# $tW$ and $tZ'$ production at hadron colliders

### Submission summary

 As Contributors: Nikolaos Kidonakis Arxiv Link: https://arxiv.org/abs/2106.12910v1 (pdf) Date submitted: 2021-06-25 08:08 Submitted by: Kidonakis, Nikolaos Submitted to: SciPost Physics Proceedings Proceedings issue: DIS2021 Academic field: Physics Specialties: High-Energy Physics - Theory High-Energy Physics - Phenomenology Approaches: Theoretical, Phenomenological

### Abstract

We present theoretical results with soft-gluon corrections for two separate processes: (1) the production of a single top quark in association with a $W$ boson in the Standard Model; and (2) the production of a single top quark in association with a heavy $Z'$ boson in new physics models with or without anomalous couplings. We show that the higher-order corrections from soft-gluon emission are dominant for a wide range of collider energies. Results are shown for the total cross sections and top-quark transverse-momentum and rapidity distributions for $tW$ and $tZ'$ production at LHC and future collider energies up to 100 TeV. The uncertainties from scale dependence and parton distribution functions are also analyzed.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

#### Published as SciPost Phys. Proc. 8, 064 (2022)

Resubmission scipost_202108_00011v1 on 5 August 2021

Submission 2106.12910v1 on 25 June 2021

## Reports on this Submission

### Anonymous Report 3 on 2021-8-4 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2106.12910v1, delivered 2021-08-04, doi: 10.21468/SciPost.Report.3341

### Report

Two referee reports have already been provided for this proceeding, and I agree with their main point:
the overlap with ttbar production in the NLO QCD corrections has been completely ignored and as said in the report 1 “this applies also to the work this proceeding is based upon”.

The authors would be correct when they state that “The topic of tW and ttbar overlap is not directly relevant to our work which focuses on soft-gluon corrections in tW and tZ' production” if the proceeding was providing only formal results concerning the specific resummation contributions. On the other hand, predictions are then denoted as “approximated NLO (aNLO)” or even aNNLO or aNNNLO and then used for phenomenological conclusions. This is very misleading in my opinion without even mentioning in the discussion how the subtraction of the ttbar contribution is performed.

Furthermore there are statements like:

- “We show that the higher-order corrections from soft-gluon emission are dominant for a wide range of collider energies”. I do not see how this has been shown here, especially it is not clear to which class of contributions "dominant" refers to.

- “Perturbative QCD corrections are typically dominated by soft-gluon contributions”. In my opinion this is a too much strong statement. One can for example think about the very well known “Giant NLO QCD K-factors” in VV or V+jets processes, which are real hard QCD radiation effects.

- “soft-gluon corrections [1–4] are numerically dominant even at very high collider energies that are quite far from threshold [5] “ Is in reference [5] the ttbar overlap discussed? If not, where can be found the information about the removal/subtraction of the ttbar overlap at 100 TeV? This information should be properly referred in the proceeding.

-“We have demonstrated in all cases that higher-order corrections are large and are dominated by soft-gluon contributions” In the conclusion, this is a very strong statement not properly supported by results, since again the ttbar overlap has not been considered.

My general opinion is that a calculation of an important contribution to the tW and tZ’ cross section has been presented in a way that can be misleading and does not properly take into account or even mention a crucial technical and phenomenological issue in NLO or higher-order terms for this process. NLO predictions are on the other hand mentioned all over the text and used to build aNNLO and aNNNLO ones. Although this is a proceeding, nevertheless I think that this aspect cannot be neglected and what NLO means in this respect should be specified.

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### Author:  Nikolaos Kidonakis  on 2021-08-05  [id 1636]

(in reply to Report 3 on 2021-08-04)

We used MadGraph for our exact NLO calculations for tW and tZ' production as detailed in [5,6]. The overlap with ttbar was taken care of in our calculations through the removal of diagrams with resonant tbar contributions (this is done via a simple command in MadGraph). We will add a sentence and reference regarding that in the proceedings, so that it is more clear and explicit. It does not in any way affect the soft-gluon resummation, so it is not at all a central point of our work, which is why we did not dwell on this matter.

The term "approximate NLO (aNLO)" has nothing to do with the overlap problem so it is not misleading. It simply involves the soft-gluon corrections at NLO coming from the 2->2 process bg->tW. For the aNNLO and aN3LO results, we match to exact NLO, and with the clarifications mentioned in the previous paragraph it should now be very clear what "exact NLO" means.

(1) We have shown explicitly in Fig. 1 (right plot) that the aNLO and NLO results for tW production are very close to each other even at very high energies. In fact, that is a central point of our work and of our recent paper in JHEP [5] where we gave more details and where we wrote in the abstract that "We find that, remarkably, the soft-gluon corrections are numerically dominant even at very high collider energies." One can see from the figure in the proceedings that the aNLO and NLO curves are practically identical at LHC energies and that even at 100 TeV they remain very close, around 7% difference for the central results. Given that the NLO corrections are around 46% over LO at 100 TeV, this clearly shows that soft-gluon contributions are dominant (around 80% of the NLO corrections) even at this very high energy. This is a remarkable finding and a major -if not the main - point of our work in [5]. We also reached similar conclusions in [6] for tZ' production.

