### Profile

Page 6:
When choosing the track to be considered as the MIP track in the case of 2 tracks (not including the MINOS matched track), why choose the one with the lower mean dE/dX and not the one with the most probable value which is lower.....
Most probable value is not well defined for each individual track since the number of points on each track is limited. Also when we calculate the mean dE/dx, we exclude any points with dE/dx > 10 MeV/cm to excluding contribution from large fluctuations so the mean dE/dx should be reliable. We added the following sentence in the note for clarification:
In calculating mean dE/dx for each track, we exclude any hits that give dE/dx > 10 MeV/cm.

Page 7:
The section title is labeled as “Nearestz cut” and not “nearest z cut” (purely a typo I assume...shows up a few places so maybe by design)
nearestz is the name of a branch in the analysis tree that is used in the analysis. Tingjun created this variable during the CC-inclusive work. The name could be improved.

Page 8:
Is there any real kinematic space that is removed from the Theta_{mu pi} from real CC1Pi. I doubt so, but I didn't see this stated in the note
The name of this cut is a little misleading. The cut is actually quite conservative. It only removes an event if there is another track that is aligned with the MINOS matched track (angle between the two tracks greater than 170 degrees) and the other track is not fully contained. This is meant to remove broken tracks. If the pion goes back-to-back with the muon but the pion track is contained, the event won't be removed. Based on Table 2, this cut would remove 1% of all neutrino interactions. From Figures 12 and 13, you can see there is a small fraction of signal events with Theta_{mu pi} larger than 170, but it is small contribution and is taken into account in the efficiency correction.

Page 10:
This is more of a general question....why do the two ratio charge ratio cuts have any discrimination power for signal compared to background. The plots well motivate the cuts, I just fail to have a physics intuition why this should be the case.....can you explain this a little
The signal we are looking for has simple topology (mostly just a muon track and a pion track) compared with the dominant DIS background (very busy events). The two ratio variables quantify the cleaning of track reconstruction and help to reject busy events where it is impossible to reconstruct all activities as individual tracks. We have added the above sentence to the note for clarification.

Page 15:
The caption of Table 5 reads funny...I think should say “Neutrino interaction cross-section systemamtic parameters considered in this analysis for the GENIE generator. The complete list can be found in \cite{}.
We have changed the caption. Thanks.

Page 15:
I'm abit confused, in the text you say you do +/- 1 sigma variation in the parameters for the neutrino interaction, but the table lists % variation. I might just be being dense, but I'm unsure the relation between these values. Did you vary things by the percentage about the nominal or +/- 1 sigma of the given value?
We added the following to the caption for clarification.
The percentage shows the amount of variation we change each parameter according to $\pm1\sigma$ uncertainty on each parameter.

Page 23:
Minor comment but the figures on Figure 15 could use labels on the y-axis
Done.

Page 28
I realize this isn't meant to be a model comparison analysis, but is it clear what isn't being taken to account in GENIE that GiBUU does and thus explains the massive difference in what you expect from GENIE when compared to data? Again, just trying to get a sense of the physics
We notice GENIE gives higher prediction of CC1$\pi^{\pm}$ cross sections compared with data and other model predictions. This is consistent with the conclusion in~\cite{Rodrigues:2016xjj} that GENIE's non-resonant background prediction has to be significantly reduced to fit the data. We do not change any default GENIE parameters in this analysis.