Results obtained in very-high-energy (VHE; E > 100 GeV) gamma-ray observations performed with the H.E.S.S. telescope array are used to investigate particle acceleration processes in the vicinity of the young massive stellar cluster Westerlund 1 (Wd 1). Imaging of Cherenkov light from gamma-ray induced particle cascades in the Earths atmosphere is used to search for VHE gamma rays from the region around Wd 1. Possible catalogued counterparts are searched for and discussed in terms of morphology and energetics of the H.E.S.S. source. The detection of the degree-scale extended VHE gamma-ray source HESS J1646-458 is reported based on 45 hours of H.E.S.S. observations performed between 2004 and 2008. The VHE gamma-ray source is centred on the nominal position of Wd 1 and detected with a total statistical significance of ~20sigma. The emission region clearly extends beyond the H.E.S.S. point-spread function (PSF). The differential energy spectrum follows a power law in energy with an index of Gamma=2.19 pm 0.08_{stat} pm 0.20_{sys} and a flux normalisation at 1 TeV of Phi_0 = (9.0 pm 1.4_{stat} pm 1.8_{sys}) x 10^{-12} TeV^{-1} cm^{-2} s^{-1}. The integral flux above 0.2 TeV amounts to (5.2 pm 0.9) x 10^{-11} cm^{-2} s^{-1}. Four objects coincident with HESS J1646-458 are discussed in the search of a counterpart, namely the magnetar CXOU J164710.2-455216, the X-ray binary 4U 1642-45, the pulsar PSR J1648-4611 and the massive stellar cluster Wd 1. In a single-source scenario, Wd 1 is favoured as site of VHE particle acceleration. Here, a hadronic parent population would be accelerated within the stellar cluster. Beside this, there is evidence for a multi-source origin, where a scenario involving PSR J1648-4611 could be viable to explain parts of the VHE gamma-ray emission of HESS J1646-458.
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