⚛️ phenomenology

Investigation of the difference in the angular distributions of $Z\to \ell^{+}\ell^{-}$ events produced in quark-antiquark, quark-gluon and gluon-gluon collisions

This paper investigates theoretical predictions for the angular distributions of Z boson decay leptons in proton-proton collisions at 13 TeV, specifically comparing contributions from quark-antiquark, quark-gluon, and gluon-gluon processes to propose experimental methods for isolating these components using angular coefficients and kinematic variables.

Original authors: Arie Bodek, Giulia-Maria Bulugean, Aran Garcia-Bellido, Hyon San Seo, Rhys Taus, Un-Ki Yang

Published 2026-09-22

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Arie Bodek, Giulia-Maria Bulugean, Aran Garcia-Bellido, Hyon San Seo, Rhys Taus, Un-Ki Yang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

At the heart of modern physics lies a quest to understand the fundamental forces that bind the universe together. One of these forces, the strong nuclear force, is responsible for holding the tiny particles inside protons and neutrons together. Scientists study this force by smashing protons into each other at incredible speeds, recreating conditions similar to those just after the Big Bang. When these protons collide, they sometimes produce a heavy, unstable particle called a Z boson. This particle quickly decays, or breaks apart, into a pair of lighter particles called leptons, which can be electrons or muons. By carefully measuring the angles at which these leptons fly apart, physicists can learn about the invisible processes that created the Z boson. These measurements act as a precise test for our theories of how matter and energy interact, helping to confirm or challenge our current understanding of the subatomic world.

A team of researchers recently turned their attention to a specific puzzle regarding these measurements. While the Large Hadron Collider, the massive machine in Switzerland where these collisions happen, is famous for finding new particles like the Higgs boson, it is also a powerful microscope for studying the strong force. The scientists focused on the Z boson because its production is dominated by processes involving gluons, the particles that carry the strong force. In fact, at the energy levels used in these experiments, only about 40 percent of Z bosons come from the collision of a quark and an antiquark, which was the traditional focus of study. The remaining majority are produced through more complex interactions involving gluons. The researchers wanted to understand how these different production methods—quark-antiquark collisions, quark-gluon collisions, and gluon-gluon collisions—change the way the resulting leptons are distributed in space.

To investigate this, the team used sophisticated computer simulations to model billions of collisions at an energy of 13 trillion electron volts, matching the conditions of the Large Hadron Collider. They tracked the Z bosons as they were created and decayed, paying close attention to the angles of the resulting leptons. In the past, measurements of these angles showed a small but persistent discrepancy that theories could not fully explain. Specifically, the data suggested that the leptons were not behaving exactly as the standard models of particle physics predicted when the Z boson had a significant amount of sideways motion. The researchers suspected that the mix of different collision types in the data was the key to unlocking this mystery.

The simulations revealed that the different ways Z bosons are produced leave distinct fingerprints on the angles of the leptons. When a Z boson is created by a quark and an antiquark, the leptons follow one specific pattern. When it is created by a quark and a gluon, or by two gluons, the pattern shifts. The study found that the overall mix of these events changes depending on how much sideways momentum the Z boson has. At low sideways momentum, the quark-antiquark process is more common, but as the sideways momentum increases, the gluon-involved processes take over. This shifting balance explains why the overall measurements of the angles looked different from what simple theories predicted.

One of the most significant findings was that the discrepancy in the angular measurements, which had puzzled scientists for some time, is largely caused by events where more than one jet of particles is produced alongside the Z boson. A jet is a spray of particles created when a quark or gluon is knocked out of the collision. The researchers discovered that when they looked only at events with zero or one jet, the measurements matched the theoretical predictions much more closely. The violation of the expected relationship between the angles only became apparent when events with two or more jets were included in the mix. This suggests that the extra complexity of multiple jets distorts the angular distribution in a way that current models struggle to describe perfectly.

The study also looked at how to isolate specific types of collisions to test these ideas in real experiments. They proposed that by selecting events containing a specific type of heavy quark called a bottom quark, which is often produced in quark-gluon collisions, scientists could isolate that particular process. This would allow experimentalists to measure the angular patterns of quark-gluon collisions directly, without the noise of other processes. The simulations showed that the patterns for these specific collisions differ significantly from the simple approximations that physicists had used in the past. The old approximations tended to overestimate the effect of these collisions, and the new, more detailed simulations provide a better guide for what to expect.

Ultimately, this work provides a clearer map of how the strong force operates during high-energy collisions. It shows that the simple picture of quarks and antiquarks colliding is not enough to describe the full complexity of the Large Hadron Collider. The gluon-rich environment creates a rich variety of interactions that must be accounted for to make precise measurements. By understanding how the different production methods contribute to the final data, physicists can refine their models and improve the accuracy of their measurements. This level of detail is crucial for future discoveries, as even tiny deviations from the predicted patterns could hint at new, unknown physics waiting to be found. The study confirms that the tools and methods used to analyze these collisions need to be as sophisticated as the collisions themselves, separating the different types of events to see the true nature of the particles involved.

