Towards a W boson mass measurement with LHCb

Martina Pili (on behalf of the LHCb Collaboration)

arxiv: 1907.02029 · v1 · pith:UCT2KN2Inew · submitted 2019-07-03 · ✦ hep-ph · hep-ex

Towards a W boson mass measurement with LHCb

Martina Pili (on behalf of the LHCb Collaboration) This is my paper

Pith reviewed 2026-05-25 09:52 UTC · model grok-4.3

classification ✦ hep-ph hep-ex

keywords W boson massLHCbPDF uncertaintyRun 2forward rapidityparton distribution functionsZ boson production

0 comments

The pith

LHCb can halve the PDF uncertainty on its W boson mass measurement with a new approach using Run 2 data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that LHCb's forward-rapidity measurements of W and Z boson production offer a complementary route to the W boson mass. All hadron-collider measurements face PDF uncertainties, yet the LHCb result can partially cancel those uncertainties in a combined average with ATLAS and CMS. The authors present a new method that targets a factor-of-two reduction in the PDF uncertainty on the LHCb measurement once Run 2 data are analyzed. If the reduction holds, the combined world average for the W mass would gain precision without requiring changes to the other experiments.

Core claim

The central claim is that a new approach to PDF uncertainty handling, applied to LHCb's forward W and Z data, should reduce the PDF uncertainty on the LHCb W-mass measurement by roughly a factor of two with Run 2 statistics, thereby making the result a useful addition to the global average.

What carries the argument

The new approach to PDF uncertainty reduction that exploits LHCb's simultaneous W and Z measurements at forward rapidities.

If this is right

The PDF uncertainty on the LHCb W mass result falls by roughly a factor of two.
Partial cancellation of PDF uncertainties occurs when the LHCb result enters the global average.
The combined precision on the W boson mass improves.
LHCb forward data become more constraining for electroweak parameters.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same forward data set could tighten PDF fits when combined with central-rapidity measurements.
Future LHCb runs might achieve still smaller uncertainties if the approach continues to scale with luminosity.
Other precision observables measured at forward rapidities could benefit from analogous uncertainty-reduction techniques.

Load-bearing premise

The proposed new approach can be implemented on actual LHCb Run 2 data and will deliver the stated factor-of-two reduction without unforeseen experimental or theoretical complications.

What would settle it

When the new method is applied to real LHCb Run 2 data the PDF uncertainty on the W mass does not shrink by approximately a factor of two.

Figures

Figures reproduced from arXiv: 1907.02029 by Martina Pili (on behalf of the LHCb Collaboration).

**Figure 1.** Figure 1: Upper: the distribution of the best-fit χ 2 versus MW for a fit to a single toy dataset from the W− sample, which assumes the LHCb Run 2 statistics, with each of the 1000 NNPDF3.1 replicas. Lower: the distribution of the MW values with a Gaussian fit function overlaid. valence u(d) quarks, with a roughly 20% contribution from annihilation of gluons with sea quarks (gqs). Contributions from the annihilatio… view at source ↗

**Figure 2.** Figure 2: The (left) W+ and (right) W+ rapidity distributions decomposed into the main partonic subprocesses. first quark generation seems to be the most important it is interesting to see if there are any obvious patterns in the corresponding PDFs for the replicas that lead to biased MW determinations. The studies in this section make use of a subset of the NNPDF3.1 replicas [PITH_FULL_IMAGE:figures/full_fig_p003… view at source ↗

**Figure 3.** Figure 3: The ratios of a subset of NNPDF3.1 replicas with respect to the central replica, for the x dependence of the d and ¯u PDFs. Each line is marked with a colour indicating the shift of the MW value determined from a fit to the p µ T distribution of a single toy dataset. since these quantities are not directly measurable with LHCb, it is interesting to study the muon kinematic distributions [PITH_FULL_IMAGE:… view at source ↗

**Figure 4.** Figure 4: The variations in the shapes of the p µ T and η distributions predicted with a subset of NNPDF3.1 replicas. Each line is marked with a colour indicating the shift of the MW value determined from a fit to the p µ T distribution of a single toy dataset. 4. The proposed method Section 3 suggested that a fit to the two-dimensional p µ T versus η distribution has potential to further constrain the PDF uncertain… view at source ↗

