Probing mixed-state dark matter and $b \to s μ^+μ^-$ anomalies in a scalar-assisted baryonic gauge theory

TL;DR

This work analyzes a gauged U(1)_B extension of the Standard Model featuring a baryon-charged scalar mediator and a mixed-state fermionic dark matter candidate, supplemented by a colored scalar S_1 that links the dark sector to quarks. The authors perform a comprehensive DM phenomenology study (relic density, direct and indirect detection) and a flavor analysis of b -> s μ^+ μ^- transitions, using SARAH/SPheno/micrOMEGAs and flavio to explore correlated constraints on the parameter space. They identify viable regions with m_DM in the hundreds of GeV to TeV range, a small gauge coupling g_B, and moderate Yukawa coupling Y_{S_1}, where DM relic density and SIDD are satisfied while flavor observables remain largely SM-like; the results emphasize the dominant role of DM physics in delimiting the common parameter space, with flavorful signatures providing complementary tests. The framework predicts testable signals for XENONnT and CTA, and collider signatures from S_1-induced processes, making the scenario falsifiable with upcoming data and motivating possible extensions such as gravitational-wave signals from U(1)_B breaking or Majorana DM realizations.

Abstract

We explore a Standard Model extension based on a local $U(1)_B$ symmetry, where a baryon-charged scalar mediates interactions between a fermionic dark matter candidate and Standard Model quarks. In this setup, the dark matter relic abundance is shaped not only by standard annihilation channels but also by additional coannihilation processes induced by a new scalar. The presence of this mediator provides a unified link between dark sector and flavor physics, yielding distinctive phenomenological consequences. We conduct a detailed study of dark matter phenomenology, emphasizing the role of the mass splitting between the dark matter particles, and the scalar mediator in determining the efficiency of coannihilation. The parameter space is examined in light of existing constraints from cosmological observations, direct and indirect detection experiments, as well as the collider searches at the \texttt{LHC}. Our analysis shows that the extended scalar sector opens up viable regions of parameter space beyond those accessible in minimal \(U(1)_B\) realizations, many of which are expected to be tested by forthcoming searches at \texttt{XENONnT} and \texttt{CTA}. Moreover, the model induces correlated signatures from flavor observables associated with the $b \to s μ^+ μ^-$ transitions as well, serving as complementary tests of the underlying framework.

Figures (14)

• Figure 1: Parameter space in the $(M_{Z'}, g_B)$ plane for two benchmark scenarios. The relic density constraint from Planck is indicated by the color coding: green points correspond to overabundant DM, orange points lie within the $2\sigma$ allowed range, and blue points give underabundant relic density. The gray shaded area is excluded by direct-detection (DD) bounds from LZ (2022, while the light-blue shaded region is ruled out by collider searches for a heavy $Z'$ boson. Top panel (a): mass splitting $\Delta M({\Psi_2,\Psi_1})=1~\text{GeV}$. Bottom panel (b): mass splitting $\Delta M({\Psi_2,\Psi_1}) = 10~\text{GeV}$. Other relevant parameters are fixed as $\lambda_S=0.32$, $\lambda_{HS}=1.29\times 10^{-2}$, $\lambda_{S_1}=10^{-2}$, $\lambda_{HS_1}=10^{-4}$, $\lambda_{SS_1}=10^{-10}$, $\sin\theta_{\text{DM}} = 0.001$, $m_s=800~\text{GeV}$, $m_{S_1}=2~\text{TeV}$, and $Y_{S_1} = 0.1$. The DM mass is varied within the range of 1 GeV to 2 TeV.
• Figure 2: The relic abundance $\Omega h^2$ in the $M_{\rm DM}-\,Y_{S_1}$ plane for two different choices of mass splitting $\Delta M(\Psi_2,\Psi_1)$. Left (a) $\Delta M(\Psi_2,\Psi_1) = 1$ GeV, Right (b) $\Delta M(\Psi_2,\Psi_1) = 10$ GeV. The color code indicates the relic density: green points are over-abundant, blue points lie within the $2\sigma$ bound of the observed value ($\Omega h^2 \simeq 0.110 \pm 0.012$), and orange points are under-abundant. The analysis is performed with fixed parameters: $\lambda_S=0.32$, $\lambda_{HS}=1.29\times 10^{-2}$, $\lambda_{S_1}=10^{-2}$, $\lambda_{HS_1}=10^{-4}$, $\lambda_{SS_1}=10^{-10}$, $\sin\theta_{\text{DM}} = 0.001$, $m_s=800~\text{GeV}$, $m_{S_1}=2~\text{TeV}$, $M_{Z'} = 1.5$ TeV, and $g_{B} = 0.05$. All displayed points are consistent with direct-detection limits from the LZ 2022 data.
• Figure 3: Relic density allowed parameter space in the $\Delta M(\Psi_2,\Psi_1)$–$\Delta M(S_1,\Psi_1)$ plane for different DM masses: (a) $M_{\rm DM}=100~\text{GeV}$, (b) $M_{\rm DM}=500~\text{GeV}$, (c) $M_{\rm DM}=800~\text{GeV}$, and (d) $M_{\rm DM}=1000~\text{GeV}$ with fixed gauge boson mass $M_{Z'} = 1.5$ TeV. The color coding denotes overabundant (green), underabundant (orange), and points consistent with the observed relic density within $2\sigma$ (blue). All displayed points are consistent with direct detection limits from experiments such as LZ 2022.
• Figure 4: Relic density allowed parameter space in the $\Delta M(\Psi_2,\Psi_1)$–$\Delta M(S_1,\Psi_1)$ plane for different DM masses: (a) $M_{\rm DM}=100~\text{GeV}$, (b) $M_{\rm DM}=400~\text{GeV}$, (c) $M_{\rm DM}=600~\text{GeV}$, and (d) $M_{\rm DM}=800~\text{GeV}$ with fixed gauge boson mass $M_{Z'} = 1$ TeV. The color coding denotes overabundant (green), underabundant (orange), and points consistent with the observed relic density within $2\sigma$ (blue). All displayed points are consistent with direct detection limits from experiments such as LZ 2022.
• Figure 5: Spin-independent dark matter - nucleon scattering cross section $\sigma_{\rm SIDD}$ as a function of the dark matter mass $M_{\rm DM}$ for different benchmark scenarios. The top row corresponds to $M_{\rm DM}=10~\text{GeV}$ with (a) $\Delta M(\Psi_2,\Psi_1)=1~\text{GeV}$ and (b) $\Delta M(\Psi_2,\Psi_1)=10~\text{GeV}$, while the bottom row corresponds to $M_{\rm DM}=1~\text{GeV}$ with (c) $\Delta M(\Psi_2,\Psi_1)=1~\text{GeV}$ and (d) $\Delta M(\Psi_2,\Psi_1)=10~\text{GeV}$. In all cases, the fixed parameters are $\lambda_{S}=0.32$, $\lambda_{HS}=1.29\times 10^{-2}$, $\lambda_{S_1}=10^{-2}$, $\lambda_{HS_1}=10^{-4}$, $\lambda_{SS_1}=10^{-10}$, $\sin\theta_{\rm DM}=0.001$, $m_{s}=800~\text{GeV}$, $m_{S_1}=2~\text{TeV}$, and $Y_{S_1}=0.1$. The $Z'$ mass $M_{Z'}$ are varied within $M_{Z'}\in[500,2000]~\text{GeV}$ with two fixed gauge coupling $g_B = 0.01,0.05$, corresponding to different $U(1)_B$ breaking scales $v_B$. Current limits from XENON1T (2018), LZ (2022), and projected XENONnT (2025) limits are also shown.