[Paper Review] $(g-2)_{e,\,μ}$ and strongly interacting dark matter with collider implications

Anirban Biswas, Sarif Khan|arXiv (Cornell University)|Dec 15, 2021

Dark Matter and Cosmic Phenomena4 citations

TL;DR

This paper proposes an extended $L_\mu - L_\tau$ model with a singlet vector-like fermion $\chi^\pm$ and a scalar ($\Phi'_2$ or $\Phi'_4$) to simultaneously explain the anomalous magnetic moments of the electron and muon, which deviate from Standard Model predictions. The model generates a one-loop contribution to $a_e$ via new Yukawa interactions while preserving the $Z_{\mu\tau}$-mediated contribution to $a_\mu$, and predicts a strongly interacting dark matter candidate in the MeV range that satisfies relic density, unitarity, and self-interaction constraints, with detectable signals in $e^+e^-$ colliders.

ABSTRACT

The quest for new physics beyond the Standard Model is boosted by the recently observed deviation in the anomalous magnetic moments of muon and electron from their respective theoretical prediction. In the present work, we have proposed a suitable extension of the minimal $L_μ-L_τ$ model to address these two experimental results as the minimal model is unable to provide any realistic solution. In our model, a new Yukawa interaction involving first generation of leptons, a singlet vector like fermion ($χ^{\pm}$) and a scalar (either an SU(2)$_{L}$ doublet $Φ^\prime_2$ or a complex singlet $Φ^\prime_4$) provides the additional one loop contribution to $a_{e}$ only on top of the usual contribution coming from the $L_μ-L_τ$ gauge boson ($Z_{μτ}$) to both electron and muon. The judicious choice of $L_μ-L_τ$ charges to these new fields results in a strongly interacting scalar dark matter in $\mathcal{O}({ m MeV})$ range after taking into account the bounds from relic density, unitarity and self interaction. The freeze-out dynamics of dark matter is greatly influenced by $3 ightarrow2$ scatterings while the kinetic equilibrium with the SM bath is ensured by $2 ightarrow2$ scatterings with neutrinos where $Z_{μτ}$ plays a pivotal role. The detection of dark matter is possible directly through scatterings with nuclei mediated by the SM $Z$ bosons. Moreover, our proposed model can also be tested in the upcoming $e^+e^-$ colliders by searching opposite sign di-electron and missing energy signal i.e. $e^{+} e^{-} ightarrow χ^{+} χ^{-} ightarrow e^{+} e^{-} \cancel{E}_T$ at the final state.

Motivation & Objective

• To resolve the long-standing discrepancy in the anomalous magnetic moments of the electron and muon beyond the Standard Model.
• To extend the minimal $L_\mu - L\tau$ model, which fails to explain both anomalies simultaneously, by introducing new fields with specific $L_\mu - L_\tau$ charges.
• To construct a viable dark matter candidate that is strongly interacting and consistent with cosmological constraints such as relic density, unitarity, and self-interaction bounds.
• To identify detectable collider signatures, particularly at $e^+e^-$ colliders, via the process $e^+e^- \to \chi^+\chi^- \to e^+e^- \cancel{E}_T$.

Proposed method

• Introduce a new Yukawa interaction involving the first-generation leptons, a vector-like fermion $\chi^\pm$, and a scalar ($\Phi'_2$ or $\Phi'_4$) to generate a one-loop contribution to $a_e$ only.
• Assign $L_\mu - L_\tau$ charges to the new fields such that the scalar dark matter candidate becomes strongly interacting, with $\mathcal{O}(\text{MeV})$ mass.
• Use the $Z_{\mu\tau}$ boson to mediate $2\to2$ scattering with neutrinos, ensuring kinetic equilibrium of dark matter with the SM bath.
• Employ $3\to2$ annihilations as the dominant freeze-out process for dark matter, significantly altering its relic abundance dynamics.
• Derive the scalar and pseudo-scalar couplings $g^{s,p}_{\phi_i}$ of the new scalar to electron and $\chi^\pm$ from the Lagrangian, using mixing angles and Yukawa couplings.
• Compute the total BSM contribution to $a_e$ as $\Delta a_e = \Delta a^{\text{scalar}}_e + \Delta a^{Z_{\mu\tau}}_e$, with $\Delta a^{Z_{\mu\tau}}_e$ inherited from the $L_\mu - L_\tau$ sector.

Experimental results

Research questions

• RQ1 Can a minimal $L_\mu - L_\tau$ model simultaneously explain the observed $(g-2)_{\mu}$ and $(g-2)_e$ anomalies?
• RQ2 What new scalar and fermion states are required to generate a one-loop contribution to $a_e$ without affecting $a_\mu$?
• RQ3 What are the cosmological and collider constraints on a strongly interacting MeV-scale dark matter candidate in this extended model?
• RQ4 How do $3\to2$ annihilations and $2\to2$ scattering with neutrinos affect the freeze-out dynamics of dark matter?
• RQ5 What are the detectable signatures of this model at future $e^+e^-$ colliders, particularly in the $e^+e^- \to \chi^+\chi^- \to e^+e^- \cancel{E}_T$ channel?

Key findings

• The model successfully explains the $4.2\sigma$ discrepancy in $a_\mu$ via the $Z_{\mu\tau}$ boson, consistent with the minimal $L_\mu - L_\tau$ model.
• A new Yukawa interaction involving $\chi^\pm$, the first-generation leptons, and a scalar ($\Phi'_2$ or $\Phi'_4$) provides a one-loop contribution to $a_e$, resolving the electron anomaly.
• The dark matter candidate is a strongly interacting scalar with mass in the $\mathcal{O}(\text{MeV})$ range, satisfying relic density, unitarity, and self-interaction bounds.
• The freeze-out of dark matter is dominated by $3\to2$ processes, with kinetic equilibrium maintained via $2\to2$ scattering with neutrinos mediated by $Z_{\mu\tau}$.
• Direct detection of dark matter is possible via $Z$-boson exchange in nucleon scattering, offering a viable detection channel.
• The model predicts a distinctive signal at $e^+e^-$ colliders: $e^+e^- \to \chi^+\chi^- \to e^+e^- \cancel{E}_T$, providing a key testable signature.