Operators from flavored dark sectors running to low energy

We consider the effective field theory generated by a heavy mediator that connects Standard Model particles to a dark sector, considering explicitly the flavor structure of the operators. In particular, we study the model independent running and mixing between operators as well as their matching at the electroweak scale. In addition to the explicit expression of the renormalization group equations, we show the numerical solutions as well as some approximate analytical expressions that help us to understand these solutions. At low energy, our results are particularly important in the case of light dark sectors communicating to the $b$ quark and can be immediately applied to flavored dark matter.

Figure 1

Feynman diagrams contributing to the wave function renormalization of fermions $\psi$ and of the Higgs doublet $H$.

Figure 2

Feynman diagrams contributing to the current corrections for pure fermions $\psi$ and Higgs currents.

Figure 3

Feynman diagrams contributing to the redundant current ${\partial }_{\nu }{B}^{\nu \mu }$.

Figure 4

Feynman diagrams contributing to the current renormalization below the EW scale.

Figure 5

Running of the Wilson coefficients above the EW scale, taking as an initial condition $(C_a{)}_{ij}(\mathrm{\Lambda })=1$ for all the values of $a$, $i$, and $j$. In the bottom left panel, $C_{d_R}\sim C_{{\ell }_L}\sim C_{e_R}$ applies to all the matrix elements, with no difference for those involving the third generation.

Figure 6

Feynman diagrams contributing to the running of the Fermi coupling below the EW scale.