$ΔM_{d,s}$, $B^0_{d,s}\toμ^+μ^-$ and $B\to X_sγ$ in Supersymmetry at Large $\tanβ$

TL;DR

This work develops an effective Lagrangian framework to analyze flavor-changing processes in the MSSM with large tanβ, incorporating SU(2)×U(1) breaking and electroweak gauge couplings. It derives analytic and semi-analytic expressions for neutral and charged Higgs couplings to quarks, including tanβ-resummed corrections and CKM-induced flavor effects via an effective CKM matrix V^{\rm eff}. The authors provide a full one-loop calculation and a controlled SU(2)×U(1) limit, offering accurate approximations (within 5–10%) and examining correlations among enhanced B decays, ΔM_{d,s}, and B→X_sγ under experimental constraints. They map out how flavor dependence enters through ε-parameters and demonstrate how to extend the formalism to flavor-nonuniversal squark masses, enabling quantitative predictions for B-physics observables in SUSY with CKM flavor violation at large tanβ. The results advance practical tools for predicting ΔM_{d,s}, BR(B^0_{d,s}→μ^+μ^−), and BR(\bar B→X_sγ) in a consistent, resummed framework.

Abstract

We present an effective Lagrangian formalism for the calculation of flavour changing neutral and charged scalar currents in weak decays including $SU(2)\times U(1)$ symmetry breaking effects and the effects of the electroweak couplings $g_1$ and $g_2$. We apply this formalism to the MSSM with large $\tanβ$ with the CKM matrix as the only source of flavour violation, heavy supersymmetric particles and light Higgs bosons. We give analytic formulae for the neutral and charged Higgs boson couplings to quarks including large $\tanβ$ resummed corrections in the $SU(2) \times U(1)$ limit and demonstrate that these formulae can only be used for a semi-quantitative analysis. In particular they overestimate the effects of large $\tanβ$ resummed corrections. We give also improved analytic formulae that reproduce the numerical results of the full approach within $5-10%$. We present for the first time the predictions for the branching ratios $B^0_{s,d}\to μ^+μ^-$ and the $B^0_{d,s}-\bar B^0_{d,s}$ mass differences $ΔM_{d,s}$ that include simultaneously the resummed large $\tanβ$ corrections, $SU(2)\times U(1)$ breaking effects and the effects of the electroweak couplings. We perform an anatomy of the correlation between the increase of the rates of the decays $B^0_{s,d}\toμ^+μ^-$ and the suppression of $ΔM_s$, that for large $\tanβ$ are caused by the enhanced flavour changing neutral Higgs couplings to down quarks. We take into account the constraint from $B\to X_s γ$ clarifying some points in the calculation of the large $\tanβ$ enhanced corrections to this decay.

Figures (6)

• Figure 1: One-loop threshold corrections to fermion propagators. $P_L\equiv{1-\gamma^5\over2}$, $P_R\equiv{1+\gamma^5\over2}$ and $q\equiv d$ or $u$.
• Figure 2: One-loop threshold corrections to fermion-gauge boson vertices.
• Figure 3: One-loop corrections to neutral Higgs-quark vertices.
• Figure 4: One-loop corrections to charged Higgs-quark vertices.
• Figure 5: Vertex corrections in the $SU(2)\times U(1)$ symmetry limit for vanishing electroweak gauge couplings. Diagrams a) and b) give rise to corrections $(\Delta_u\mathbf{Y}_d)^{JI}$. Corrections $(\Delta_d\mathbf{Y}_d)^{JI}$ are generated by similar diagrams with outgoing $H^{(u)}$ replaced by incoming $H^{(d)}$ and factors $\mu^\ast$ and $A_u^\ast$ in diagrams a) and b) replaced by $A_d$ and $\mu$, respectively. Diagrams c) and d) give rise to corrections $(\Delta_d\mathbf{Y}_u)^{JI}$. Corrections $(\Delta_u\mathbf{Y}_u)^{JI}$ are generated by similar diagrams with outgoing $H^{(d)}$ replaced by incoming $H^{(u)}$ and factors $\mu^\ast$ and $A_d^\ast$ in diagrams c) and d) replaced by $A_u$ and $\mu$, respectively.