Erratum to: A search for $$\upmu ^+ \rightarrow \textrm{e}^+ \upgamma $$ with the first dataset of the MEG II experiment

This erratum corrects Fig. 6 of the original article. There was a rounding error in the evaluation of the upper limit and confidence level curve for the constant PDF analysis used for cross check. Such an error caused distortions in presence of a very small number of fitted signal events and therefore is particularly evident in the distribution of pseudo-experiments for B90≲0.5×10-12 but it affects the whole range. With the constant PDF approach, the corrected 90% C.L. upper limit on the branching ratio, including systematic uncertainties, is B90=0.96×10-12. Also the B90s in the time side-bands changed. This correction does not change the results quoted in the original article obtained with the per-event PDF analysis. (Figure presented.) Comparison of the branching ratio upper limits (without systematic uncertainties) extracted by the two likelihood analyses when run over a common ensemble of pseudo-experiments (red dots). The results obtained on real data are also shown, for the analysis region (black star) and four fictitious analysis regions in the time side-bands: -3ns<-2ns, -2ns<-1ns, 1ns<2ns, 2ns<3ns (blue dots)