Hints of large tan(beta) in flavour physics

TL;DR

The paper investigates the MSSM in the large $\tan\beta$ regime with heavy squarks and Minimal Flavor Violation, motivated by Belle's $B_u \to \tau\nu$ hints and the precise $\Delta M_{B_s}$ measurement. It shows that with $M_{\tilde q}$ and $A_U$ in the TeV range and $\tan\beta$ of order 30–50, one can naturally obtain a $5$–$30\%$ suppression of $\mathcal{B}(B_u \to \tau\nu)$, a sizable $a_\mu$ contribution, a SM-like $m_{h^0}$ around $120$ GeV, and only small non-standard effects in $\Delta M_{B_s}$ and $\mathcal{B}(B \to X_s \gamma)$; these correlations arise from resummed $\tan\beta$-enhanced corrections and a structured MFV parameter space with $\epsilon_0$ and $\epsilon_Y$ controlling down-type Yukawa corrections. Neutral-Higgs exchanges can greatly enhance $\mathcal{B}(B_{s,d} \to \ell^+\ell^-)$ within current bounds, while heavy Higgs and stop mixing choices restrict such enhancements; the work also points to normalization strategies (e.g., using $\Delta M_{B_d}$) to reduce SM uncertainties. Overall, the framework provides concrete, testable predictions for upcoming measurements of $\mathcal{B}(B_u \to \tau\nu)$, $\mathcal{B}(B_{s,d} \to \ell^+\ell^-)$, and $(g-2)_\mu$, and highlights potential LFV signatures in leptonic decay ratios as additional probes. The scenario thus offers a natural, testable path to reconcile flavor observables with a heavy-squark MSSM at large $\tan\beta$.

Abstract

Motivated by the first evidence of the B -> tau nu transition reported by Belle and by the precise DeltaM_{B_s} measurement by CDF, we analyse these and other low-energy observables in the framework of the MSSM at large tan(beta). We show that for heavy squarks and A terms (M_squarks, A_U > 1 TeV) such scenario has several interesting virtues. It naturally describes: i) a suppression of BR(B->tau nu) of (10-40)%, ii) a sizable enhancement of (g-2)_mu, iii) a heavy SM-like Higgs (m_h ~ 120 GeV), iv) small non-standard effects in DeltaM_{B_s} and BR(B -> X_s gamma) (in agreement with present observations). The possibilities to find more convincing evidences of such scenario, with improved data on BR(B -> tau nu), BR(B -> l+ l-) and other low-energy observables, are briefly discussed.

Figures (3)

• Figure 1: Dependence of the lightest Higgs boson mass on the average squark mass ($M_{\tilde{q}}$), $\tan\beta$, and $A_U$.
• Figure 2: $B$-physics observables and $(g-2)_\mu$ in the $M_{H^{\pm}}$--$\tan\beta$ plane. The four plots correspond to: $[\mu,A_U]=[0.5,0]$ TeV (upper left); $[\mu,A_U]=[1,0]$ TeV (upper right); $[\mu,A_U]=[0.5,-1.0]$ TeV (lower left); $[\mu,A_U]=[0.5,-2.0]$ TeV (lower right). The exclusion regions for ${\mathcal{B}}(B_s\to \mu^+\mu^-)$ and ${\mathcal{B}}(B_s \to X_s\gamma)$ correspond to the limits in Eqs. (\ref{['eq:Bll_lim']}) and (\ref{['eq:bsg_lim']}), respectively (see main text for more details).
• Figure 3: $B$-physics observables and $(g-2)_\mu$ in the $M_{H^{\pm}}$--$\tan\beta$ plane. The four plots correspond to: $[\mu,A_U]=[1.0,-1.0]$ TeV (upper left); $[\mu,A_U]=[1.0,-2.0]$ TeV (upper right); $[\mu,A_U]=[1.0,1.0]$ TeV (lower left); $[\mu,A_U]=[1.0,2.0]$ TeV (lower right). The exclusion regions for ${\mathcal{B}}(B_s\to \mu^+\mu^-)$ and ${\mathcal{B}}(B_s \to X_s\gamma)$ correspond to the limits in Eqs. (\ref{['eq:Bll_lim']}) and (\ref{['eq:bsg_lim']}), respectively (see main text for more details).