We report on Suzaku and Chandra observations of the young supernova remnant CTB37B, from which TeV gamma-rays were detected by the H.E.S.S. Cherenkov telescope. The 80 ks Suzaku observation provided us with a clear image of diffuse emission and high-quality spectra. The spectra revealed that the diffuse emission is comprised of thermal and non-thermal components. The thermal component can be represented by an NEI model with a temperature, a pre-shock electron density and an age of 0.9(0.7-1.1) keV, 0.4(0.3-0.5) cm^{-3} and 650(350-3150) yr, respectively. This suggests that the explosion of CTB37B occurred in a low-density space. A non-thermal power-law component was found from the southern region of CTB37B. Its photon index of ~1.5 and a high roll-off energy (>15 keV) indicate efficient cosmic-ray acceleration. A comparison of this X-ray spectrum with the TeV gamma-ray spectrum leads us to conclude that the TeV gamma-ray emission seems to be powered by either multi-zone Inverse Compton scattering or the decay of neutral pions. The point source resolved by Chandra near the shell is probably associated with CTB37B, because of the common hydrogen column density with the diffuse thermal emission. Spectral and temporal characteristics suggest that this source is a new anomalous X-ray pulsar.
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