Addressing the LHC flavor anomalies with horizontal gauge symmetries

We study the impact of an additional $U(1{)}^{\prime }$ gauge symmetry with flavor-dependent charges for quarks and leptons on the LHC flavor anomalies observed in $B\to K^{*}{\mu }^{+}{\mu }^{-}$, $R(K)=B\to K{\mu }^{+}{\mu }^{-}/B\to K{e}^{+}{e}^{-}$, and $h\to \mu \tau$. In its minimal version with two scalar doublets, the resulting model naturally explains the deviations from the Standard Model observed in $B\to K^{*}{\mu }^{+}{\mu }^{-}$ and $R(K)$. The CMS access in $h\to \mu \tau$ can be explained by introducing a third scalar doublet, which gives rise to a prediction for $\tau \to 3\mu$. We investigate constraints from flavor observables and direct LHC searches for $pp\to Z^{\prime }\to {\mu }^{+}{\mu }^{-}$. Our model successfully generates the measured fermion-mixing matrices and does not require vectorlike fermions, unlike previous attempts to explain these anomalies.

Figure 1

Left: $m_{\beta \beta }$ vs lightest neutrino mass (in blue) as predicted by the two vanishing minors $(m_{\nu }^{-1}{)}_{22}=0=(m_{\nu }^{-1}{)}_{33}$ in combination with the $3\sigma$ values for ${\theta }_{ij}$ and $\mathrm{\Delta }{m}_{ij}^2$ from Ref. [67]. The diamond marks the best-fit point. The dotted black lines show the standard allowed $3\sigma$ range for normal ordering. The red regions are disfavored by GERDA [72] (conservative limit) and Planck [69, 70]. Right: Correlation of ${\sin }^2{\theta }_{23}$ with $m_{\beta \beta }$ due to the two vanishing minors. The yellow region denotes the $1\sigma$ range for ${\theta }_{23}$, and the diamond marks the best-fit point.

Figure 2

$R_{B_q}$ and $R_{{ϵ}_K}$ as a function of $C_9^{\mu \mu }$ for different values of $a$ taking into account the $Z^{\prime }$ contribution only. The horizontal gray regions are excluded by $\mathrm{\Delta }{m}_{B_q}$ and ${ϵ}_K$, while the vertical ones are excluded by $B\to K^{*}{\mu }^{+}{\mu }^{-}$ and $R(K)$. We used $m_{Z^{\prime }}=3\mathrm{TeV}$ for the renormalization group for the $\mathrm{\Delta }F=2$ processes. Note that the dependence on $m_{Z^{\prime }}$ is therefore only logarithmic.

Figure 3

Allowed regions in the $\tan \beta –\alpha$ plane assuming that $C_9^{\mu \mu }$ is reproduced by the $Z^{\prime }$ contribution within $2\sigma$ for $a=1/3$ for $m_H=300\mathrm{GeV}$ and $m_A=350\mathrm{GeV}$ (yellow), $m_A=300\mathrm{GeV}$ (red), and $m_A=250\mathrm{GeV}$ (blue). The gray region is excluded by $b\to s\gamma$ [84]. Dashed lines indicate $\cos (\alpha -\beta )=\pm 0.4$ for reference.

Figure 4

Limits on $q\overline{q}\to Z^{\prime }\to \mu \overline{\mu }$ from ATLAS [88] (black, allowed region down right) and the $2\sigma$ limits on $C_9^{\mu \mu }$ to accommodate $B\to K^{*}{\mu }^{+}{\mu }^{-}$ and $B\to K{\mu }^{+}{\mu }^{-}/B\to K{e}^{+}{e}^{-}$ (red, allowed regions inside the cone). Solid (dashed) lines are for $a=1/2$ ($a=1/3$). For $a=1/2$, the green shaded region is allowed (similar for $a=1/3$ using the dashed bounds).

Figure 5

Limits on $m_{Z^{\prime }}/g^{\prime }$ vs $a$ from NTP (gray), $B_s–{\overline{B}}_s$ mixing (red), and $C_9^{\mu \mu }$ (green). The horizontal lines indicate some values of interest: $a=1$, $1/2$, and $1/3$. Not shown are LHC limits (see Fig. 4).

Figure 6

Allowed regions in the $m_{Z^{\prime }}/g^{\prime }–\sin ({\theta }_R)$ plane for $a=1/3$: the horizontal stripes correspond to $h\to \mu \tau$ ($1\sigma$) for $\tan {\beta }_{23}=70,40$ and $\cos ({\alpha }_{23}-{\beta }_{23})=0.25$, and (light) blue stands for (future) $\tau \to 3\mu$ limits at 90% C.L. The gray regions are excluded by the $2\sigma$ range for $C_9^{\mu \mu }$ [see Eq. (56)]. In this range, ATLAS limits constrain $m_{Z^{\prime }}\gtrsim 2.5\mathrm{TeV}$ (see Fig. 4).