Lawrence Berkeley National Laboratory

Subsequent to the release of our original paper, we discovered in the context of preparing our technical supplement [1] for journal publication that a typographical error had existed in the text file that the analysis program used to construct the beam polarization "database" for both the original analysis, published in Ref. [2], and our final analysis. The electron-beam polarization P e and the analyzing power A y cancel exactly in the ratio R , which is proportional to the ratio P t / P l of the transferred polarization components. On the other hand, the extraction of the relative e dependence of P l / P Born l relies on knowledge of the beam polarization. As such, data taking was interrupted roughly every two days during the GEp - 2 ? experiment to perform invasive measurements of the beam polarization using the Hall C Moller polarimeter [3]. The run range affected by the typographical error was entirely contained within the data collected at Q 2 = 2.5 GeV 2 with a beam energy of E e = 3.680 GeV during January 2008. The data from this configuration were combined with the data collected at E e = 3.548 GeV due to the nearly complete overlap of these two settings in terms of Q 2 and e acceptance. It is worth remarking that this typographical error went unnoticed for so long because it only affected a small fraction of the data (less than half of the combined data for ? e ? = 0.790 ) and the difference between the actually assigned beam polarization and the polarization that should have been assigned was comparable in magnitude to the point-to-point systematic uncertainty of the measurement itself. As such, its effect did not show up in various diagnostic plots and statistical tests, such as the time stability of the extracted P l / P Born l ratio. The data for both E e = 3.548 and E e = 3.680 GeV were reprocessed using the corrected beam polarizations to determine the effect of the typographical error on the combined physics results at ? e ? = 0.790 . Because the value of P e cancels in the ratio R , changes in the assumed beam polarization can only affect the results for R via statistical fluctuations due to changes in the relative weighting of different run ranges in the unbinned maximum-likelihood estimators for R . These effects are negligible on the scale of both the statistical and the systematic uncertainties of the data. More noticeable changes are expected in the ratio P l / P Born l since the extracted value of P l is inversely proportional to the assumed value of P e . Table I shows the effect of the corrected beam polarization database on the polarization transfer observables for the combined data for the ? e ? = 0.790 setting, the only measurement affected by the typographical error. The analyzing power did not need to be recalibrated since it was determined using the ? e ? = 0.153 data, which were not affected by the typographical error. As expected, the change in the ratio R is negligible. The value of P Born l , which is computed event by event from the global fit described in the Appendix of the original paper and does not depend on P e , is also unchanged. The magnitudes of P t , P l , and P l / P Born l are reduced by a common multiplicative factor, reflecting the fact that the beam polarization had been underestimated for the run range affected by the typographical error. The most important result of the corrected analysis is that the ratio P l / P Born l has decreased by 0.0024 from 1.0167 to 1.0143, a change comparable in magnitude to the statistical uncertainty but small compared to the total and point-to-point systematic uncertainties. The P l / P Born l result for the original publication [2] would be reduced by the same multiplicative factor as the final result. The physics conclusions of both publications are not materially changed by this correction. (Table Presented). (Figure Presented).