Efficient phase-space generation for hadron collider event simulation

Dear editors,

We would like to first of all thank the referees for their detailed responses to our work. Please find below the response to their reports. Additionally, we include a pdfdiff of the original version with the new updated version for the ease of the referees.

Report 1: 1. We have added a sentence when discussing the limits of the number of s-channels describing what is Chili and what is Chili (basic). 2. Thank you for pointing out the typo. It has now been corrected. 3. We have added the information for Sherpa for the color summed results along with the Chili and Chili+NF results. 4. We have added a new table containing the timing information (broken down into optimization time and generation time) for the same set of processes that are included in the Chili+NF comparison. 5. We have decided to leave this to a future work. 6. We have clarified this in the main text.

Report 2: 1. We mention in Section III that the W^+ and Z boson production processes include the leptonic decays. Therefore, the Breit-Wigner resonance mappings are used there. We have added the mappings to the end of the section. The additional jets are only QCD jets and no additional electroweak resonances are considered. The text has been modified to make that more clear. 2. We believe it is not inconsistent to treat the Higgs and tops as on-shell while appropriately handling the off-shell decays of the W and Z bosons. This is due to the fact that the width of the Higgs and the top are significantly smaller than the W and Z bosons, and can be well approximated by separating the calculation into a production and decay component using the narrow width approximation for the Higgs and top. 3. We added some more details on our QCD color treatment and furthermore added the relevant citations. Added text is: “To allow performance tests from low to high particle multiplicity, we use Comix’ default color-dressed sampling of the QCD color space [49], unless explicitly stated otherwise. For the same reason, color sampling is also used when using Amegic [39].” 4. We have added a brief description of the recursive phase-space generator in Comix to App.C and referred to the original publication for details. 5. We added a separate appendix for the definition of our unweighting efficiency. 6. We clarified this to talk about the slightly higher unweighting efficiency for processes with less than 5 additional jets and excluding photon+jet production. 7. We have added explicitly what the minimum number of s-channel parameterizations are for each process. 8. We point out that the complete integrator outperforms the basic one for all pieces except for the photon+5j calculation for the boosted case. This difference may be attributed to the poor integration uncertainty obtained by the Chili methods. Additionally, we made a comment about how the performance for the Higgs production with VBF cuts are similar for the complete integrator and the basic integrator. We have modified the text accordingly as well. 9. We included a brief description of the main components of NLO calculations in the dipole subtraction formalism in Sec.III 10. We have reformulated this sentence and added a footnote on the polynomial scaling with the number of external particles of the dipole-based integrator. 11. We have defined the cut efficiency in the main text. 12. We have added some definitions of coupling layers. And have clarified the goals of using the networks. 13. We thank the referee for pointing out the typo. It has been corrected. 14. This has been clarified to point to the fact that the variance loss tends to result in a symmetrical distribution, and therefore there is a less sharp upper edge in the weight distribution. The sharpness of this upper edge is directly related to the unweighting efficiency. 15. We have reformulated the conclusions and added a sentence to the introduction to clarify that the main aim of the paper is to provide a new phase-space integration algorithm that not only has good performance but also offers a solution applicable to many-core CPU and GPU computing. As such, the fact that our new integrator is comparable in performance to Sherpa, and better only in some cases, is acceptable and not particularly noteworthy. Indeed, its main feature is its simplicity, making it a portable solution. 16. We have added the preprint number for Ref. 60. There is no arXiv entry for Ref. 61

Report 3: 1. Thank you for pointing out this typo. This has been corrected 2. We agree and have rephrased the sentence to clarify how the mappings build up a multi-channel. The sentence now reads, “One of the main obstacles to scaling such approaches to high multiplicity has been the fact that the underlying phase-space mappings are used as individual mappings in a multi-channel phase-space generator.” 3. We rephrased this to make it clear that narrow weight distributions lead to good unweighting efficiencies, but highlight that a sharper upper edge is still more important.

Again, we would like to thank the referees for their insightful comments and through review of our work.

Regards, Joshua Isaacson (on behalf of the authors)

The points are given above in the comments