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Coloring mixed QCD/QED evolution

by Leif Gellersen, Stefan Prestel, Michael Spannowsky

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Leif Gellersen · Stefan Prestel
Submission information
Preprint Link: scipost_202205_00005v1  (pdf)
Date accepted: 2022-07-06
Date submitted: 2022-05-10 09:45
Submitted by: Gellersen, Leif
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Phenomenology
Approaches: Computational, Phenomenological


Parton showers are crucial components of high-energy physics calculations. Improving their modelling of QCD is an active research area since shower approximations are stumbling blocks for precision event generators. Naively, the interference between sub-dominant Standard-Model interactions and QCD can be of similar size to subleading QCD corrections. This article assesses the impact of QCD/QED interference effects in parton showers, by developing a sophisticated shower including QED, QCD at fixed color, and employing complete tree-level matrix element corrections for individual $N_C=3$ color configurations to embed interference. The resulting simulation indicates that QCD/QED interference effects are small for a simple test case and dwarfed by electro-weak resonance effects.

Author comments upon resubmission

\section*{Report 1}
We would like to acknowledge the work of the Referee in producing detailed comments. Unfortunately, it appears that some crucial aspects of the manuscript might have gone unnoticed when preparing the review. We have previously already commented in detail on the individual points that the referee prepared, so that we refrain from repetition.

In any case, we have seriously re-considered the manuscript in light of the report, since the questions by the referee indicated that our presentation was not clear enough. Consequently, we have made a significant effort to improve the presentation. In particular, we have
\item refined the notation in Section II.B
\item added a number of clarifying comments, and a clarifying equation to Section II.B
\item extended the discussion of matrix-element corrections and their benefits in Section II.C, and clarified the notation w.r.t. Section II.B
\item clarified the differences between leading-color and fixed-color matrix element corrections.
These changes have, we believe, led to a significant clarification of the method and novel developments, and thus should address the (potential cause of the) questions raised by the referee.

\section{Report 2}

We would like to thank Referee 2 for the detailed and constructive feedback. In the following, we adress the requested changes one by one.

\item {\bf In Eq. (1), after the 1st term in the 2nd line, the dot (before +) should be removed.}


\item {\bf Plots in Figs. 1-5 are a bit too small - in the printed version of the paper they are barely legible.}

We increased the size of Figs. 1 \& 2, and the script size of Figs. 3-5 to improve legibility.

\item {\bf In Figs. 3-5, the authors do not specify the meaning of the 3rd axis (corresponding to colors). If it corresponds to the number of generated events, it would be better - in my opinion - to normalize the corresponding histograms to 1.}

We normalized the histograms to 1 and mention the meaning of the third axis in the caption of Fig. 3.

\item {\bf In Figs. 3-5, left plots: in the horizontal axis, $p_\perp$ should be divided by the physical unit (e.g., $p_\perp$/GeV), as the argument of the log-function should be dimensionless.}

We added the unit in the respective axis labels.

\item {\bf In Figs. 6-9, the physical unit (GeV, I suppose) for the invariant mass in the horizontal axis is missing.}

We added the units in Figs. 6-9.

\item {\bf In Fig. 8, there is a spike in the ratio distribution at the invariant mass value of 140 which probably results from statistical fluctuations - I would recommend generating a higher statistics sample in order to clarify this.}

Done. With increased statistics, the spurious spike is significantly reduced.

\item {\bf In Fig. 9, the ratio distribution in the RHS plot seems to be cut at the top - the scale in the vertical axis is too small.}

Done. We increased the upper scale plot limit.

\item {\bf On page 7, in the 3rd line of the 2nd paragraph the authors write: "the amplitude will be modified by a factor 1". Does this mean that it will be unmodified, or something is missing there?}

Yes, we updated the text to be clearer.

\item {\bf Two lines below the above, the phrase "with different but identical quark color indices" sounds like a contradiction.}

We clarified the text. We mean that color and anticolor index of the gluon are identical, and different from the $q \bar q$ color index.

