  Measured disk masses seem to be too low to form the observed population of
planetary systems. In this context, we develop a population synthesis code in
the pebble accretion scenario, to analyse the disk mass dependence on planet
formation around low mass stars. We base our model on the analytical sequential
model presented in Ormel et al. 2017 and analyse the populations resulting from
varying initial disk mass distributions. Starting out with seeds the mass of
Ceres near the ice-line formed by streaming instability, we grow the planets
using the Pebble Accretion process and migrate them inwards using Type-I
migration. The next planets are formed sequentially after the previous planet
crosses the ice-line. We explore different initial distributions of disk masses
to show the dependence of this parameter with the final planetary population.
Our results show that compact close-in resonant systems can be pretty common
around M-dwarfs between $0.09-0.2$ $M_{\odot}$ only when the disks considered
are more massive than what is being observed by sub-mm disk surveys. The
minimum disk mass to form a Mars-like planet is found to be about $2 \times
10^{-3}$ $M_{\odot}$. Small variation in the disk mass distribution also
manifest in the simulated planet distribution. The paradox of disk masses might
be caused by an underestimation of the disk masses in observations, by a rapid
depletion of mass in disks by planets growing within a million years or by
deficiencies in our current planet formation picture.
