Pseudo-Nambu-Goldstone Dark Matter in Flux Compactification

TL;DR

The paper tackles the challenge of a dark matter candidate that yields the observed relic density while remaining consistent with stringent direct-detection limits. It proposes pseudo-Nambu-Goldstone DM arising as the Wilson-line zero mode in a six-dimensional U(1)_χ theory on a magnetized torus, leveraging a geometric shift symmetry from extra-dimensional translations. Two realizations are analyzed—χ-neutral and χ-charged Higgs sectors—both exhibiting momentum-transfer suppression of the direct-detection amplitude via t-channel cancellation and satisfying relic abundance, unitarity, and Higgs-invisible-width constraints, with viable DM masses spanning tens of GeV to multi-TeV. The results connect DM mass and Higgs/flux parameters to the compactification scale, typically placing the KK scale at the TeV region and maintaining perturbativity (g/L < 1), thereby offering a geometrically motivated and cosmologically viable pNG DM scenario.

Abstract

We study a six-dimensional U(1)$_χ$ gauge theory compactified on a magnetized torus, where the zero mode of the extra-dimensional gauge field (a Wilson-line (WL) scalar field) plays the role of a pseudo-Nambu-Goldstone (pNG) dark matter (DM) candidate. The pNG DM is naturally included by construction without introducing an additional scalar field. We show that the leading spin-independent DM-nucleus amplitude is suppressed by momentum transfer in our model as expected from the pNG DM model. This suppression allows the model to evade the current severe direct-detection bounds while achieving the observed thermal relic abundance in well-defined regions of parameter space.

Figures (8)

• Figure 1: $t$-channel $\chi f \to \chi f$ scattering mediated by $h_{1,2}$.
• Figure 2: DM mass $m_\chi$ vs $v_h/v_s$
• Figure 3: DM mass $m_\chi$ vs effective flux $fL^2$
• Figure 5: DM mass vs effective gauge coupling $g/L$
• Figure 6: Zoom-in of Fig. \ref{['fig:Q>0_300GeV_a']}