**Figure 5.** Figure 5: The distribution of the PDF uncertainty evaluated for 1000 toy datasets using three different methods: p µ T fit without weighting, p µ T fit with weighting, (p µ T ,η) fit with weighting. The one-dimensional unweighted distribution is arbitrarily scaled down by a factor of ten. 4.1 Simultaneous fit Given the results shown in the previous section it is now interesting to consider the combination of the tw… view at source ↗

**Figure 6.** Figure 6: Left: The distribution of the PDF uncertainty evaluated for 1000 toy datasets using a simultaneous fit. Right: PDF uncertainty as a function of the p µ T range used in the simultaneous fit. The bands report the mean and the RMS of the distribution of the PDF uncertainty evaluated for 1000 toy datasets. 4.2 Dependence on the detector acceptance The study was so far restricted to events with 30 < p µ T < 50 … view at source ↗

read the original abstract

LHCb provides unique opportunities to study $W$ and $Z$ boson production at forward rapidities at the LHC. It has recently been suggested that a measurement of the $W$ boson mass by LHCb would complement measurements by ATLAS and CMS. All measurements of the $W$ mass at hadron colliders are subject to PDF uncertainties, but there would be a partial cancellation of the overall PDF uncertainty when the LHCb result is included in an average with measurements by ATLAS and CMS. Here we review measurements of $W$ and $Z$ boson production by LHCb, and report on a new study of the PDF uncertainty on the LHCb measurement of the $W$ mass. The latter study includes the proposal of a new approach that should reduce the PDF uncertainty by roughly a factor of two with LHCb Run 2 data.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

LHCb sketches a forward-rapidity method that could halve the PDF uncertainty on a future W mass measurement, but the note gives no equations, plots, or validation for the claimed reduction.

read the letter

The core takeaway is that this short note reviews LHCb's existing W and Z results and floats a new approach to cut the PDF uncertainty on a W mass measurement by roughly a factor of two when combined with ATLAS and CMS. The forward kinematics are the selling point for partial cancellation in the global average. That idea is worth noting for anyone doing electroweak fits or PDF combinations. The review section does a clean job of pulling together the published LHCb cross-section measurements and explaining why they matter for a mass analysis. It is straightforward and cites the right prior work without overclaiming. The soft spot is exactly what the stress-test flags: the factor-of-two number is a projection from an internal study, not a result extracted from Run 2 data with real detector response, efficiencies, and background subtraction. The abstract and text supply no equations, no breakdown of the new method, and no cross-checks, so the central claim cannot be assessed from what is written. This is a proposal, not a delivered measurement. The paper is mainly useful to people already following LHCb electroweak plans or global W-mass averages who want an early heads-up on a possible analysis direction. A reader expecting a full method or validated uncertainty reduction will come away empty. It is coherent on its own terms as a conference-style note, so it deserves a serious referee rather than a desk reject; the underlying complementarity argument is standard but the specific forward-region proposal is worth checking in a full paper if the collaboration follows through.

Referee Report

2 major / 1 minor

Summary. The manuscript reviews existing LHCb measurements of W and Z boson production at forward rapidities and reports on a new study proposing an approach to reduce the PDF uncertainty on a prospective W boson mass measurement by roughly a factor of two with Run 2 data, enabling partial cancellation of PDF uncertainties in a combined average with ATLAS and CMS results.

Significance. If the proposed PDF-reduction method can be validated and implemented, the unique forward kinematic coverage of LHCb would provide a valuable independent constraint, strengthening the overall precision of the W-mass world average beyond what is achievable from central-rapidity measurements alone.

major comments (2)

[Abstract] Abstract: the central claim of a factor-of-two PDF-uncertainty reduction is stated as the outcome of 'a new study' but is unsupported by any equations, simulation details, validation plots, or data-selection criteria, preventing assessment of whether the projection survives translation to real data.
[Section describing the new study] Section describing the new study (the only section that could contain the supporting material): the factor-of-two reduction is presented as a projection rather than a result obtained by applying the method to recorded LHCb Run 2 data, including lepton identification efficiencies, background subtraction, and the precise folding of the new PDF constraint into the mass fit; these steps remain untested in the manuscript and are load-bearing for the claim.

