Muon $g-2$ and semileptonic $B$ decays in Bélanger-Delaunay-Westhoff model with gauge kinetic mixing

Abstract

In the model proposed by Bélanger, Delaunay and Westhoff (BDW), a new sector consisted of vectorlike fermions and two complex scalars is charged under an extra Abelian symmetry $U(1)_X$. In this paper, we generalize the BDW model by introducing the kinetic mixing between the $U(1)_X$ and the standard model $U(1)_Y$ gauge fields. The new physics contributions to the muon anomalous magnetic moment and the Wilson coefficients $C_{9,10}^{(')}$ are obtained analytically. We have explored the free parameter space of the model, taking into account various constraints on the muon $g-2$ using recent data from the E989 experiment at Fermilab, the lepton universality violation in terms of $R_K$ and $R_{K^*}$, and the branching ratios of the semileptonic decays, $B^+ \rightarrow K^+ μ^+ μ^-$ and $B^0 \rightarrow K^{*0} μ^+ μ^-$, the LEP and LHC searches for sleptons and $Z'$ boson, as well as the perturbative requirement. The viable parameter regions of the model are identified. In the presence of the gauge kinetic mixing term, those regions are enlarged and significantly deformed in comparison to the case with vanishing kinetic mixing. In the near future, the E989 experiment with the projected sensitivity will be able to test significant parts of the currently allowed parameter regions.