Some Properties of the Very High Q^2 Events of HERA

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The kinematic reconstruction of neutral current high Q^2 events at HERA is discussed in detail using as an example the recently published events of the H1 and ZEUS collaborations at Q^2 > 15000 GeV^2 and M > 180 GeV, which are more numerous than expected from Standard Model predictions. Taking into account the complete information of these events, the mass reconstruction is improved and the difference between the average mass of the samples of the two experiments is reduced from 26+/-10 GeV to 17+/-7 GeV, but remains different enough to render unlikely an interpretation of the excess observed by the two collaborations as originating from the decay of a single narrow resonance.
Version accepted for publication in Zeitschrift f. Physik. Minor modifications. Plain latex, 5 figures

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