Minimal Flavour Violation: an effective field theory approach

TL;DR

The paper constructs a general effective-field-theory framework for Minimal Flavour Violation (MFV), tying all flavor and CP violation to SM Yukawa spurions and exploring one- or two-Higgs-doublet extensions. It derives a complete dimension-six MFV operator basis, maps initial conditions to a set of ε_i parameters, and confronts current experimental bounds—most notably from B → X_sγ—to bound the new-physics scale Λ in the TeV range. In the two-Higgs-doublet case, it develops a systematic method to resum tanβ-enhanced Higgs-mediated FCNC amplitudes, highlighting potentially large effects in B → ℓ^+ℓ^- and B_s–B̄_s mixing, while providing two-loop SUSY contributions to B → X_sγ. Overall, MFV provides a coherent, testable framework linking FCNC processes across K and B sectors and guiding future flavor-physics explorations and model-building.

Abstract

We present a general analysis of extensions of the Standard Model which satisfy the criterion of Minimal Flavour Violation (MFV). We define this general framework by constructing a low-energy effective theory containing the Standard Model fields, with one or two Higgs doublets and, as the only source of SU(3)^5 flavour symmetry breaking, the background values of fields transforming under the flavour group as the ordinary Yukawa couplings. We analyse present bounds on the effective scale of dimension-six operators, which range between 1 and 10 TeV, with the most stringent constraints imposed by B -> X_s gamma. In this class of theories, it is possible to relate predictions for FCNC processes in B physics to those in K physics. We compare the sensitivity of various experimental searches in probing the hypothesis of MFV. Within the two-Higgs-doublet scenario, we develop a general procedure to obtain all tan(beta)-enhanced Higgs-mediated FCNC amplitudes, discussing in particular their impact in B -> l^+l^-, Delta M_B and B -> X_s gamma. As a byproduct, we derive some two-loop tan(beta)-enhanced supersymmetric contributions to B -> X_s gamma previously unknown.

Figures (6)

• Figure 1: Fit of $\Delta F=2$ data in MFV models. Left: fit of $\bar{\rho}$ and $\bar{\eta}$ in models with minimal flavour violation. The dotted lines denotes 68% CL intervals imposed by the observables insensitive to $|C_0(M_W^2)|$, namely $|V_{ub}|$, $\Delta M_{B_d}/\Delta M_{B_s}$ and $a^{CP}_{\Psi K}$. Input values are shown in table \ref{['tab:data']}. Right: $\Delta \chi^2$ of the global CKM fit as a function of the scale of the operator ${\cal O}_0$.
• Figure 2: Bounds on the scale of the operators ${\cal O}_{F1}$ (left) and ${\cal O}_{G1}$ (right) from $B\to X_s \gamma$.
• Figure 3: Branching ratios of various processes involving $d_i\to d_j \nu\bar{\nu}$ transitions as functions of the scale of the effective operator ${\cal O}_{\ell 1}$. The bands represent $1\sigma$ uncertainties, taking into account the present determination of the CKM parameters.
• Figure 4: Comparison of the effectiveness of different rare modes in setting future bounds on the scale of the operator ${\cal O}_{\ell 1}$. The vertical axis indicates the relative precision of an hypothetic measurement of the rate, with central value equal to the SM expectation. The curves in the two panels are obtained assuming an uncertainty of 10% (left) or 1% (right) on the corresponding overall CKM factor (e.g. $|V_{tb}^* V_{td}|^2$ in the case of $B_d\to\mu^+\mu^-$).
• Figure 5: Large $\tan\beta$ effects: $B\to \ell^+\bar{\ell}^-$ (continuous line), $\Delta M_{B_s}$ (dashed red line), $B\to X_s \gamma$ (dotted blue line), $B\to X \tau\bar{\nu}_\tau$ (dot-dashed green line). Left and right panels correspond to $\epsilon_2 = \epsilon_0$ and $\epsilon_2=-\epsilon_0$, respectively, in addition to the constraints in eqs. (\ref{['eq:e_choice']}).