Technical Summary: Investigation of Angular Distributions in Z → ℓ⁺ℓ⁻ Events

Problem Statement
Measurements of the angular distributions of leptons from Z boson decays at the Large Hadron Collider (LHC) serve as critical tests of perturbative Quantum Chromodynamics (QCD) and inputs for precision electroweak measurements. While existing measurements of angular coefficients ( $A_0$ through $A_7$ ) by ATLAS, CMS, and LHCb generally agree with QCD predictions for $A_0$ , a persistent discrepancy exists regarding the Lam-Tung (L-T) relation. The L-T relation predicts $A_0 - A_2 = 0$ at leading order (LO). However, experimental data reveals a violation where $A_2 < A_0$ , and the magnitude of this violation is larger than predicted by current theoretical simulations. Existing measurements have not separated the contributions of different partonic subprocesses (quark-antiquark, quark-gluon, and gluon-gluon) or investigated the dependence of this violation on final-state jet multiplicity, leaving the origin of the discrepancy unclear.

Methodology
The authors utilize the powheg-MiNNLOPS event generator (referred to as MiNNLO), matched to Pythia 8.2 for parton showering, to simulate proton-proton collisions at $\sqrt{s} = 13$ TeV. The study focuses on the Drell-Yan process $pp \to \gamma^*/Z \to \ell^+\ell^-$ ( $\mu^+\mu^-$ or $e^+e^-$ ) within the Z boson mass region ( $80 < M_{\ell\ell} < 100$ GeV).

Key methodological steps include:

Subprocess Separation: The simulation explicitly categorizes events into three representative subprocesses: quark-antiquark annihilation ( $qq \to \gamma^*/Z g$ ), quark-gluon Compton scattering ( $qg \to \gamma^*/Z q$ ), and gluon-gluon scattering ( $gg \to \gamma^*/Z q\bar{q}$ ).
Frame Definition: Angular distributions are analyzed in the Collins-Soper (CS) frame, where angles $\theta$ and $\phi$ are defined relative to the bisector of the proton beam directions.
Coefficient Extraction: The angular coefficients $A_0$ and $A_2$ are extracted by fitting the differential cross-sections of the generated Monte Carlo (MC) samples. The study compares direct fitting methods against the method of moments to ensure consistency.
Kinematic Dependence: The analysis investigates $A_0$ and $A_2$ as functions of the Z boson transverse momentum ( $p_T^Z$ ), rapidity ( $y_Z$ ), and final-state jet multiplicity (specifically distinguishing between inclusive samples and those with $\le 1$ jet).
Experimental Proposal: The paper proposes specific experimental strategies to isolate subprocesses, notably using events with a single $b$ -tagged jet to predominantly select the $qg$ Compton process.

Key Results

Subprocess Dominance: At $\sqrt{s} = 13$ TeV, Z boson production is dominated by gluon-initiated processes. The $qq$ channel accounts for only approximately 40% of the total cross-section in the Z-mass region, while the $qg$ fraction increases from about half at $p_T^Z = 0$ to 0.8 at high $p_T^Z$ .
Rapidity Independence: The angular coefficients $A_0$ and $A_2$ are found to be consistent across different rapidity regions ( $|y_Z| < 1$ and $1 < |y_Z| < 2.4$ ) for all subprocesses.
Origin of Lam-Tung Violation: The study confirms that the violation of the Lam-Tung relation ( $A_0 \neq A_2$ ) in the inclusive sample originates primarily from events with more than one hadronic jet in the final state. In samples restricted to events with $\le 1$ jet, the violation is significantly reduced, consistent with the expectation that additional QCD radiation (multi-jet events) smears the $\phi$ distribution.
Discrepancy with Data: The authors note that while their MC study attributes the L-T violation to multi-jet events, the violation observed in ATLAS (8 TeV) and CMS (13 TeV) data is larger than that predicted by the MiNNLO simulation. This suggests that multi-jet events may be mismodeled in current MC generators.
Parametrization of Coefficients:
- $qq$ Process: $A_0^{qq}$ follows the geometric prediction $A_0^{qq} = p_T^2 / (M^2 + p_T^2)$ well for $p_T^Z < 200$ GeV.
- $qg$ Process: The previously proposed approximation $A_0^{qg} \approx 5p_T^2 / (M^2 + 5p_T^2)$ significantly overestimates the simulated values, particularly at high $p_T^Z$ . The authors propose a new parametrization using a weighted sum of geometric forms with fitted parameters ( $\alpha = 0.55, \beta = 1.30$ ).
- $gg$ Process: Similarly, the standard approximation overestimates $A_0^{gg}$ . A new parametrization is provided ( $\alpha = 0.9, \beta = 0.35$ ).
$b$ -Tagged Jet Strategy: The analysis of $A_0$ for specific quark flavors in the $qg$ process shows that events with a single $b$ -tagged jet in the final state are predominantly produced via the $bg \to bZ$ subprocess. This provides a viable experimental method to isolate and test the $qg$ angular coefficient predictions.

Significance and Claims
The paper claims to provide a more differential understanding of angular coefficients by disentangling the contributions of $qq$, $qg$, and $gg$ subprocesses. It identifies that the inclusive Lam-Tung violation is driven by multi-jet topologies, offering a specific target for experimental verification (comparing inclusive vs. $\le 1$ jet samples). Furthermore, the paper challenges the validity of existing theoretical approximations for $A_0^{qg}$ and $A_0^{gg}$ , providing new parametrizations based on NNLO-accurate simulations. Finally, it proposes a concrete experimental avenue—using single $b$ -tagged jet events—to experimentally validate the $qg$ subprocess predictions, which are currently difficult to isolate in inclusive measurements. The authors conclude that the larger-than-predicted violation in experimental data suggests a need for improved modeling of multi-jet events in QCD simulations.

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