Lepton flavor of four-fermion operator and fermion portal dark matter

We study the ultraviolet realization of semileptonic four-fermion operator $O_{ledq}^{αβ11}$ that incorporates Majorana dark matter (DM) in both lepton-flavor-conserving (LFC) and lepton-flavor-violating (LFV) scenarios at the one-loop level via box diagram, which effectively alleviates the lower bounds on the new physics scale. The interplay between the model-independent constraints on the Wilson coefficients and DM direct detection, relic density, and collider searches in the context of fermion portal DM model with two mediators is investigated. We find that both the projected future constraint on the LFC Wilson coefficient $C_{ledq}^{2211}/Λ^2< (12.3~\text{TeV})^{-2}$ from the measurements of neutrino non-standard interaction in the next-generation neutrino oscillation experiments, and LFV constraint $C_{ledq}^{1211}/Λ^2< \left(2.2\times 10^3~\text{TeV} \right)^{-2}$ from ongoing charged-lepton-flavor-violation searches, provide a complementary exploration of the parameter space encompassing the DM mass and scalar mass. With the colored mediator mass typically around $2~\text{TeV}$, the sensitivity of the indirect constraints on the four-fermion operator could surpass those of collider searches and DM direct detection, in scenarios where the masses of the DM and scalar are close. By ensuring the correct DM relic density, however, we obtain that the collider searches and DM direct detection are more sensitive to the electroweak scale DM and scalar compared to the indirect constraints.

💡 Research Summary

The paper investigates a UV completion of the semileptonic dimension‑6 four‑fermion operator (O_{ledq}^{\alpha\beta11}=(\bar L_\alpha e_\beta)(\bar d_R Q)) that incorporates a Majorana dark‑matter (DM) candidate. The authors construct a “fermion‑portal” DM model containing a Z₂‑odd Majorana fermion (\chi), a scalar mediator (S), a colored scalar (\phi_d), and a vector‑like SU(2) doublet fermion (F). The interaction Lagrangian features four real Yukawa‑type couplings (f_{LS}, f_{\chi S}, f_{FQ}, f_{d\chi}).

At one‑loop level a “dark loop” box diagram generates the effective operator. The Wilson coefficient is found to be
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