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arxiv: 2604.25678 · v1 · submitted 2026-04-28 · ✦ hep-ex

Recognition: unknown

Measurement of the Z to μ^+μ^- angular coefficients in pp collisions at sqrt{s} = 13 TeV as functions of transverse momentum and rapidity

CMS Collaboration
Authors on Pith no claims yet

Pith reviewed 2026-05-07 14:07 UTC · model grok-4.3

classification ✦ hep-ex
keywords angular coefficientsDrell-Yan processZ boson productionmuon pair productiontransverse momentum dependencerapidity dependenceperturbative QCD
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The pith

The eight angular polarization coefficients A0 to A7 are measured double-differentially in the Drell-Yan production of muon pairs.

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

The paper extracts the coefficients that fully describe the angular distribution of muons from Z boson decays in proton-proton collisions. These coefficients are obtained in eight intervals of the muon pair's transverse momentum and two intervals of its rapidity, all within the narrow invariant-mass window around the Z mass. The measured values are then compared directly to next-to-next-to-leading-order perturbative QCD calculations. Agreement with the predictions would confirm that the dominant partonic mechanisms are understood at this order, while any systematic mismatch would point to incomplete higher-order effects or other contributions to the production process.

Core claim

The measurement determines the eight angular coefficients A0 through A7 that appear in the differential cross section for Drell-Yan muon-pair production. The coefficients are extracted as functions of the transverse momentum and rapidity of the muon pair in the mass range 81-101 GeV and are compared with theoretical predictions calculated at next-to-next-to-leading order in perturbative quantum chromodynamics, thereby supplying information on the underlying partonic dynamics and Z production mechanisms.

What carries the argument

The eight angular polarization coefficients A0 to A7 that parameterize the full angular dependence of the muon pair in the Collins-Soper frame of the Drell-Yan process.

If this is right

  • The results supply a direct test of the accuracy of perturbative QCD calculations for vector-boson production at this collider energy.
  • Any region of kinematic space where the measured coefficients depart from the predictions would indicate the need for additional higher-order corrections or resummation.
  • The double-differential data set constrains the parton-level dynamics that enter Z-boson production.

Where Pith is reading between the lines

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

  • When these coefficients are included in global parton-distribution fits, they can tighten constraints on the gluon and quark densities at moderate momentum fractions.
  • A future measurement extending to higher transverse momentum or lower invariant mass could expose the onset of electroweak corrections or possible new-physics contributions.
  • The same angular framework can be applied to other vector-boson processes to test the universality of the extracted coefficients.

Load-bearing premise

Detector acceptance, efficiency, and background contributions can be modeled and corrected without introducing significant bias inside the chosen double-differential bins.

What would settle it

A statistically significant deviation between the measured coefficients and the next-to-next-to-leading-order QCD predictions that persists after all experimental uncertainties are accounted for, particularly in the highest transverse-momentum interval.

Figures

Figures reproduced from arXiv: 2604.25678 by CMS Collaboration.

Figure 1
Figure 1. Figure 1: The definition of the CS frame and angles view at source ↗
Figure 2
Figure 2. Figure 2: Distributions of events as functions of cos view at source ↗
Figure 3
Figure 3. Figure 3: Left: Polarization coefficients A0 to A3 measured in the CS frame in bins of p µµ T for |y µµ | < 1. The data points are shown as black circles. The POWHEG +MINNLO and the MADGRAPH5 aMC@NLO predictions are represented by the red circles and blue squares, re￾spectively, slightly displaced horizontally for improved visibility. The vertical bars (hatched boxes) represent the statistical (systematic) uncertain… view at source ↗
Figure 4
Figure 4. Figure 4: Same as Fig. 3, for the polarization coefficients view at source ↗
Figure 5
Figure 5. Figure 5: Same as Fig. 3, for the 1 view at source ↗
Figure 6
Figure 6. Figure 6: Same as Fig. 4, for the 1 view at source ↗
Figure 7
Figure 7. Figure 7: Left: Difference A0 − A2 measured in the CS frame in bins of p µµ T for |y µµ | < 1 (upper) and 1 < |y µµ | < 2.4 (lower). Right: Corresponding differences between the predicted and measured values. sponding A0 − A2 values. The POWHEG+MINNLO and MADGRAPH5 aMC@NLO predictions are also shown in the figures. Tables A.1–A.3, in the Appendix, provide the measured values. The A0 values from data and POWHEG+MINNL… view at source ↗
read the original abstract

A measurement of the eight angular polarization coefficients, $A_0$ to $A_7$, in the cross section for the Drell$-$Yan production of two muons is presented. The analysis is based on proton-proton (pp) collision data recorded with the CMS detector at the LHC at a center-of-mass energy of $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 140 fb$^{-1}$. The coefficients are determined double differentially in eight intervals of transverse momentum and two intervals of rapidity of the muon pair $\mu^+\mu^-$. The results are presented for the $\mu^+\mu^-$ invariant mass range 81$-$101 GeV and are compared with theoretical predictions calculated at next-to-next-to-leading order in perturbative quantum chromodynamics. The measurement provides relevant information about the underlying partonic dynamics and the Z boson production mechanisms.

