  We consider the R\'{e}nyi entanglement entropy of bosonic Luttinger liquids
under a particle bipartition and demonstrate that the leading order finite-size
scaling is logarithmic in the system size with a prefactor equal to the inverse
Luttinger parameter. While higher order corrections involve a microscopic
length scale, the leading order scaling depends only on this sole dimensionless
parameter which characterizes the low energy quantum hydrodynamics. This result
contrasts the leading entanglement entropy scaling under a spatial bipartition,
for which the coefficient is universal and independent of the Luttinger
parameter. Using quantum Monte Carlo calculations, we explicitly confirm the
scaling predictions of Luttinger liquid theory for the Lieb-Liniger model of
$\delta$-function interacting bosons in the one dimensional spatial continuum.
