The MFV limit of the MSSM for low tan(beta): meson mixings revisited

TL;DR

The paper reframes flavor violation in the MSSM using MFV as an EFT with SM Yukawa spurions, showing that new flavor-violating structures become CKM-like functions of the Yukawas, especially at low $\tan \beta$. It applies this to the $\Delta F = 2$ amplitudes in $B_s$ and $B_d$ mixing, finding predominantly positive SUSY contributions from the interplay of chargino and gluino boxes that remain modest in size relative to current lattice uncertainties. The study demonstrates that MFV MSSM is not CMFV since gluino- and Higgs-box induced operators beyond the SM contribute non-negligibly; it argues that the conventional Universal Unitarity Triangle is not generally valid, and advocates an MFV-UT constructed from $\beta_{\psi K_S}$ and tree-level determinations of $|V_{ub}|$ or $\gamma$, yielding testable correlations such as a preference for $\gamma>80^\circ$ given large $|V_{ub}|$. The results emphasize the sensitivity to lattice inputs (e.g., $\xi$) and upcoming measurements of $\gamma$ at the LHC as crucial tests of MFV in the MSSM.

Abstract

We apply the effective field theory definition of Minimal Flavour Violation (MFV) to the MSSM. We explicitly show how, by this definition, the new sources of flavour and CP violation present in the MSSM become functions of the SM Yukawa couplings, and cannot be simply set to zero, as is common wisdom in phenomenological MSSM studies that assume MFV. We apply our approach to the MSSM Delta B = 2 Hamiltonian at low tan(beta). The limit of MFV amounts to a striking increase in the predictivity of the model. In particular, SUSY corrections to meson-antimeson mass differences Delta M(d,s) are always found to be positive with respect to the SM prediction. This feature is due to an interesting interplay between chargino and gluino box diagrams (the dominant contributions) in the different mass regimes one can consider. Finally, we point out that, due to the presence of gluinos, the MFV MSSM does not belong -- even at low tan(beta) -- to the class of models with the so-called `constrained' MFV (CMFV), in which only the SM operator (V-A)x(V-A) contributes to Delta M(d,s). Consequently, for the MSSM and in the general case of MFV, one should not use the Universal Unitarity Triangle (UUT), relevant for CMFV models, but a MFV-UT constructed from beta(psi KS) and |V(ub)| or gamma from tree level decays. In particular, with the measured value of beta(psi KS), MFV implies a testable correlation between |V(ub)| and gamma. With the present high value of |V(ub)|, MFV favours gamma > 80 degrees.

Figures (13)

• Figure 1: Feynman diagrams describing meson-antimeson oscillations in the MSSM. The crossed diagrams (second row) are needed only if the fermion in the loop is a Majorana particle. The notation for the various lines is the same as in Rosiek.
• Figure 2: Lego plot showing the alignment of the phase of SUSY contributions to the SM phase in the MFV MSSM $\mathcal{M}_{12}$ for the case of $B_s$. In this example SUSY scales are (GeV): $\mu=1000$, $\overline m=200$, $M_{\tilde{g}}=500$, $M_1=100$, $M_2=500$. In the legend, $\Delta M_s$ is calculated from the absolute value formula, keeping the sign of the real part. The percentage gives the integrated number of hits for which $\Delta M_s^{\rm NP}>0$.
• Figure 3: Distribution of values for $\Delta M_s^{\rm NP}$ in the MFV MSSM: sum of the contributions (left panel) and separate SUSY contributions (right panel). The distribution results from scanning the MFV parameters $a_i$, $b_i$, after choosing SUSY scales as (GeV): $\mu=200$, $\overline m=300$, $M_{\tilde{g}}=300$, $M_1=500$, $M_2=500$. In the plot and in the legend, $\Delta M_s$ is calculated from the absolute value formula, keeping the sign of the real part. The percentage gives the integrated number of hits for which $\Delta M_s^{\rm NP}>0$. [See also text, mass regime (A).]
• Figure 4: Same as Fig. \ref{['fig:sum-mu200']} but for SUSY scales chosen as (GeV): $\mu=500$, $\overline m=300$, $M_{\tilde{g}}=300$, $M_1=100$, $M_2=200$. [See also text, mass regime (B).]
• Figure 5: Same as Fig. \ref{['fig:sum-mu200']} but for SUSY scales chosen as (GeV): $\mu=1000$, $\overline m=300$, $M_{\tilde{g}}=300$, $M_1=100$, $M_2=500$. [See also text, mass regime (C).]