In this article, we study the low-regularity Cauchy problem of a one
dimensional quadratic Schrodinger system with coupled parameter Ξ±β(0,1). When 21β<Ξ±<1,we prove the global well-posedness in
Hs(R) with s>β41β, while for 0<Ξ±<21β, we
obtain global well-posedness in Hs(R) with s>β85β. We
have adapted the linear-nonlinear decomposition and resonance decomposition
technique in different range of Ξ±