Scattering for the mass super-critical perturbations of the mass critical nonlinear Schr\"odinger equations

We consider the Cauchy problem for the nonlinear Schr"odinger equation with double nonlinearities with opposite sign, with one term is mass-critical and the other term is mass-supercritical and energy-subcritical, which includes the famous two-dimensional cubic-quintic nonlinear Schr"odinger equaton. We prove global wellposedness and scattering in $H^1({\mathbb{R}}^d)$ below the threshold for non-radial data when $1\le d\le 4$.