore forms spontaneously, as a solution of the gravitational dynamics. Nothing is assumed about their existence, position or tension.
We then derive the consequences of this geometry for the matter sector. Massless bulk fermions obey
$\left(\partial_{u} + \frac{\partial_ur^{}(u)}{2r(u)} + 2\partial_u\gamma(u)\right) Y(u) = 0$
along $u$. The solution is sharply peaked at $u_{1}$ and $u_{2}$. On the compact factor, a normalisable chiral zero mode requires a suitable background gauge field. Each bulk fermion then has one chiral zero mode per brane, and the two sets of modes are effectively decoupled, because $|Y(u)|^{2}$ is exponentially small between the branes. The Higgs vacuum expectation value differs on the two branes, so masses and couplings on brane-2 are free up to $m_{D}$. The gauge zero mode behaves differently: it is constant along $u$, so the $Z$ boson is common to both branes.
Dimensional reduction of the neutral-current action reflects this structure. Besides the canonical on-brane vertices, it produces off-diagonal neutrino–$Z$ couplings weighted by the overlap of the two profile functions. Exponential localisation makes this overlap of order $\exp\left[-m(u_{2}-u_{1})\right]$, that is about $10^{-35}$ for an interbrane distance $u_{2}-u_{1} \approx 80\,m_{D}^{-1}$ and $m \sim 1$. The geometry thus supplies an exponentially small parameter without fine-tuning. A seesaw with the brane-2 vacuum expectation value places a superheavy sterile neutrino on the hidden brane, and the off-diagonal vertex lets it decay at a rate suppressed by the squared overlap. The resulting lifetime is cosmological, so the particle is a dark-matter candidate.
The decay $\nu^{(2)} \to \nu^{(1)} Z^{\ast} \to \nu^{(1)}\nu^{(1)}\bar{\nu}^{(1)}$ gives a quasi-monochromatic flux peaked at $E_{\nu} \sim m_{2}$. We estimate the diffuse rate and compare it with IceCube and KM3NeT data, including KM3-230213A at $2.2 \times 10^{8}\,\mathrm{GeV}$. The competing annihilation channel $\bar{\nu}^{(2)}\nu^{(2)} \to Z^{\ast} \to \bar{\nu}^{(1)}\nu^{(1)}$ falls about 18 orders of magnitude short, because its production rate scales as $m_{2}^{-4}$.
