Non-intersection exponents of fully packed trails on the square lattice

Fully packed trails on the square lattice are known to be described, in the long distance limit, by a collection of free non compact bosons and symplectic fermions, and thus exhibit some properties reminiscent of Brownian motion, like vanishing fuseau exponents. We investigate in this paper the situation for their non-intersection exponents. Our approach is purely numerical, and based both on transfer matrix and Monte Carlo calculations. We find some evidence for non-intersection exponents given by CFT formulas similar to the Brownian case, albeit slightly different in their details.