  We present new velocities for 62 globular clusters in M104 (NGC 4594, the
Sombrero Galaxy), 56 from 2dF on the AAT and 6 from Hydra on WIYN. Combined
with previous data, we have a total sample of 108 M104 globular cluster
velocities, extending to 20 arcmin radius (~60 kpc), along with BVR photometry
for each of these. We use this wide-field dataset to study the globular cluster
kinematics and dark matter content of M104 out to 10 arcmin radius (30 kpc). We
find no rotation in the globular cluster system. The edge-on nature of M104
makes it unlikely that there is strong rotation which is face-on and hence
unobserved; thus, the absence of rotation over our large radial range appears
to be an intrinsic feature of the globular cluster system in M104. We discuss
ways to explain this low rotation, including the possibility that angular
momentum has been transferred to even larger radii through galaxy mergers. The
cluster velocity dispersion is ~230 km/s within several arcmin of the galaxy
center, and drops to ~150 km/s at ~10 arcmin radius. We derive the mass profile
of M104 using our velocity dispersion profile, together with the Jeans equation
under the assumptions of spherical symmetry and isotropy, and find excellent
agreement with the mass inferred from the stellar and gas rotation curve within
3 arcmin radius. The M/L_V increases from ~4 near the galaxy center to ~17 at 7
arcmin radius (~20 kpc, or 4 R_e), thus giving strong support for the presence
of a dark matter halo in M104. More globular cluster velocities at larger radii
are needed to further study the low rotation in the globular cluster system,
and to see if the dark matter halo in M104 extends beyond a radius of 30 kpc.