minor comments (1)

The title accurately signals the forward-looking character of the work; no change needed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed review and constructive comments on our short note proposing a PDF-reduction approach for a prospective LHCb W-mass measurement. The manuscript is explicitly framed as a review plus projection study rather than a completed analysis on recorded data. We respond point-by-point below.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim of a factor-of-two PDF-uncertainty reduction is stated as the outcome of 'a new study' but is unsupported by any equations, simulation details, validation plots, or data-selection criteria, preventing assessment of whether the projection survives translation to real data.

Authors: The abstract condenses the outcome of the dedicated study described in the body. That study uses existing LHCb forward-rapidity measurements and PDF eigenvector sets to quantify the reduction via partial cancellation when combined with central-rapidity results; it is a Monte-Carlo-based projection, not a data analysis. We agree the abstract could be clarified and will revise it to state explicitly that the factor-of-two estimate is obtained from a simulation study of the proposed PDF constraint. revision: partial
Referee: [Section describing the new study] Section describing the new study (the only section that could contain the supporting material): the factor-of-two reduction is presented as a projection rather than a result obtained by applying the method to recorded LHCb Run 2 data, including lepton identification efficiencies, background subtraction, and the precise folding of the new PDF constraint into the mass fit; these steps remain untested in the manuscript and are load-bearing for the claim.

Authors: The manuscript is titled 'Towards a W boson mass measurement' and its purpose is to outline the kinematic advantage of LHCb and to present a new PDF-constraint idea with a quantitative estimate of its impact. The projection employs the statistical precision and PDF sensitivity expected from published LHCb Run-2 analyses; it does not attempt the full experimental chain (efficiencies, backgrounds, mass-fit implementation) because those belong to a future measurement paper. The PDF-reduction factor is demonstrated at the level of the parton luminosities and their propagation to m_W, which is the novel element being proposed. We therefore maintain that the projection is appropriately scoped for this note and does not require the full data-analysis machinery to be valid. revision: no

Circularity Check

0 steps flagged

No circularity: forward-looking proposal with no fitted derivations or self-referential reductions

full rationale

The paper is explicitly a proposal and review of existing LHCb W/Z measurements plus a new study projecting PDF uncertainty reduction. No equations, parameter fits, or derivation chains are presented that could reduce to inputs by construction. The factor-of-two claim is framed as a projection from the study, not an output obtained from actual data fitting. This matches the default case of a self-contained proposal without load-bearing self-citations or fitted-input predictions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The document is a proposal for an analysis approach; no free parameters, axioms, or invented entities are introduced in the abstract.

pith-pipeline@v0.9.0 · 5667 in / 933 out tokens · 38392 ms · 2026-05-25T09:52:59.332793+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages · 11 internal anchors

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ATLAS, Measurement of the W-boson mass in pp collisions at√s = 7 TeV with the ATLAS detector, Eur. Phys. J.C78, no.11, 898 (2018), arXiv:1701.07240

work page internal anchor Pith review Pith/arXiv arXiv 2018

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work page arXiv 2012

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work page internal anchor Pith review Pith/arXiv arXiv 2012

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work page internal anchor Pith review Pith/arXiv arXiv 2015

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work page internal anchor Pith review Pith/arXiv arXiv 2016

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work page internal anchor Pith review Pith/arXiv arXiv 2016

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LHCb, Measurement of the forward-backward asymmetry in Z/γ∗→ µ +µ− decays and determination of the effective weak mixing angle, JHEP 11 (2015) 190, arXiv:1509.07645

work page internal anchor Pith review Pith/arXiv arXiv 2015

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work page internal anchor Pith review Pith/arXiv arXiv 2015

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work page internal anchor Pith review Pith/arXiv arXiv 2019

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S. Alioli, P. Nason, C. Oleari and E. Re, NLO vector-boson production matched with shower in POWHEG, JHEP 07 (2008) 060, arXiv:0805.4802

work page internal anchor Pith review Pith/arXiv arXiv 2008

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PYTHIA 6.4 Physics and Manual

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