  Weakly Interacting Massive Particles (WIMPs) are a theoretical class of
particles that are excellent dark matter candidates. WIMP annihilation or decay
may produce essentially monochromatic gamma rays detectable by the Fermi Large
Area Telescope (LAT) against the astrophysical gamma-ray emission of the
Galaxy. We have searched for spectral lines in the energy range 5--300 GeV
using 3.7 years of data, reprocessed with updated instrument calibrations and
an improved energy dispersion model compared to the previous Fermi-LAT
Collaboration line searches. We searched in five regions selected to optimize
sensitivity to different theoretically-motivated dark matter density
distributions. We did not find any globally significant lines in our a priori
search regions and present 95% confidence limits for annihilation cross
sections of self-conjugate WIMPs and decay lifetimes. Our most significant fit
occurred at 133 GeV in our smallest search region and had a local significance
of 3.3 standard deviations, which translates to a global significance of 1.5
standard deviations. We discuss potential systematic effects in this search,
and examine the feature at 133 GeV in detail. We find that both the use of
reprocessed data and of additional information in the energy dispersion model
contribute to the reduction in significance of the line-like feature near 130
GeV relative to significances reported in other works. We also find that the
feature is narrower than the LAT energy resolution at the level of 2 to 3
standard deviations, which somewhat disfavors the interpretation of the 133 GeV
feature as a real WIMP signal.
