dwarfs [@laughlin04]. [@kennedy08] predicted that the probability that an $0.6~{M_\odot}$ star has at least one giant planet is $2\%$. The slope $\alpha$ of the planetary mass function ($dN/d\ln M\sim M^\alpha$) is $-0.31\pm0.2$ according to @cumming08, for other estimates, see, e.g., @cassan12. For super-Jupiters, the planetary mass function should be even steeper because their mass is close to the total mass of the disk. We may expect that the probability that an $0.6~{M_\odot}$ star has a $2-4~M_{\rm Jup}$ mass object is $\approx1\%$ or even smaller. Thus, detection of a super-Jupiters beyond the snow line of a late-type stars challenges the core-accretion theory.

It is hard to discover super-Jupiters around low-mass stars using either radial velocities or transit methods if the planetary orbit is beyond the snow line. For a $0.5M_{\odot}$ star, the snow line is located at about $1.3~{\rm AU}$. If the planet is twice further, then its orbital period is $5.9~{\rm yr}$ and the radial velocity amplitude is $25(M_{p}/M_{\rm Jup})~{\rm m~s^{-1}}$, where $M_p$ is the mass of the planet. Although the amplitude is large, the long orbital period of the planet makes detection difficult. None of the radial velocity detected planets is a super-Jupiter beyond the snow line on a 