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.

Referee Report

2 major / 1 minor

Summary. The manuscript presents a measurement of the eight angular polarization coefficients A0 to A7 in the Drell-Yan process Z → μ⁺μ⁻ using 140 fb⁻¹ of 13 TeV pp collision data recorded with the CMS detector. The coefficients are extracted double-differentially in eight intervals of dimuon transverse momentum and two intervals of rapidity, restricted to the 81-101 GeV invariant-mass window, and compared to next-to-next-to-leading-order perturbative QCD predictions.

Significance. If the experimental corrections hold, the result supplies high-statistics, double-differential data on Z-boson polarization that can constrain partonic dynamics and test the accuracy of NNLO calculations in a kinematic regime where higher-order effects and parton distributions are relevant. The large integrated luminosity and fine binning constitute a clear experimental strength.

major comments (2)
  1. [analysis and coefficient extraction] The extraction of A0–A7 from the observed cosθ* and φ* distributions (described in the analysis section) relies on simulation-based corrections for detector acceptance, reconstruction efficiency, trigger, and backgrounds in each of the 8 pT × 2 y bins. No explicit validation is shown that residual data-MC differences in the angular variables inside these bins are negligible, especially at low pT where acceptance varies rapidly; any such mismatch directly biases the extracted coefficients and undermines the theory comparison.
  2. [results and systematic uncertainties] Table or figure presenting the final A_i values with uncertainties must include a breakdown of the systematic component arising from the acceptance/efficiency modeling; without it, it is impossible to judge whether the quoted precision is realistic or whether the double-differential binning has amplified modeling uncertainties.
minor comments (1)
  1. [abstract] The abstract states the mass window and binning but does not quote the total number of selected events or the typical statistical precision per bin; adding these numbers would help readers assess the measurement's reach.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments on our manuscript. We address each major comment below and outline the revisions we will make to strengthen the presentation of the analysis and results.

read point-by-point responses

  1. Referee: The extraction of A0–A7 from the observed cosθ* and φ* distributions (described in the analysis section) relies on simulation-based corrections for detector acceptance, reconstruction efficiency, trigger, and backgrounds in each of the 8 pT × 2 y bins. No explicit validation is shown that residual data-MC differences in the angular variables inside these bins are negligible, especially at low pT where acceptance varies rapidly; any such mismatch directly biases the extracted coefficients and undermines the theory comparison.

    Authors: We agree that explicit validation of residual data-MC differences in the angular variables is essential, particularly at low pT. The manuscript describes the correction procedure and includes some data-MC comparisons in the supplementary material, but we will add a dedicated subsection and representative figures in the main text showing post-correction cosθ* and φ* distributions in data versus simulation across the pT and y bins. These will quantify any residuals and confirm they are covered by the assigned systematics, thereby reinforcing the reliability of the coefficient extraction. revision: yes

  2. Referee: Table or figure presenting the final A_i values with uncertainties must include a breakdown of the systematic component arising from the acceptance/efficiency modeling; without it, it is impossible to judge whether the quoted precision is realistic or whether the double-differential binning has amplified modeling uncertainties.

    Authors: We acknowledge the value of a detailed systematic breakdown for assessing the quoted precision. The current manuscript quotes the total systematic uncertainty; we will add a new table (or expanded panel in the results figure) that explicitly decomposes the systematic contributions, with a dedicated column or row for acceptance/efficiency modeling uncertainties, for each A_i in every pT and y bin. This will allow direct evaluation of modeling effects in the double-differential measurement. revision: yes

Circularity Check

0 steps flagged

Experimental measurement of angular coefficients is data-driven with no circular reduction

full rationale

The paper reports a direct experimental extraction of A0–A7 coefficients from observed muon angular distributions in pp collisions, after standard detector corrections and background subtraction, then compares the results to independent NNLO pQCD calculations. No equation or step defines the target coefficients in terms of themselves, renames a fit as a prediction, or relies on a self-citation chain for the central claim. The derivation chain from raw data to double-differential coefficients is externally benchmarked and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The measurement rests on standard assumptions of the Drell-Yan process and angular parameterization; no new free parameters, axioms, or invented entities are introduced beyond established particle physics tools.

axioms (1)
  • domain assumption The angular distribution of muon pairs from Z decay can be fully described by eight coefficients A0 to A7 in a chosen reference frame.
    This is the standard parameterization used in Drell-Yan angular analyses.

pith-pipeline@v0.9.0 · 5464 in / 1233 out tokens · 84575 ms · 2026-05-07T14:07:45.169571+00:00 · methodology

discussion (0)

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Reference graph

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