Analysis of Neutral Higgs-Boson Contributions to the Decays B_s -> l^+l^- and B -> K l^+l^-

TL;DR

This work analyzes Higgs-boson–induced contributions to the rare decays $\bar{B}_s\to l^+l^-$ and $\bar{B}\to K l^+l^-$ within the effective $b\to s l^+l^-$ framework, focusing on type-II 2HDM and SUSY with minimal flavour violation in the large $\tan\beta$ regime. By deriving compact expressions for the scalar and pseudoscalar Wilson coefficients and imposing constraints from $b\to s\gamma$, $\bar{B}_s\to \mu^+\mu^-$, and $\bar{B}\to K^{(*)}\mu^+\mu^-$, the paper shows that Higgs-mediated effects are strongly model-dependent: negligible in the 2HDM type II due to charged Higgs bounds, but potentially substantial in SUSY MFV within allowed parameter regions. Model-independent bounds on scalar/pseudoscalar couplings imply $|R_S|,|R_P| \lesssim 4$, and the averaged forward–backward muon asymmetry in $\bar{B}\to K\mu^+\mu^-$ is limited to about $\pm 4\%$, with the decay spectra and rates largely constrained by current data. Overall, the findings highlight the complementary role of $\bar{B}_s\to \mu^+\mu^-$ in constraining new scalar interactions and the limited, yet potentially observable, MFV SUSY effects in rare B decays.

Abstract

We report on a calculation of Higgs-boson contributions to the decays B_s -> l^+l^- and B -> K l^+l^- (l=e, mu) which are governed by the effective Hamiltonian describing b -> s l^+ l^-. Compact formulae for the Wilson coefficients are provided in the context of the type-II two-Higgs-doublet model (2HDM) and supersymmetry (SUSY) with minimal flavour violation, focusing on the case of large tan(beta). We derive, in a model-independent way, constraints on Higgs-boson-mediated interactions, using present experimental results on rare B decays including b -> s gamma, B_s -> mu^+ mu^-, and B -> K^(*) mu^+ mu^-. In particular, we assess the impact of possible scalar and pseudoscalar interactions transcending the standard model (SM) on the branching ratio of B_s -> mu^+ mu^- and the forward-backward (FB) asymmetry of mu^- in B -> K mu^+ mu^- decay. We find that the average FB asymmetry, which is unobservably small within the SM, and therefore a potentially valuable tool to search for new physics, is predicted to be no greater than 4% for a nominal branching ratio of about 6x10^{-7}. Moreover, striking effects on the decay spectrum of B -> K mu^+ mu^- are already ruled out by experimental data on the B_s -> mu^+ mu^- branching fraction. In addition, we study the constraints on the parameter space of the 2HDM and SUSY with minimal flavour violation. While the type-II 2HDM does not give any sizable contributions to the above decay modes, we find that SUSY contributions obeying the constraint on b -> s gamma can affect significantly the branching ratio of B_s -> mu^+ mu^-. We also comment on previous calculations contained in the literature.

Figures (8)

• Figure 1: Diagrams contributing to the $b\to s l^+l^-$ transition, within the 2HDM. The corresponding counterterms are displayed in Eqs. (\ref{['counterterm:1']}) and (\ref{['counterterm:2']}).
• Figure 2: SUSY contributions to the process $b\to s l^+l^-$, as described in Sec. \ref{['computation']}, with indices $a=1,2,\dots,6$; $i,j=1,2$; $k=1,2,3$. The counterterms for the penguin diagrams are given in Eqs. (\ref{['counterterm:1']}) and (\ref{['counterterm:2']}).
• Figure 3: Constraints on the coefficients $R_S$ and $R_P$ as determined from the upper limit on ${\mathcal{B}}\,(\bar{B}_s\to \mu^+\mu^-)$. (a) For $R_{10}=1$ and $f_{B_s}=210 \pm 30\ {\text{MeV}}$. The dark region indicates the allowed region. (b) For the central value $f_{B_s}=210\ {\text{MeV}}$ and two choices of $R_{10}$: $-2$ (solid line) and $2$ (dashed line), as described in the text.
• Figure 4: The average FB asymmetry in $\bar{B}\to K\mu^+\mu^-$ as a function of $(R_9,R_{10})$ for $R_S=-4$, $R_P=0$, and $R_7=1$ consistent with the upper limit on ${\mathcal{B}}\,(\bar{B}_s\to \mu^+\mu^-)$. Also shown is the corresponding branching ratio of $\bar{B}\to K \mu^+\mu^-$ (see the text for details).
• Figure 5: Allowed ranges of $R_9$ and $R_{10}$ as determined from the upper limit on ${\mathcal{B}}\,(\bar{B}\to K^*\mu^+\mu^-)$ for $R_S=-4$, $R_P=0$, and $R_7=\pm 1$. Note that the values of $R_{S,P}$ are consistent with experimental data on $\bar{B}_s\to \mu^+\mu^-$.