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

Abstract

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.

Comments: 17 pages, 4 figures, version published in Physical Review D