More about F-term uplifting

We study moduli stabilization and a realization of de Sitter vacua in generalized F-term uplifting scenarios of the KKLT-type anti-de Sitter vacuum, where the uplifting sector X directly couples to the light Kahler modulus T in the superpotential through, e.g., stringy instanton effects. F-term uplifting can be achieved by a spontaneous supersymmetry breaking sector, e.g., the Polonyi model, the ORaifeartaigh model and the Intriligator-Seiberg-Shih model. Several models with the X-T mixing are examined and qualitative features in most models {it even with such mixing} are almost the same as those in the KKLT scenario. One of the quantitative changes, which are relevant to the phenomenology, is a larger hierarchy between the modulus mass m_T and the gravitino mass $m_{3/2}$, i.e., $m_T/m_{3/2} = {cal O}(a^2)$, where $a sim 4 pi^2$. In spite of such a large mass, the modulus F-term is suppressed not like $F^T = {cal O}(m_{3/2}/a^2)$, but like $F^T = {cal O}(m_{3/2}/a)$ for $ln (M_{Pl}/m_{3/2}) sim a$, because of an enhancement factor coming from the X-T mixing. Then we typically find a mirage-mediation pattern of gaugino masses of ${cal O}(m_{3/2}/a)$, while the scalar masses would be generically of ${cal O}(m_{3/2})$.