\item {\bf On page 6, in footnote 2, the authors introduce the abbreviation FC without explanation of its meaning, similarly for the abbreviations LC and MEC on page 7.}

We do not use FC and LC in the text any longer, and introduce MEC before its further use.

\item {\bf Section II.A, in the 1st line of the 2nd paragraph: "evolution variables" $\rightarrow$ "evolution variable".}


\item {\bf Appendix A: in the bottom left box: "hisories" $\rightarrow$ "histories".}



List of changes

Referee report 2 suggested several improvements of the manuscript. We have performed the relevant changes and documented these in the author comments. Referee report 1 raised several questions which we have addressed by changing and improving notation. Again, these changes are more conveniently documented in the author comments. Below, we list additional minor changes mainly related to typos.

\section{Additional changes}
Besides the corrections mentioned above, we included the following minor corrections:
\item Switch last two color flows in first line of Eq. 1.
\item Add brackets and a factor of 2 in Eq. 3.
\item Fix typesetting of sub-indices in Eq. 6.
\item Remove word "additional" below Eq. 20.
\item Remove one of two "both"s in caption of Fig. 9.
\item Add some missing arrow heads and fix spacing in Fig. 10.
\item Fix some umlauts in references.

Published as SciPost Phys. 13, 034 (2022)

Reports on this Submission

Anonymous Report 4 on 2022-7-3 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202205_00005v1, delivered 2022-07-03, doi: 10.21468/SciPost.Report.5324


My biggest problem is the treatment of the color in this article as I rose my concern in my first report. The color is handled via the so called "fixed color shower" following the idea of Ref [14]. It is hard to understand this method and even harder to justify in the pQCD framework. Obviously, it is hard to implement a a full color evolution in parton shower and with current techniques it looks hopeless. But we have the full theory of the color evolution in parton showers and in my opinion every implementation for a better color treatment must be a systematical approximation of full theory. The proposed method is not like that. It a parton shower implementation but it cannot be consider as QCD or its systematical approximation.

I noticed that part of Section II.B was rewritten and it was a little helpful for me to have some idea of the "fixed color shower" algorithm.
This paper is as "cryptic" for as Ref[14] respect to the color treatment and the origin of the "fixed color shower" algorithm. It would have been nice to have precise mathematical definition before implementation. The notation is rather confusing .

There are two things what I would highlight here in this report:
1) In color evolution the no splitting operator (aka Sudakov factor/operator) is a time ordered exponential of a non-trivial operator in the color space. This is a big complication and not easy to solve. The method discussed in this paper is not even close to that. There were similar attempt in the literature in the past by Plaetzer an Sjoedahl.

2) This is connected to the point 1). The shower cross section (with a proper color evolution) is independent of the choice of the color basis. One can use the usual trace basis or the color flow basis or just any convenient basis. The cross section must be independent of this choice. Of course when we apply some systematically improvable approximation in order to be able to implement something there is some dependence but that is controlled.
The algorithm discussed here is color basis dependent and it leads to cross section that depends on the color basis choice.

I understand the motivation and there are similar attempts in the literature for the color treatment beyond the leading color approximation and that is why I don't want to stop the publication of this paper, although I don't like it at all. The presented method can be useful for some specialized cross section calculation (if they can justify it) or the method can be adopted for numerical calculation of analytic resummation projects, or used for education purposes.

  • validity: ok
  • significance: low
  • originality: ok
  • clarity: low
  • formatting: good
  • grammar: perfect

Anonymous Report 3 on 2022-6-8 (Invited Report)


The authors have responded to all my comments/suggestions and introduced appropriate corrections in the manuscript. Furthermore, they have added some clarifications and a few additional corrections. I agree with all of this and have no further comments. Therefore, I recommend this manuscript for publication in the Scipost Physics journal.

  • validity: high
  • significance: high
  • originality: high
  • clarity: top
  • formatting: perfect
  • grammar: perfect

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