Towards theory constraints on ultralight dark matter from quantum gravity

TL;DR

The paper investigates whether ultralight scalar dark matter (ULDM) couplings to the Standard Model through dimension-five operators can be generated by quantum gravity within the framework of asymptotically safe (AS) gravity. Employing a functional renormalization group approach with an Einstein–Hilbert gravity sector and a minimal ULDM–gauge sector, it computes the beta functions for the ULDM mass $m_\phi^2$ and the dimension-five coupling $\zeta$ to $F^{\mu\nu}F_{\mu\nu}$, obtaining that $\beta_{\zeta}$ is proportional to $\zeta$ and thus $\zeta_* = 0$ at the AS fixed point. The study shows that ULDM–gauge interactions are not generated in AS gravity, and perturbative quantum gravity cannot induce $\zeta$ either; when compared with other dimension-five operators (ALP–photon, Weinberg operator), the results suggest a general tendency for such operators to be irrelevant at AS fixed points, reinforcing the predictive power of AS gravity. Consequently, nuclear-clock experiments attempting to probe ULDM via these dimension-five couplings would not detect such effects in AS gravity, although non-minimal UV completions could alter this picture; the work also outlines avenues for refining the analysis, including Lorentzian-signature studies and extended truncations.

Abstract

Ultralight scalar dark matter may couple to the Standard Model through dimension-five operators that contain the field-strength tensors of the gauge interactions. Recent progress in nuclear clocks is projected to increase the sensitivity to such couplings by several orders of magnitude. Future experimental constraints may even have Planck-scale sensitivity, calling for a study of such couplings in a framework that includes quantum gravity. We take a first step towards providing the theoretical constraints on such couplings that arise in asymptotically safe gravity. We find evidence that such couplings vanish in asymptotically safe gravity and are also not generated in a perturbative quantum-gravity regime that describes quantum gravity as an effective field theory.

Figures (3)

• Figure 1: The first line contributes to the running scalar field mass $m_\phi$ and anomalous dimension $\eta_\phi$. The second line contributes to the gauge anomalous dimension $\eta_A$. Finally, the third and fourth lines give the running of $\zeta$. Double lines represent graviton fields, single lines scalar fields, and wiggly lines gauge fields. All vertices and propagators are fully dressed. The cross represents the regulator insertion $k\partial_k \mathfrak R_k$, which must be applied to all loop propagators in turn. Symmetrization with respect to exchange in external momenta is understood.
• Figure 2: Regions of relevance of the critical exponents of the squared scalar mass and the ULDM-photon-coupling, as a function of the gravitational sector fixed point values. Different types of hatchings indicate the regions where different critical exponents are relevant. In the unhatched region, both couplings are irrelevant. The gradient indicates the value of the photon anomalous dimension, with darker (lighter) colors indicating smaller (larger) values. The dashed line indicates where $|\eta_A|=2$, and delimits the region up until which we trust our approximation. In the diamond-hatched region, both couplings are relevant, and can thus yield viable ULDM phenomenology. This region is however beyond the region of trust of the approximation.
• Figure 3: Regions of relevance of the ALP and $\zeta$ coupling, as a function of the gravitational sector fixed point values. As in \ref{['fig:GFP_crits_lambda_g_LdW_gauge']}, the gradient indicates the value of the photon anomalous dimension, with darker (lighter) colors indicating smaller (larger) values. The dashed line indicates where $|\eta_A|=2$, and delimits the region up until which we trust our approximation.