Higgs-mediated FCNCs: Natural Flavour Conservation vs. Minimal Flavour Violation

TL;DR

This work analyzes how two mechanisms—Natural Flavour Conservation (NFC) and Minimal Flavour Violation (MFV)—suppress flavour-changing neutral currents in multi-Higgs models, arguing that MFV is more robust under quantum corrections. It develops a detailed MFV framework, including the possibility of flavour-blind CP phases, and derives the resulting impacts on ΔF=2 amplitudes, CP-violating observables, and rare decays, with explicit attention to neutral-Higgs exchange. The authors show that MFV can accommodate a large B_s mixing phase and can alleviate tensions between ε_K and S_ψK_S while preserving CKM-driven suppression of FCNCs, predicting distinctive correlations among observables such as S_ψφ, S_ψK_S, ε_K, ΔM_s, and Br(B_{s,d}→μ^+μ^−). They propose B_{s,d}→μ^+μ^− as a clean experimental probe of the MFV Higgs sector and compare MFV realizations to existing literature, clarifying which models remain compatible with MFV and protected against excessive FCNCs.

Abstract

We compare the effectiveness of two hypotheses, Natural Flavour Conservation (NFC) and Minimal Flavour Violation (MFV), in suppressing the strength of flavour-changing neutral-currents (FCNCs) in models with more than one Higgs doublet. We show that the MFV hypothesis, in its general formulation, is more stable in suppressing FCNCs than the hypothesis of NFC alone when quantum corrections are taken into account. The phenomenological implications of the two scenarios are discussed analysing meson-antimeson mixing observables and the rare decays B -> mu+ mu-. We demonstrate that, introducing flavour-blind CP phases, two-Higgs doublet models respecting the MFV hypothesis can accommodate a large CP-violating phase in Bs mixing, as hinted by CDF and D0 data and, without extra free parameters, soften significantly in a correlated manner the observed anomaly in the relation between epsilon_K and S_psi_K.

Figures (4)

• Figure 1: Tree-level Higgs-mediated contributions to $\Delta F=2$ amplitudes.
• Figure 2: Correlation between $S_{\psi K_S}$ and $S_{\psi\phi}$ (left) and between the new phases in the $B_d$ and $B_s$ mixing (right) originating in the CP-violating Higgs-mediated $\Delta F=2$ amplitudes in Eqs. (\ref{['eq:M12dHiggsMFV']})--(\ref{['eq:M12sHiggsMFV']}). In both plots the blue (dark) points have been obtained with the CKM phase $\beta$ fixed to its central value ($\sin(2\beta)=0.739$): the spread is determined only by the condition imposed on $\Delta M_s$ (see text). The horizontal lines indicate the $\pm1\sigma$ range of $S_{\psi K_S}^{\text{exp}}$. On the left plot the $\pm 1\sigma$ error due to the uncertainty in the extraction of $\beta$ (light points) and the SM prediction (black vertical line) are also shown. The dashed blue (dark) line in the right plot represents $\phi_{B_s} = \left( m_d/m_s \right) \phi_{B_s}$.
• Figure 3: Correlation between $\varepsilon_K$ and $S_{\psi K_S}$ with the inclusion of the CP-violating Higgs-mediated $\Delta F=2$ amplitudes in Eqs. (\ref{['eq:M12dHiggsMFV']})--(\ref{['eq:M12sHiggsMFV']}). Notations as in Figure \ref{['fig:sin2b']}.
• Figure 4: Correlation between ${\rm Br}(B_s\to\mu^+\mu^-)$ and ${\rm Br}(B_d\to\mu^+\mu^-)$ in presence of scalar amplitudes respecting the MFV hypothesis. The horizontal dotted line represent the present experimental limit on ${\rm Br}(B_s\to\mu^+\mu^-)$ from Ref. :2007kv.