On Kaluza-Klein States from Large Extra Dimensions

TL;DR

This paper develops a concrete brane-world scenario in which gravity propagates in a 4+n dimensional bulk while gauge and matter fields are confined to a 3+1 dimensional brane. By compactifying on a torus, the authors show that each KK level contains one massive spin-2 state, (n−1) massive spin-1 states, and n(n−1)/2 massive spin-0 states, all degenerate with mass m_{ vec} = 2π|{ vec}|/R, which reorganize through a geometric Higgs-like mechanism. They derive the complete couplings of these KK states to Standard Model fields, finding that spin-1 KK modes decouple and spin-0 KK modes couple only via the dilaton trace, and provide the full interacting Lagrangian and Feynman rules. The work further analyzes low-energy phenomenology at energies above 1/R but below M_S, deriving effective 4-fermion and f f VV interactions from KK sums, exploring real KK emission and one-loop corrections from virtual KK states, and highlighting that KK sums yield observable effects despite the Planck-suppressed couplings. The results point to potentially detectable signatures at TeV-scale experiments and motivate cosmological considerations of KK states in the early universe.

Abstract

We consider the novel Kaluza-Klein (KK) scenario where gravity propagates in the $4+n$ dimensional bulk of spacetime, while gauge and matter fields are confined to the 3+1 dimensional world-volume of a brane configuration. For simplicity we assume compactification of the extra $n$ dimensions on a torus with a common scale $R$, and identify the massive KK states in the four-dimensional spacetime. For a given KK level $\vec{n}$ there are one spin-2 state, $(n-1)$ spin-1 states and $n(n-1)/2$ spin-0 states, all mass-degenerate. We construct the effective interactions between these KK states and ordinary matter fields (fermions, gauge bosons and scalars). We find that the spin-1 states decouple and that the spin-0 states only couple through the dilaton mode. We then derive the interacting Lagrangian for the KK states and Standard Model fields, and present the complete Feynman rules. We discuss some low energy phenomenology for these new interactions for the case when 1/R is small compared to the electroweak scale, and the ultraviolet cutoff of the effective KK theory is on the order of 1 TeV.

Figures (6)

• Figure 1: Feynman diagrams for (a) four-fermion interactions and (b) ${\overline f}f VV$ interactions. We represent KK states by double-sinusoidal curves.
• Figure 2: Feynman diagrams for $e^-e^+\rightarrow\gamma+KK$.
• Figure 3: One-loop self-energy diagrams of the scalar particle.
• Figure 4: Three-point vertex Feynman rules. The KK states are plot in double-sinusoidal curves. The symbols $C_{\mu\nu,\rho\sigma}$, $D_{\mu\nu,\rho\sigma}(k_1,k_2)$ and $E_{\mu\nu,\rho\sigma}(k_1,k_2)$ are defined in Eqs. (\ref{['C']}), (\ref{['D']}) and (\ref{['E']}) respectively. $m_\Phi$, $m_A$ and $m_\psi$ are masses of the scalar, vector and fermion. $\omega=\sqrt{2\over3(n+2)}$, $\kappa=\sqrt{16\pi G_N}$ and $\xi$ is the gauge-fixing parameter.
• Figure 5: Four-point vertex Feynman rules. $g$ is the gauge coupling and $f^{abc}$ the structure constant of the Lie algebra, $gT^a\rightarrow eQ_f$ for QED. The symbols $C_{\mu\nu,\rho\sigma}$ and $F_{\mu\nu,\rho\sigma\lambda}(k_1,k_2,k_3)$ are defined in Eqs. (\ref{['C']}) and (\ref{['F']}).