Comparison of ZEUS Data with Standard Model Predictions for e^+ p -> e^+ X Scattering at High x and Q^2

Using the ZEUS detector at HERA, we have studied the reaction e^+ p -> e^+ X for Q^2 > 5000 GeV^2 with a 20.1 pb^{-1} data sample collected during the years 1994 to 1996. For Q^2 below 15000 GeV^2, the data are in good agreement with Standard Model expectations. For Q^2 > 35000 Gev^2, two events are observed while 0.145+-0.013 events are expected. A statistical analysis of a large ensemble of simulated Standard Model experiments indicates that with probability 6.0%, an excess at least as unlikely as that observed would occur above some Q^2 cut. For x>0.55 and y>0.25, four events are observed where 0.91+-0.08 events are expected. A statistical analysis of the two-dimensional distribution of the events in x and y yields a probability of 0.72% for the region x>0.55 and y>0.25 and a probability of 7.8% for the entire Q^2 > 5000 GeV^2 data sample. The observed excess above Standard Model expectations is particularly interesting because it occurs in a previously unexplored kinematic region.