Leading bounds on micro- to picometer fifth forces from neutron star cooling

Abstract

The equivalence principle and the inverse-square law of gravity could be violated at short distances ($10^{-6}$ to $10^{-12}$ meters) by scalars sporting a coupling $g_N$ to nucleons and mass $\mathrm{eV}\lesssim m_φ\lesssim\rm MeV$. We show for the first time that stringent bounds on the existence of these scalars can be derived from the observed cooling of nearby isolated neutron stars (NSs). Although NSs can only be used to set limits comparable to the classic SN 1987A cooling bound in the case of pseudoscalars such as the QCD axion, the shallow temperature dependence of the scalar emissivity results in a huge enhancement in the effect of $φ$ on the cooling of cold NSs. As we do not find evidence of exotic energy losses, we can exclude couplings down to $g_N\lesssim 5 \times 10^{-14}$. Our new bound supersedes all existing limits on scalars across six orders of magnitude in $m_φ$. These conclusions also extend to Higgs-portal models, for which the bound on the scalar-Higgs mixing angle is $\sinθ\lesssim 6\times 10^{-11}$.

Figures (6)

• Figure 1: Our new limit on the scalar-nucleon coupling $g_N$ at 95% CL as a function of the scalar mass from neutron star cooling. We show the limit alongside other astrophysical bounds (green) Hardy:2016kmeBottaro:2023gepHardy:2024gwy and laboratory tests of the inverse-square law (gray) Chen:2014oda. For comparison with the conventional parametrization of fifth forces, we also show the coupling in terms of the equivalent strength of a Yukawa force relative to gravity, $|\alpha|$, along the right-hand axis, and the range of that force $\lambda = m_\phi^{-1}$ along the top axis. We assume equal coupling to protons and neutrons.
• Figure S1: Schematic pair of Feynman diagrams contributing to nucleon-nucleon bremsstrahlung. The dark bubble represents an insertion of the nuclear interaction potential.
• Figure S2: Cooling light-curves derived from the best fit NS model for J1605 assuming no BSM physics. We compare the behavior of the light-curves for the unperturbed NS model ($g_N=0$) and by adding on top of the NS model the emissivity of scalars with coupling strength $g_N=2\times10^{-13}$.
• Figure S3: Full landscape of constraints on the scalar-nucleon coupling for scalar masses smaller than $\sim$keV. The bound from this work is shown in green. Laboratory constraints from tests of the violation of the inverse square law and the weak equivalence principle are shown in red and purple respectively. The references for these bounds are as follows: MICROSCOPE Berge:2017ovyBerge:2021yyeMICROSCOPE:2022doy, Eöt-Wash Smith:1999crKapner:2006siLee:2020zjt, Wuhan Ke:2021jtj, HUST Tu:2007zzYang:2012zzbTan:2016vwuTan:2020vpf, IUPUI Chen:2014oda.
• Figure S4: Limits on the scalar coupling to nucleons multiplied by the pseudoscalar coupling to electrons. We show the combined astrophysical bound on this coupling combination in green, which is derived by multiplying the neutron star cooling bound from this work with the tip-of-the-red-giant branch bound from Ref. Capozzi:2020cbu. Existing laboratory bounds are shown in purple (Eöt-Wash Heckel:2008hw, QUAX Crescini:2017uxs, NIST Wineland:1991zz, $e^+ e^-$ penning trap Fan:2023hci, SMILE Lee:2018vaq), while future projections are shown as dashed lines (ACME Agrawal:2023lmw, ultracold molecules Agrawal:2023lmw, QUAX Crescini:2016lwj). The combined Lab $\times$ Astro bound is derived by multiplying the laboratory bound on the scalar-nucleon coupling from Fig. \ref{['fig:ScalarNucleon']} with the red giant bound on pseudoscalars Capozzi:2020cbu.