Lepton flavor violation induced by dark matter

Guided by gauge principles we discuss a predictive and falsifiable UV complete model where the Dirac fermion that accounts for the cold dark matter abundance in our Universe induces the lepton flavor violation (LFV) decays $\mu \to e\gamma$ and $\mu \to eee$ as well as $\mu -e$ conversion. We explore the interplay between direct dark matter detection, relic density, collider probes and lepton flavor violation to conclusively show that one may have a viable dark matter candidate yielding flavor violation signatures that can be probed in the upcoming experiments. In fact, keeping the dark matter mass at the TeV scale, a sizable LFV signal is possible, while reproducing the correct dark matter relic density and meeting limits from direct-detection experiments.

Figure 1

Feynman diagrams relevant for the dark matter phenomenology. The first, second and third diagram refer to an s-channel annihilation through a $Z^{\prime }$, a pseudoscalar and a scalar, respectively. The fourth and fifth diagrams are t-channel induced via exchange of either a $W^{\prime }$ or a charged Higgs boson. The t-channel versions of first and second diagrams are also responsible for DM-nucleon scattering. The scattering rate induced by a pseudoscalar is momentum suppressed at the fourth power; therefore only the t-channel $Z^{\prime }$ exchange is important for direct dark matter detection.

Figure 2

Relic density for the Dirac dark matter fermion $N_1$, allowing for coannihilation with nearly degenerate fermions $N_2$ and $N_3$ for different $Z^{\prime }$ masses. The impact of coannihilation is very mild—it just changes the thickness of the curves.

Figure 3

A summary plot that includes the dark matter relic density (blue), direct detection constraints (shaded red and brown) and collider limits (horizontal black lines), in the $M_{Z^{\prime }},M_{N1}$ mass plane. $N_1$ is the lightest new neutral fermion in the leptonic triplet of $SU(3{)}_L$. Current and projected limits are included in the figure. See text for details.

Figure 4

Diagram that contributes to the $\mu \to e\gamma$ decay. The mixing between the dark matter fermions $N_i$ is responsible for the LFV signal. Since we adopted $N_1$ to be the lightest fermion, we take only the leading order terms involving $N_1$, and set aside the other similar diagrams involving the heavier fermions.

Figure 5

Signal region for lepton flavor violation in green, overlaid with current and projected bounds stemming from direct dark matter detection and collider experiments. The dark matter relic density curves are depicted in blue, the collider bounds are represented by vertical black lines, and the current and projected direct-detection bounds are represented by red and brown regions, respectively.