Threshold corrections to m_b and the bbar{b} -> H⁰_i production in CP-violating SUSY scenarios

The inclusion of supersymmetric threshold corrections to the $b$-quark mass has dramatic consequences in scenarios with large CP-mixing effects in the Higgs sector. In particular, when the phase of the combination $M_{\tilde{g}}\mu$ is $\sim 180^{\rm o} \pm 30^{\rm o}$, the lightest-sbottom squark becomes tachyonic and, possibly, the $b$-quark Yukawa coupling nonperturbative for values of $\tan \beta$ ranging from intermediate up to large or very large, depending on the size of $arg(A_t\mu)$, $arg(A_b\mu)$, and the details of the spectrum. For these scenarios, when allowed, as well as scenarios with different values of $arg(M_{\tilde{g}}\mu)$, the cross sections for the production of the three neutral-Higgs bosons through $b$-quark have rather interesting dependences on $arg(A_t\mu)$ and $arg(A_b\mu)$, and the deviations induced by the $m_b$ corrections are rather large. In general, such production channel cannot be neglected with respect to the production through gluon fusion. For large CP-mixing effects, the lightest neutral-Higgs boson can be mainly CP odd and the $b$-quark fusion becomes its main production mechanism. Searches at the Tevatron and the LHC can easily detect such a Higgs boson, or constrain the CP-violating scenarios that allow it.