  We introduce a natural "massive" version of the Brownian loop soup of Lawler
and Werner which displays conformal covariance and exponential decay. We show
that this massive Brownian loop soup arises as the near-critical scaling limit
of a random walk loop soup with killing and is related to the massive SLE(2)
identified by Makarov and Smirnov as the near-critical scaling limit of a
loop-erased random walk with killing. We conjecture that the massive Brownian
loop soup describes the zero level lines of the massive Gaussian free field,
and discuss possible relations to other models, such as Ising, in the
off-critical regime.
