Cosmic Coincidence and Asymmetric Dark Matter in a Stueckelberg Extension
We discuss the possibility of cogenesis generating the ratio of baryon asymmetry to dark matter in a Stueckelberg U(1) extension of the standard model and of the minimal supersymmetric standard model. For the U(1) we choose $L_{\mu}-L_{\tau}$ which is anomaly free and can be gauged. The dark matter candidate arising from this extension is a singlet of the standard model gauge group but is charged under $L_{\mu}-L_{\tau}$. Solutions to the Boltzmann equations for relics in the presence of asymmetric dark matter are discussed. It is shown that the ratio of the baryon asymmetry to dark matter consistent with the current WMAP data, i.e., the cosmic coincidence, can be successfully explained in this model with the depletion of the symmetric component of dark matter from resonant annihilation via the Stueckelberg gauge boson. For the extended MSSM model it is shown that one has a two component dark matter picture with asymmetric dark matter being the dominant component and the neutralino being the subdominant component (i.e., with relic density a small fraction of the WMAP cold dark matter value). Remarkably, the subdominant component can be detected in direct detection experiments such as SuperCDMS and XENON-100. Further, it is shown that the class of Stueckelberg models with a gauged $L_{\mu}-L_{\tau}$ will produce a dramatic signature at a muon collider with the $\sigma(\mu^+\mu^-\to \mu^+\mu^-,\tau^+\tau^-)$ showing a detectable $Z’$ resonance while $\sigma(\mu^+\mu^-\to e^+e^-)$ is devoid of this resonance. Asymmetric dark matter arising from a $U(1)_{B-L}$ Stueckelberg extension is also briefly discussed. Finally, in the models we propose the asymmetric dark matter does not oscillate and there is no danger of it being washed out from oscillations.
💡 Research Summary
The paper investigates a unified framework in which the observed coincidence between the baryon asymmetry and the dark‑matter density (the “cosmic coincidence”) emerges naturally from a Stueckelberg‑type extension of the Standard Model (SM) and its minimal supersymmetric version (MSSM). The authors introduce an extra Abelian gauge symmetry, (U(1){L{\mu}-L_{\tau}}), which is anomaly‑free and can be gauged without additional exotic fermions. A SM‑singlet scalar (\chi) is charged under this new symmetry and serves as the dark‑matter candidate. Because (\chi) carries no SM gauge charges, it interacts with the visible sector only through the new gauge boson (Z’).
The central idea is “cogenesis”: a primordial lepton asymmetry generated in the early universe is transferred to both the baryon sector (via sphalerons) and the dark sector (via the (L_{\mu}-L_{\tau}) charge of (\chi)). The authors write down coupled Boltzmann equations for the symmetric and asymmetric components of (\chi). The asymmetric component, characterized by a conserved charge (\eta_{\chi}), survives to the present epoch, while the symmetric component is efficiently depleted through resonant annihilation mediated by the (Z’) boson. By choosing the resonance condition (M_{Z’}\simeq 2 m_{\chi}), the thermally averaged cross section (\langle\sigma v\rangle) is enhanced by several orders of magnitude, ensuring that the relic density of the symmetric part is negligible. Consequently the final dark‑matter abundance is directly proportional to the initial asymmetry, (\Omega_{\chi}\propto \eta_{\chi}), and the ratio (\Omega_{\rm DM}/\Omega_{B}) automatically falls in the observed range (≈5) without fine‑tuning.
When the construction is embedded in the MSSM, the model predicts a two‑component dark‑matter scenario. The usual neutralino remains as a subdominant component, typically contributing only a few percent of the total cold‑dark‑matter density. Because the neutralino still interacts via the usual weak interactions, it can be probed by upcoming direct‑detection experiments such as SuperCDMS and XENON‑100. In contrast, the dominant component (\chi) is essentially invisible to nuclear recoil searches, its interactions being mediated solely by the leptophilic (Z’).
A striking phenomenological consequence is the predicted signature at a future muon collider. Since the (Z’) couples only to muon and tau flavors, the processes (\mu^{+}\mu^{-}\to \mu^{+}\mu^{-}) and (\mu^{+}\mu^{-}\to \tau^{+}\tau^{-}) exhibit a clear resonance at (\sqrt{s}=M_{Z’}), whereas (\mu^{+}\mu^{-}\to e^{+}e^{-}) shows no such feature. This flavor‑non‑universal behavior provides a clean discriminator against other (Z’) models and could be observed with modest luminosity.
The authors also briefly discuss a similar construction based on a gauged (U(1)_{B-L}) Stueckelberg extension. While the basic mechanism of asymmetric dark‑matter generation remains, the (B-L) gauge boson couples to electrons as well, leading to stronger constraints from electron‑positron colliders and from precision electroweak data.
An important theoretical point is the stability of the asymmetric component. In many asymmetric‑dark‑matter models, particle–antiparticle oscillations can wash out the asymmetry. Here, the Stueckelberg mass term together with exact conservation of the (L_{\mu}-L_{\tau}) charge forbids such oscillations, guaranteeing that the initial asymmetry is preserved throughout cosmic history.
In summary, the paper delivers four major results: (1) a natural explanation of the baryon‑to‑dark‑matter ratio via cogenesis; (2) an efficient depletion mechanism for the symmetric dark‑matter component through resonant (Z’) annihilation; (3) a viable two‑component dark‑matter picture in the MSSM context, with the subdominant neutralino within reach of next‑generation direct‑detection experiments; and (4) a distinctive, flavor‑specific resonance signature at a muon collider that can confirm the leptophilic nature of the new gauge interaction. These predictions are testable in the near future, offering a concrete pathway to validate Stueckelberg‑based asymmetric dark‑matter models.