(2) The statement on "Perturbative QCD corrections ..." was in a sentence in the first paragraph that explicitly refers to top-quark processes. So this is a correct statement since all processes involving tops that we have studied are dominated by soft gluons. Even though both the sentence and the overall paragraph make it clear that we are discussing top processes, we actually think that the statement would apply to most QCD processes overall. Many other processes have been studied where soft-gluon corrections are dominant. "Typically" means in most cases, not always, so even that would be a defensible statement. But, in any case, we did not make a statement for all QCD processes but specifically for top-quark processes.

(3) The overlap was removed for all energies, via the procedure we mentioned above. The soft-gluon corrections are dominant throughout, as explained above.

[4] Again, Figure 1 fully supports this statement (see also [5,6]), and the overlap removal was included in the calculation as described above.

There was nothing misleading about the presentation of our work in this proceedings or in the multiple papers that were published on these topics by us in various journals (JHEP, PRD, EPJC) but we are happy to have clarified these matters for the referee. The reason we did not dwell on them at length (except briefly in [3]) is due to their peripheral nature to our considerations and purposes, which focus on the remarkable applicability of soft-gluon calculations even at very high future-collider energies.

### Anonymous Report 2 on 2021-7-27 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2106.12910v1, delivered 2021-07-27, doi: 10.21468/SciPost.Report.3301

### Report

This article does not contain new information directly, but rather summarises some relatively recent results obtained by the authors regarding soft-gluon corrections tW and tZ' production at hadron colliders. The authors correctly reference to these published results and for a proceedings it is quite normal to simply summarise the current situation.

The only improvement to this manuscript that I consider to be necessary is to also include the references to the NLO predictions presented in the plots (and not just to the articles where these plots were taken from), including the information on how the top pair production contributions were removed from these NLO calculations --I could not find the latter in the references from which the plots are taken. This would be needed to completely understand what is meant by "NLO".

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### Author:  Nikolaos Kidonakis  on 2021-08-05  [id 1635]

(in reply to Report 2 on 2021-07-27)

We will add the reference to the NLO results in the plots, and we will explain that we used removal of the diagrams with resonant tbar contributions at NLO in our calculations to address the overlap with ttbar production.

### Anonymous Report 1 on 2021-7-19 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2106.12910v1, delivered 2021-07-19, doi: 10.21468/SciPost.Report.3258

### Report

The authors present theoretical predictions for top and V (W, Z) associated production, including the effects of soft gluon resummation. Results are not original, as they are mostly based on previous work of the authors. However, this is quite usual for a conference proceeding, so I do not consider it as a weakness.

The main weakness I see is that (in general, this applies also to the work this proceeding is based upon) authors seem not to consider the quite vast literature about the problem of process overlapping between tW and ttbar at NLO (0805.3067, 0908.0631,1009.2450, 1607.05862). Such an overlapping, and the corresponding subtraction, introduce uncertainties which are of the order of ± 10%, roughly of the same size of the approximate-NNLO corrections.
As a matter of wording: The authors claim these effects to be'Large corrections': however, beyond NLO, effects are quite mild (10% or less as mentioned before). I would recommend a rephrasing.

After these points have been fixed, I can reconsider this work for publication on SciPost Proceedings.

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### Author:  Nikolaos Kidonakis  on 2021-07-20  [id 1592]

(in reply to Report 1 on 2021-07-19)

The topic of tW and ttbar overlap is not directly relevant to our work which focuses on soft-gluon corrections in tW and tZ' production. By the same token, the papers that the referee mentions came after the important contribution of soft gluons in tW production was known (see Ref. [1] as well as hep-ph/0701080 and Ref. [2]) yet they did not discuss these soft-gluon corrections, which again highlights the fact that these are separate matters.

However, we want to bring to the attention of the referee that the tW/ttbar overlap has actually been discussed at some length by one of us (N.K.) in 1612.06426 (Ref. [3]) where again it was stressed that it does not affect the resummation which is for a 2->2 process. A short proceedings paper with very limited space is not an appropriate place to discuss peripheral matters when we don't even have the space to address central issues to our work. In fact, we did not even think it necessary to discuss this in Ref. [5] since we would just be repeating what was covered in [3] without anything new to contribute to that issue. The main point of the section in our proceedings on tW production was that the soft-gluon approximation is excellent for a wide energy range and that the corrections are important (and similarly for tZ' production). But what we can do in response to the referee's comment is to add a short sentence to the proceedings referring to the discussion in Ref. [3] (and references therein).

Regarding "large corrections" we did not actually refer only to aNNLO but broadly to all soft-gluon corrections. We do of course find that the soft-gluon corrections are large, and we note that there is no precise quantitative definition of this term. But we can easily change "large" to "significant" or "substantial" or "important" or some other (still imprecise) term (in fact, we have already used some of those terms as well in the text).