A Modified Slicing Method with Multi-Dimensional Unfolding to Measure Hadron-Argon Cross Sections

Round 1

Reviewer 1 Report

Please see my comments in the attached pdf with suggested English language edits (red).

Comments for author File: Comments.pdf

In attached.

Author Response

Thank you for your corrections to the language in my paper. I corrected them and uploaded the new version. All changes following suggestions from both reviewers are highlighted. Also note all plots are updated. (Because it involves random number generation so the results may look different within statistical fluctuation, but the conclusions are the same.) Below are a few responses to your comments.

Footnote 11: The English in this footnote makes it difficult to interpret. Re-write.

Sorry for the confusion. I rewrote it as “The null-value events need to be included rather than cut directly, because it is possible for them to be assigned with a normal value in the measured space described in Section 4.4, which should be handled by the response matrix.”

Figure 8 (a): This figure should be update (formatting) so that the reader CAN visualize its meaning.  Otherwise, it should be deleted.

I was debating whether to delete this figure. The bin size is too small (9261*9261 matrix) and it is sparse so the bin colors are hard to visualize. However, for the completeness of the described procedure and consistency with the other subplots, I decided to keep it, and added a footnote to explain. It is similar for Figure 12 (c).

Footnote 16: The reference this footnote refers to, does not comport with the text.  Cowan's paper uses R^{-1} in the conventional sense.  Also, the paper is not divided into Chapters.  Please correct reference.

I keep the same reference, but change the notation of R^{-1} in the paper into \widetilde{R}. Thanks for the heads up.

Author Response File: Author Response.pdf

Reviewer 2 Report

Overall, this is a well-written description of an interesting analysis technique. I only have a number of minor editorial comments which I hope will improve the clarity and flow of the document. 

I only have a few scientific comments:

1. I suggest referencing 10.1103/PhysRevD.99.052007

which is a compilation of existing pion-nucleus cross section data and a constraint on a final state interaction model. It also illustrates the lack of pion-Ar measurements.

L16: "many types of hadrons": I think the type of hadrons that are typically emitted from the nucleus is quite limited, namely nucleons and pions. Many intermediate states (resonances, etc.) may be involved, so I would suggest mentioning the relevance of these intermediate processes.

L97: If the hadron comes to a rest, doesn't it mean that the hadron has expended all its energy without interacting? In that case, there wouldn't be "daughter particles which can be used to determine the type of interaction." There may be daughter particles from a decay, but in that wouldn't be a (hadronic) interaction.

L112: Isn't ID_ini always 1? Or can a track appear somewhere in the middle of the argon volume?

Figure 2: it may be useful to say more about what these curves are. I suspect they are not entirely arbitrary. Are they actually some model of a hadron-nucleus cross section? If not, are the features intended to mimic expected features such as resonances?

Figure 8: why does one cut off the histogram at 1000 MeV? Wouldn't it be natural to extend the histogram as far as there are an appreciable number  incident particles? Or is the point that the method can handle an overflow bin? If so, I would be clear about this choice.

L231: It would also be useful to provide information of what this threshold is. Did you in fact allow it to be energy-dependent, or did you keep it constant as a function of energy? In the latter case, I would state this explicitly and make clear that you did not actually consider an energy-dependent threshold.

L238/Figure 9: It would be useful to describe the level of migration and how it was motivated. If it is constant as a function of energy, I would also state this as an explicit assumption.

Figure 13: see previous comment regarding chi^2/dof on L181

L326: I don't see how publishing the re-smearing matrix "eliminates" the unfolding error. It allows others to reproduce it and use their own matrices/assumptions, but I doesn't solve the problem as far as I understand.

L37: at this stage it is not clear what is being binned. If the aforementioned "slices" are equivalent to these "bins" I would continue to use "slices". Otherwise, explain what quantity is being binned. 

L89: While it is explained later, the relationship/equivalence between the energy bins and the slices could be made clearer and more explicit at the start of this discussion. (e.g. include the explanation in L127-128 earlier in the text).

L92: Something not quite right with this sentence. Maybe "Ref [13] describes  a study in the ProtoDUNE-SP experiment [14], where the thin-slice method was first proposed and each energy bin is directly considered as a slice . . . "

L109: "On the contrary": I would find some other words for this, e.g. "In contrast . . ". Otherwise, the I expect the statement to somehow contradict or undermine the previous sentence.

L124: This sentence didn't make sense to me. Don't N_ini and N_end come directly from the track start and end while N_inc is the being derived in equation 12?

L138: It would be useful to have some outline of what follows. It seems you start with some proof of principle using true values to illustrate the procedure, and then go on to include efficiencies, resolution, and migration to increase the realism.

L161: "For E_ini . . ": this sentence (and the study that follows) seems to assume that there is one beam setting with a range of momentum, whereas most test beams will allow you to change the momentum setting. This assumption/simplification could be explicitly stated.

Footnote 8: I can imagine situations where event weights are used but it is not clear at this point why they would be introduced. Some example of why this would be useful could be included.

L181: It is not generally true that chi2/Nbins ~1 means that there is a good fit. If the number of bins is large, then even a small deviation of this ratio from 1 can indicate a bad fit. The chi2 probability, which is calculated by considering chi2 and Ndof separately, accounts for this correctly.

L186: I did not understand what is meant by a "higher dimensional space", especially since the method starts by collapsing the variables into a single dimension. "Higher dimension" suggests to me introducing additional degrees of freedom but I don't see that happening here.

L218: Same here . .  if the point is that a more realistic analysis with efficiencies, migration, etc. will introduce correlations between the measured cross sections, then I would just say that.

L228: It would be useful to explain what this "Score" is supposed to represent? An energy-dependent efficiency for accepting the event in to the sample?  

L314: I think there could be a better word than "imperfections". If I understood correctly, what is being referred to here are "assumptions" and "approximations". 

Author Response

Thank you for your comments. In the attached PDF, the first four pages are the responses to your comments. The following pages are the updated paper following suggestions from both reviewers and all revisions are highlighted. Also note all plots are updated. (Because it involves random number generation so the results may look different within statistical fluctuation, but the conclusions are the same.)

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The updated draft is ready for publication.