# Simultaneously determining the $W^{\pm}$ boson mass and parton shower model parameters

### Submission summary

 As Contributors: Oliver Lupton Arxiv Link: https://arxiv.org/abs/1907.09958v2 Date submitted: 2019-12-13 Submitted by: Lupton, Oliver Submitted to: SciPost Physics Discipline: Physics Subject area: High-Energy Physics - Experiment Approaches: Experimental, Computational, Phenomenological

### Abstract

We explore the possibility of simultaneously determining the $W$ boson mass, $m_{W}$, and QCD-related nuisance parameters that affect the $W$ boson $p_{\mathrm{T}}$ spectrum from a fit to the $p_{\mathrm{T}}$ spectrum of the muon in the leptonic decay $W\rightarrow\mu\nu$. The study is performed using pseudodata generated using Pythia and the muon is required to fall in a kinematic region corresponding to the approximate acceptance of the LHCb detector. We find that the proposed method performs well and has little trouble disentangling variations in the muon $p_{\mathrm{T}}$ spectrum due to $m_{W}$ from those due to the $W$ boson $p_{\mathrm{T}}$ model.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1907.09958v2 on 13 December 2019

## Reports on this Submission

### Strengths

1. Good background, context and motivation for the studies performed.
2. Technically/statistically sound procedure with comprehensive description of the methodology.
3. Good visualisation of the results.

### Weaknesses

1. Extremely simplified model.
2. Lack of quantitative results on the uncertainty in the W transverse momentum distribution and its relationship to the additional uncertainty on the extracted W mass.

### Report

The issue which is explored is highly relevant to measurements of the W mass at the LHC, and the studies which are performed are technically sound and well described. The model which is used is however extremely simplified and very far from what would be used in a real measurement, though these limitations are accurately acknowledged in the paper. It is not straightforward to compare the in-situ constraints achieved by the fit with this toy model to existing theoretical predictions or to understand how this is related quantitatively to the residual uncertainty on the W mass.

### Requested changes

The paper would benefit from both a visualisation and quantification of the post-fit uncertainty on the W transverse momentum distribution itself in the different scenarios, and how this relates to the residual uncertainty on the extracted W mass.

I would suggest at least one illustrative plot showing the W transverse momentum distribution with postfit uncertainty bands for one of the scenarios, possibly with additional lines showing variations from individual parameters and/or post-fit eigenvectors to visualise the correlation structure.

This could possibly also be extended to plots in the style of Fig. 8 showing the relationship between the uncertainty on the W pT distribution at one or more values vs the fit range in muon pT, which could then be compared to the corresponding uncertainty on mW itself.

• validity: high
• significance: ok
• originality: good
• clarity: top
• formatting: excellent
• grammar: excellent

### Strengths

the paper “Simultaneously determining the W boson mass and parton shower model parameters”
by O. Lupton and M. Vesterinen is a study of fits of the muon pt spectrum in W decays from Pythia generated pseudo-data in a kinematic region similar to the acceptance of the LHCb experiment . They fit simultaneously the W mass and two Pythia parameters , relevant for shaping the W pt distribution. The main result of the paper is that the correlation of the W mass with these two parameters is in the 30\%-60\% region depending on the rage of the fit.

I think the paper is technically sound and reports a wealth of information about those fits: correlations among the parameters, dependence on the fit range.

### Weaknesses

The question that comes natural is: what do we learn from these fits ?
\begin{enumerate}
\item The abstract says “that there is little trouble in disentangling variations in the muon pt spectrum due to Mw from those due to the W boson pt model”. This is not surprising: Mw generates (almost) a singularity in the muon spectrum in the W reference frame, which is then smeared by the W Pt. The two parameters in the study cannot be *very* correlated with Mw unless one restrict the study of the spectrum in a small region near Mw/2.
\item The author themselves recognise that the proposed method is not suited for a W mass measurement with small systematic uncertainty , see second paragraph at page 2. And they correctly do not provide an estimate of the systematic uncertainty on Mw following from the method that they propose.
\end{enumerate}

### Report

Dear Editor,

the paper “Simultaneously determining the W boson mass and parton shower model parameters”
by O. Lupton and M. Vesterinen is a study of fits of the muon pt spectrum in W decays from Pythia generated pseudo-data in a kinematic region similar to the acceptance of the LHCb experiment . They fit simultaneously the W mass and two Pythia parameters , relevant for shaping the W pt distribution. The main result of the paper is that the correlation of the W mass with these two parameters is in the 30\%-60\% region depending on the rage of the fit.

I think the paper is technically sound and reports a wealth of information about those fits: correlations among the parameters, dependence on the fit range. The question that comes natural is: what do we learn from these fits ?
\begin{enumerate}
\item The abstract says “that there is little trouble in disentangling variations in the muon pt spectrum due to Mw from those due to the W boson pt model”. This is not surprising: Mw generates (almost) a singularity in the muon spectrum in the W reference frame, which is then smeared by the W Pt. The two parameters in the study cannot be *very* correlated with Mw unless one restrict the study of the spectrum in a small region near Mw/2.

\item The author themselves recognise that the proposed method is not suited for a W mass measurement with small systematic uncertainty , see second paragraph at page 2. And they correctly do not provide an estimate of the systematic uncertainty on Mw following from the method that they propose.
\end{enumerate}

The important question is - in my opinion - to which precision the W pt spectrum can be modelled from the proposed variations, and in general using parton-shower algorithms ? This question is not addressed in the paper. And I think it cannot be answered in a robust way. Another interesting and correlated question- not addressed in the paper - is : how well do we need to know the W pt spectrum in order to have a systematic uncertainty on W mass smaller than say 10 MeV ? There is a generic statement at page 1, however would be nice to see if there are peculiarities in this special forward kinematic region.

For the reasons mentioned above I find that this paper adds little information to the public discussion on the W mass measurement.

In the conclusions the authors say that “In an actual measurement of mW it would, of course, be preferable to apply the same technique (eg simultaneous fit of Mw and some nuisance parameters) using predictions from tools that contain higher order electroweak and QCD corrections, which naturally leads to the question of what parameters can legitimately be varied in this case” . This is a more interesting subject, but it is not discussed in the paper.

• validity: ok
• significance: low
• originality: good
• clarity: high
• formatting: excellent
• grammar: excellent