Testing Minimal $U(2{)}^3$ Right-Handed Flavor Breaking in a Singlet-Scalar Vector-Like Quark Portal

We study a portal of a $Z_2$-odd singlet scalar and a vector like down quark, in which a right handed flavor breaking spurion extends the portal coupling from $b_R$ to $d_R$ and $s_R$. This single coupling vector links the $b\to s$, $b\to d$, and $s\to d$ transitions. We compute the one loop dipole and $\mathrm{\Delta }F=2$ Wilson coefficients, and show that a real scalar generates no $\mathrm{\Delta }F=2$ amplitude at one loop. Using a seven observable profile likelihood of $B$ meson mixing, ${\epsilon }_K$, and radiative decays, with the CKM, lattice, and short distance inputs treated as nuisance parameters, we compare a generic spurion, minimal $U(2{)}^3$ with a free size of the light quark couplings, and a CKM-aligned ansatz. We have found that the present data cannot yet test the flavor structure: the Standard Model is compatible with the data, with a pseudo experiment $p$-value of $0.20$, and no direction of the light quark couplings can be excluded at 95% CL. For $M_D\simeq m_{\mathcal{S}}=1$ TeV and $\mathrm{\mid }{\lambda }_b\mathrm{\mid }=1$, the relative light quark coupling ${\epsilon }_R$ is bounded at 95% CL by $0.227$ for a generic spurion and by $0.211$ for minimal $U(2{)}^3$. More precise measurements of the $B_s$ mixing phase at the LHC and of $\sin 2\beta$ at LHCb and Belle-II, together with improved lattice and CKM inputs, can make the minimality of the flavor structure testable if a deviation from the Standard Model is observed.