The actual mass of a particle in coarse-grained molecular dynamics

Question

Hi, everyone

If I use LJ unit with fix langevin command, and set both the mass and damping parameter as 1, does it mean the actual mass of a particle in this system is m=sigma^2*lambda^2/epsilon? If the sigma, epsilon and lambda (damping coefficient for the solvent) of the system are given. (Since t=sqrt(m*sigma^2/epsilon) and damp=m/ lambda, it follows m=sigma^2*lambda^2/epsilon, where sigma, epsilon and lambda are distance, energy and damping coefficient in Langevin equation respectively.)

I really want to make sure of it because many papers for coarse-grained model just set the mass and damping parameter as 1 or without a mention of these and rarely have explanations.