Charge and Color Breaking conditions associated with the top quark Yukawa coupling

In the MSSM, the Charge and Color Breaking (CCB) vacuum in the plane $(H_2,\tilde{t}_L, \tilde{t}_R)$ typically deviates largely from all D-flat directions, due to the large effects induced by the presence of the top quark Yukawa coupling. As a result, the critical CCB bound on the trilinear soft term $A_t$ becomes more restrictive than the D-flat bound $A_t^2 \le 3 (m_{\tilde{t}_L}^2+m_{\tilde{t}_R}^2+m_2^2)$. For large $\tan \beta$, we consider the effect of a splitting between the soft squark masses $m_{\tilde{t}_L},m_{\tilde{t}_R}$ on this optimal CCB bound and give a useful approximation for it, accurate within 1% in all interesting phenomenological cases. The physical implications on the top squark mass spectrum and the one-loop upper bound on the lightest CP-even Higgs boson mass are also discussed in a model-independent way.