Anatomy of new physics in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mover accent="true"><mml:mi>B</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math>mixing

We analyze three different new physics scenarios for $\ensuremath{\Delta}F=2$ flavor-changing neutral currents in the quark sector in the light of recent data on neutral-meson mixing. We parametrize generic new physics contributions to ${B}_{q}\mathrm{\text{\ensuremath{-}}}{\overline{B}}_{q}$ mixing, $q=d$, $s$, in terms of one complex quantity ${\ensuremath{\Delta}}_{q}$, while three parameters ${\ensuremath{\Delta}}_{K}^{tt}$, ${\ensuremath{\Delta}}_{K}^{ct}$, and ${\ensuremath{\Delta}}_{K}^{cc}$ are needed to describe $K\mathrm{\text{\ensuremath{-}}}\overline{K}$ mixing. In scenario I, we consider uncorrelated new physics contributions in the ${B}_{d}$, ${B}_{s}$, and $K$ sectors. In this scenario, it is only possible to constrain the parameters ${\ensuremath{\Delta}}_{d}$ and ${\ensuremath{\Delta}}_{s}$ whereas there are no nontrivial constraints on the kaon parameters. In scenario II, we study the case of minimal flavor violation (MFV) and small bottom Yukawa coupling, where $\ensuremath{\Delta}\ensuremath{\equiv}{\ensuremath{\Delta}}_{d}={\ensuremath{\Delta}}_{s}={\ensuremath{\Delta}}_{K}^{tt}$. We show that $\ensuremath{\Delta}$ must then be real, so that no new $CP$ phases can be accommodated, and express the remaining parameters ${\ensuremath{\Delta}}_{K}^{cc}$ and ${\ensuremath{\Delta}}_{K}^{ct}$ in terms of $\ensuremath{\Delta}$ in this scenario. Scenario III is the generic MFV case with large bottom Yukawa couplings. In this case, the kaon sector is uncorrelated to the ${B}_{d}$ and ${B}_{s}$ sectors. As in the second scenario one has ${\ensuremath{\Delta}}_{d}={\ensuremath{\Delta}}_{s}\ensuremath{\equiv}\ensuremath{\Delta}$, however, now with a complex parameter $\ensuremath{\Delta}$. Our quantitative analyses consist of global Cabibbo-Kobayashi-Maskawa (CKM) fits within the Rfit frequentist statistical approach, determining the standard model parameters and the new physics parameters of the studied scenarios simultaneously. We find that the recent measurements indicating discrepancies with the standard model are well accommodated in Scenarios I and III with new mixing phases, with a slight preference for Scenario I that permits different new $CP$ phases in the ${B}_{d}$ and ${B}_{s}$ systems. Within our statistical framework, we find evidence of new physics in both ${B}_{d}$ and ${B}_{s}$ systems. The standard model hypothesis ${\ensuremath{\Delta}}_{d}={\ensuremath{\Delta}}_{s}=1$ is disfavored with $p$-values of $3.6\ensuremath{\sigma}$ and $3.3\ensuremath{\sigma}$ in Scenarios I and III, respectively. We also present an exhaustive list of numerical predictions in each scenario. In particular, we predict the $CP$ phase in ${B}_{s}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\phi}$ and the difference between the ${B}_{s}$ and ${B}_{d}$ semileptonic asymmetries, which will be both measured by the LHCb experiment.