b-physics signals of the lightest CP-odd Higgs in the NMSSM at large tan beta

We investigate the low energy phenomenology of the lighter pseudoscalar $A_1^0$ in the NMSSM. The $A_1^0$ mass can naturally be small due to a global $U(1)_R$ symmetry of the Higgs potential, which is only broken by trilinear soft terms. The $A_1^0$ mass is further protected from renormalization group effects in the large $\tan \beta$ limit. We calculate the $b \to s A_1^0$ amplitude at leading order in $\tan \beta$ and work out the contributions to rare $K$, $B$ and radiative $\Upsilon$-decays and $B -\bar B$ mixing. We obtain constraints on the $A_1^0$ mass and couplings and show that masses down to ${\cal{O}}(10)$ MeV are allowed. The $b$-physics phenomenology of the NMSSM differs from the MSSM in the appearance of sizeable renormalization effects from neutral Higgses to the photon and gluon dipole operators and the breakdown of the MSSM correlation between the $B_s \to \mu^+ \mu^-$ branching ratio and $B_s - \bar B_s$ mixing. For $A_1^0$ masses above the tau threshold the $A_1^0$ can be searched for in $b \to s \tau^+ \tau^-$ processes with branching ratios $\lsim 10^{-3}$.