Correlation between Delta M_s and B^0_{s,d} --> mu^+ mu^- in Supersymmetry at Large tan beta

TL;DR

This work examines the MSSM with CKM as the sole source of flavor violation at large $\tan\beta$, linking enhancements in $BR(B^0_{s,d}\to\mu^+\mu^-)$ to suppressions in $\Delta M_s$ via Higgs-mediated FCNCs. It derives analytic, resummed expressions for neutral and charged Higgs couplings in the $SU(2)\times U(1)$ limit and analyzes the interplay between double-Higgs penguin contributions to $\Delta M_s$ and Higgs-penguin–driven $\mu^+\mu^-$ decays. The results show that for $0.8\le (\Delta M_s)^{\rm exp}/(\Delta M_s)^{\rm SM}\le 0.95$ the rare decay rates are bounded within $BR(B^0_s\to\mu^+\mu^-)^{\max} \sim 4\!\times\!10^{-8}$ to $6\!\times\!10^{-7}$ and $BR(B^0_d\to\mu^+\mu^-)^{\max} \sim 10^{-9}$ to $1.4\times10^{-8}$; when $(\Delta M_s)^{\rm exp}\ge (\Delta M_s)^{\rm SM}$ large enhancements are disfavored. The study also notes that significant squark-mixing could reverse the trend, increasing both observables. If correlations fail, it would signal new sources of flavor violation beyond CKM.

Abstract

Considering the MSSM with the CKM matrix as the only source of flavour violation and heavy supersymmetric particles at large $\tanβ$, we analyze the correlation between {\it the increase} of the rates of the decays $B^0_{s,d}\to μ^+μ^-$ and {\it the suppression} of $ΔM_s$, that are caused by the enhanced flavour changing neutral Higgs couplings to down-type quarks. We give analytic formulae for the neutral and charged Higgs couplings to quarks including large $\tanβ$ resummed corrections in the $SU(2)\times U(1)$ limit and comment briefly on the accuracy of this approximation. For $0.8\le (ΔM_s)^{\rm exp}/(ΔM_s)^{\rm SM}\le 0.95$ we find $6\cdot 10^{-7}\ge BR(B^0_s\ra μ^+μ^-)^{\rm max} \ge 4\cdot 10^{-8}$ and $1.4\cdot 10^{-8}\ge BR(B^0_d\ra μ^+μ^-)^{\rm max}\ge 1\cdot 10^{-9}$. For $(ΔM_s)^{\rm exp} \ge (ΔM_s)^{\rm SM}$ substantial enhancements of $B^0_{s,d}\raμ^+μ^-$ relative to the expectations based on the Standard Model are excluded. With $(ΔM_s)^{\rm exp}>15.0/$ps a conservative analysis of $(ΔM_s)^{\rm SM}$ gives $BR(B^0_s\ra μ^+μ^-)\simlt1.2\cdot10^{-6}$ and $BR(B^0_d\ra μ^+μ^-)\simlt3\cdot10^{-8}$. However, we point out that in the less likely scenario in which the squark mixing is so large that the neutral Higgs contributions dominate $ΔM_s$, the rates for $B^0_{s,d}\to μ^+μ^-$ increase with increasing $ΔM_s$ and the bounds in question are weaker. Violation of all these correlations and bounds would indicate new sources of flavour violation.

Figures (4)

• Figure 1: Vertex corrections in the $SU(2)\times U(1)$ symmetry limit. Diagrams a) and b) give rise to corrections $(\Delta_u\mathbf{Y}_d)^{JI}$, diagrams c) and d) to corrections $(\Delta_d\mathbf{Y}_u)^{JI}$.
• Figure 2: Double penguin diagrams contributing to $\Delta M_s$.
• Figure 3: Dominant diagrams contributing to $B^0_{s,d}\rightarrow l^+l^-$ decays at large $\tan\beta$.
• Figure :