How large could CP violation in neutral $B$ meson mixing be? Implications for baryogenesis and upcoming searches

CP violation in neutral $B$ meson oscillations is an experimental observable that could be directly related to the baryon asymmetry of the Universe through the $B$-Mesogenesis mechanism. As this phenomenon is highly suppressed in the Standard Model, it could also be a sensitive probe for many new physics scenarios that modify neutral meson mixing. Motivated by these facts, and the timely $B$ physics program at the LHC and Belle II, we analyze how large CP violation in the mixing of neutral $B_d$ and $B_s$ meson systems could be. We answer this question, in light of current experimental data, within three different scenarios, namely: (i) generic heavy new physics only affecting the mass mixing $M_{12}^q$, (ii) vector-like quark extensions that introduce deviations of 3$\times$3 CKM unitarity, and (iii) light new physics modifying the decay mixing $\Gamma_{12}^q$. We find that enhancements of the semileptonic asymmetries, that measure the amount of CP violation in mixing, at the level of $10^{-3}$ for the $B_d$ system and $10^{-4}$ for the $B_s$ system can be achieved within scenarios (i) and (ii), while they are much more suppressed in realistic UV completions triggering scenario (iii). With respect to cosmology, the difficulty of finding large CP asymmetries in our analysis puts the $B$-Mesogenesis mechanism in tension. Finally, we conclude that upcoming experimental searches for CP violation in $B$ meson mixing at LHCb and Belle II are unlikely to detect a new physics signal for the most generic models.