  Many extensions of the Standard Model posit the existence of heavy particles
with long lifetimes. In this Letter, results are presented of a search for such
particles, which decay at a significant distance from their production point,
using a final state containing charged hadrons and an associated muon. This
analysis uses a data sample of proton-proton collisions at sqrt(s)= 7 TeV
corresponding to an integrated luminosity of 4.4 fb-1 collected in 2011 by the
ATLAS detector operating at the Large Hadron Collider. Results are interpreted
in the context of R-parity violating supersymmetric scenarios. No events in the
signal region are observed and limits are set on the production cross section
for supersymmetric particles, multiplied by the square of the branching ratio
for a neutralino to decay to charged hadrons and a muon, as a function of the
neutralino lifetime. To allow these limits to be used in a variety of models,
they are presented for a range of squark and neutralino masses.
