  In the cosmological paradigm, cold dark matter dominates the mass content of
the Universe and is present at every scale. Candidates for dark mater include
many extensions of the standard model, with a Weakly Interacting Massive
Particle (WIMP) in the mass range from 50 GeV to greater than 10 TeV. The
self-annihilation of WIMPs in astrophysical regions of high dark matter density
can produce secondary particles including Very High Energy (VHE) gamma rays
with energies up to the dark matter particle mass. The VERITAS array of
Cherenkov telescopes, designed for the detection of VHE gamma rays in the 100
GeV-10 TeV energy range, is an appropriate instrument for the detection of dark
matter. Among the possible astrophysical targets, dwarf spheroidal galaxies
(dSphs) of the Local Group are promising targets to search for the annihilation
signature of dark matter due to their proximity and large dark matter content.
We report here on extensive observations conducted by VERITAS on the nearby
Segue 1 satellite galaxy, which is currently considered as one of the best
dSphs for dark matter studies. The results are discussed in the framework of
WIMP models, with a special emphasis on leptophilic DM models invoked to
explain the recent cosmic ray lepton anomalies.
