Stellar cooling limits on KK gravitons and dark dimensions

TL;DR

This work revisits stellar cooling bounds on KK gravitons in the dark-dimension framework, introducing resonant in-medium photon mixing and a pion-induced production channel to the standard bremsstrahlung mechanism. Across red giants, neutron stars, and SN 1987A, the authors find that SN 1987A sets the strongest constraints, with the pion channel often dominating the emissivity over bremsstrahlung. For two and three extra dimensions, they derive bounds on the KK mass scale of $m_{ m KK} \gtrsim 0.6\,\mathrm{eV}$ and $m_{ m KK} \gtrsim 500\,\mathrm{eV}$, respectively, while one extra dimension remains less constrained than laboratory tests. They also explore decays within the KK tower, showing that KK-number violation can weaken SM-decay signals relative to cooling bounds, though decays could still offer detectable signatures in future observations such as Cas A or nearby SN events. Overall, the analysis highlights the critical role of pion physics and SN models in constraining dark-dimension scenarios and outlines paths for improving robustness and reach in forthcoming work.

Abstract

We revisit cooling bounds on light Kaluza-Klein (KK) gravitons, as arise in the dark dimension scenario, considering red giants, neutron stars, and supernovae. In addition to bremsstrahlung, we account for two novel production channels: resonant mixing with the in-medium photon and a pion-induced process in supernovae. The strongest limits arise from SN 1987A, with the emissivity from the pion process exceeding that from bremsstrahlung by a factor of a few. Given present uncertainties, we obtain a bound on the KK mass scale of $m_{\rm KK}\gtrsim 0.6\,{\rm eV}$ $(\gtrsim 500\,{\rm eV})$ for 2 (3) extra dimensions. Improved understanding of the properties of pions in supernovae could strengthen these limits to roughly ${\rm eV}$ $({\rm keV})$. For 1 extra dimension, the bounds are weaker than those from laboratory searches. We also show that constraints from KK graviton decays to Standard Model particles are less stringent than the cooling bounds if there is KK number violation at the level typically assumed in the dark dimension scenario, although these bounds could be strengthened by future observations.

Figures (6)

• Figure 1: The energy-momentum relation of a KK graviton of mass $m_h=5{\, {\rm MeV}}$ (dashed black). $m_h$ determines the plasma frequencies $\omega_p$, and hence the locations in a star, where resonant production occurs. For the longitudinal mode, there is a resonance whenever $\omega_p \geq m_h$. For transverse modes, there is a resonance when $\omega_p\in \left[\sqrt{2/3}m_h, m_h\right]$. The regions spanned by all such longitudinal (transverse) photon dispersions in a typical protoneutron star are shown in shaded red (blue) (specifically the $20M_\odot$ progenitor model discussed in Section \ref{['sec: supernova']}, which has maximum $\omega_p\simeq 14\,{\rm MeV}$). Representative dispersion curves are plotted in bold red (blue), and the resonance points where they intersect the KK graviton curve are marked with solid dots.
• Figure 2: The regions within a protoneutron star core where the different resonances can occur for a KK graviton of mass $5{\, {\rm MeV}}$, using the same model of the star as in Figure \ref{['fig:dispersions1']}. A longitudinal resonance occurs whenever $m_x\leq\omega_p(r)$, and therefore throughout the region $0<r<r_1$ where $\omega_p(r_1)=m_x$ (shaded red). In the limit that the electrons are relativistic, a transverse resonance only occurs if $\omega_p(r)\leq m_x \leq \sqrt{3/2} \omega_p(r)$. This therefore takes place in some shell $r_1<r<r_2$ where $\omega_p(r_2)=\sqrt{2/3}m_x$ (shaded blue). Here $r_1\approx16{\, {\rm km}}$ and $r_2\approx18{\, {\rm km}}$.
• Figure 3: Left: The observed photon luminosity and age of the neutron star $J1605$ with uncertainties (red), and the best fit cooling curves assuming only Standard Model energy loss (blue, "SM") and including also energy loss to KK gravitons with $2$ extra dimensions of radius $2\times 10^{-4}\,{\rm m}$ (dashed purple). Combining the likelihoods over all $5$ neutron stars, the latter theory is excluded. Right: The energy loss to photons ($L_\gamma^\infty$), neutrinos ($L_\nu^\infty$), and KK gravitons ($L_h^\infty$) in the same large extra dimensional theory as plotted in the left panel.
• Figure 4: The four Feynman diagrams contributing to the pion process $p \pi^-\rightarrow nh$.
• Figure 5: The energy emission spectrum $dQ/(d\omega dVdt)$ to a KK graviton of mass $50\,{\rm MeV}$ (with energy $\omega$) at a typical point in a protoneutron star (see main text). We show the spectra from bremsstrahlung emission ("Brem.") and the pion process. For the latter, we plot the spectra obtained with the two sets of assumptions described in the main text (labelled "$\pi^-$(a)" and "$\pi^-$(b)").