Comment by nimish

This is a lot of words to say that the field oscillations (i.e., particles) require very high energy. This shows up as the mass-(energy) of the particle, or stiffness of the field; take your pick.

Whether you call that stiffness or mass is a little beside the point IMO -- it shows up in the Yukawa force as an exponential dependence on that parameter which means the force quickly decays to zero unless the parameter is 0.