B Anomalies in Two Higgs Doublet Model with Flavor Symmetry

The long-standing flavor anomalies in $b \to s \ell^+ \ell^-$ and $b \to c \ell \nu$ persist. In this work, we explore a specific flavor-gauged two-Higgs doublet model (FG2HDM) extended by a scalar singlet, with an imposed $U(1)$ flavor symmetry. Compared to the Standard Model (SM), four additional scalars and one neutral gauge boson $Z'$ are added to the particle spectrum. The special Yukawa coupling matrices, due to the $U(1)$ symmetry, lead to flavor-changing neutral Higgs (FCNH) interactions uniquely occurring in the down-type quark sector, while the new gauge boson $Z'$ induces flavor-changing neutral current (FCNC) interactions in the down-type quark sector as well. The two distinct types of anomalies can be accommodated simultaneously in such a model. Incorporating scalar and vector contributions to $b \to s \ell^+ \ell^-$ and $B_s^0$-$\bar{B}_s^0$ mixing, along with charged Higgs contributions to $b \to c \ell \nu$, we investigate the parameter space in FG2HDM and find substantial room in the solution space. Specifically, in the SM-like model setup, the data suggests that $m_{Z'} < 450\, \text{GeV}$, $\tan\beta < 28$, and $g'/m_{Z'} > 3.5 \times 10^{-4} \, \text{GeV}^{-1}$, while there are fewer constraints on heavy scalars, which can be further tested by a combination of other observables.