⚛️ high-energy experiments

Measurement of the fragmentation properties of jets containing $\Upsilon$ (nS) mesons in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using proton-proton collision data at $\sqrt{s}$ = 13 TeV, this study measures the fragmentation properties of jets containing $\Upsilon$ (nS) mesons and finds that current Monte Carlo models, including recent quarkonia production developments, fail to satisfactorily describe the observed longitudinal and transverse momentum projections.

Original authors: CMS Collaboration

Published 2026-07-29

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: CMS Collaboration

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

Imagine the universe as a giant, chaotic kitchen where the fundamental ingredients of matter are constantly being tossed together. In this kitchen, the most famous chefs are protons, which smash into each other at nearly the speed of light inside a massive ring called the Large Hadron Collider (LHC). When these protons collide, they don't just break apart; they explode into a shower of new particles. Among these particles are "heavy quarks," which are like the heavy, dense ingredients of the universe. When a heavy quark meets its anti-quark partner, they stick together to form a bound state called a "quarkonium." Think of this like a heavy-duty magnet snapping shut.

The big mystery scientists are trying to solve is how these magnets form and behave when they are born inside a chaotic storm of other particles. Specifically, they want to know how much of the "storm's" energy the magnet grabs for itself. In physics terms, this is called "fragmentation." It's like watching a specific drop of water try to ride a wave: does it surf right at the crest, carrying most of the wave's energy, or does it get tossed around, carrying only a tiny bit? Scientists have computer programs, like digital chefs, that try to simulate this kitchen. They have written recipes (theories) to predict exactly how much energy these heavy magnets should grab. But until now, no one had checked if these recipes actually match what happens in the real, high-speed kitchen.

This paper is a report from the CMS experiment, a giant detector at the LHC that acts like a super-fast camera taking pictures of these proton collisions. The scientists looked at data from 138 billion billion collisions (an integrated luminosity of 138 fb⁻¹) where protons smashed together at a center-of-mass energy of 13 TeV. They focused on a specific type of heavy magnet called the $\Upsilon(nS)$ meson (pronounced "upsilon"), which is made of bottom quarks. They didn't just look at the magnets; they looked at the "jets" of particles that the magnets were born inside. A jet is like a spray of debris shooting out from the collision point.

The team measured two main things to see how the $\Upsilon$ meson was riding its jet. First, they measured the "longitudinal" profile, which is like asking: "How much of the jet's forward speed is the $\Upsilon$ meson actually carrying?" They call this number $z$ . Second, they measured the "transverse" profile, which asks: "How much is the $\Upsilon$ meson wobbling side-to-side relative to the jet's path?" They call this $p_{rel}^T$ .

When they compared their real-world measurements to the predictions from the computer programs (specifically versions of a program called PYTHIA 8.240 and the newer PYTHIA 8.310), they found a mismatch. The computer simulations predicted that the $\Upsilon$ mesons would be very "isolated," meaning they would carry a huge chunk of the jet's energy and stay very close to the center of the spray. However, the real data showed something different. The actual $\Upsilon$ mesons were carrying less energy than the computers predicted and were wobbling more side-to-side. In other words, the real magnets were getting tossed around more by the storm than the recipes suggested.

The authors found that even the newest version of the computer program, which included some updated rules for how particles interact, still couldn't perfectly match the data. The simulations consistently underestimated the amount of extra "mess" (hadronic activity) inside the jets and overestimated how much energy the $\Upsilon$ mesons kept for themselves. While the newer simulations moved in the right direction, they were still not good enough to describe the reality observed in the detector.

This result suggests that our current understanding of how heavy quarks turn into these bound states inside a jet is incomplete. The paper concludes that the models used to describe these processes need improvement. It doesn't say the theories are wrong, but rather that they are missing some details about how the heavy quarks interact with the surrounding particles. This measurement adds a new piece to the puzzle of the "quarkonium polarization puzzle," a long-standing mystery in physics about why these particles behave differently than our best theories predict. The scientists hope that by providing these precise measurements of how the $\Upsilon$ mesons share energy with their jets, they can help theorists refine their recipes so that the digital kitchen finally matches the real one.

Technical Summary: Measurement of the Fragmentation Properties of Jets Containing $\Upsilon(nS)$ Mesons

Problem and Motivation
The production of quarkonia (bound states of heavy quark-antiquark pairs) involves both perturbative and non-perturbative aspects of Quantum Chromodynamics (QCD). While the initial heavy quark-antiquark pair production can be described perturbatively, the subsequent evolution into a physical quarkonium state requires non-perturbative modeling, often addressed via Non-Relativistic QCD (NRQCD). A longstanding discrepancy, known as the "quarkonium polarization puzzle," exists between theoretical predictions (which suggest predominantly transverse polarization at high transverse momentum) and experimental observations (which show very mild polarization).

Recent measurements of jets containing $J/\psi$ mesons have revealed that Monte Carlo (MC) generators, specifically PYTHIA 8.2 and 8.3, underestimate the amount of additional hadronic activity inside jets containing quarkonia. These discrepancies suggest deficiencies in the modeling of long-distance matrix elements (LDMEs) and the fragmentation of parton showers into quarkonia. While previous studies focused on charmonium ( $J/\psi$ ), bottomonium ( $\Upsilon$ ) production offers a potentially cleaner testing ground due to the larger mass of the bottom quark, which provides a harder scale and better separation between perturbative and non-perturbative regimes. This paper addresses the lack of data on the fragmentation properties of jets containing $\Upsilon(nS)$ mesons ( $\Upsilon(1S)$ , $\Upsilon(2S)$ , and $\Upsilon(3S)$ ) to provide new constraints on NRQCD modeling.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 138 fb $^{-1}$ (2016–2018).

Event Selection: $\Upsilon$ candidates are reconstructed via their decay into oppositely charged muon pairs ( $\mu^+\mu^-$ ). Muons are required to have $p_T > 6$ GeV and $|\eta| < 1.4$ . The dimuon system must have $p_T > 15$ GeV and $|y| < 1.2$ .
Jet Association: The selected $\Upsilon$ candidates must be constituents of a reconstructed jet. Jets are clustered using the anti- $k_T$ algorithm with a distance parameter $R=0.4$ . To correct for the bias introduced by including muons in the jet energy scale (which is typically calibrated on inclusive jets without muons), a "muon subtraction" method is employed: the four-momenta of the muons are subtracted from the jet four-momentum before applying standard corrections. Jets are required to have $p_T > 60$ GeV and $|\eta| < 1.5$ .
Yield Determination: The invariant mass distribution of the dimuon pairs is fitted using a maximum likelihood approach. The signal components ( $\Upsilon(1S)$ , $\Upsilon(2S)$ , $\Upsilon(3S)$ ) are modeled with Crystal-Ball functions, while the background is described by a third-order Chebyshev polynomial.
Observables: Two fragmentation variables are measured:
1. Longitudinal profile ( $z$ ): The fraction of the jet momentum carried by the $\Upsilon$ meson along the jet axis, defined as $z = (\vec{p}_{jet} \cdot \vec{p}_{\Upsilon}) / |\vec{p}_{jet}|^2$ .
2. Transverse profile ( $p_{rel}^T$ ): The momentum of the $\Upsilon$ meson perpendicular to the jet axis, defined as $p_{rel}^T = |\vec{p}_{jet} \times \vec{p}_{\Upsilon}| / |\vec{p}_{jet}|$ .
Unfolding: Detector-level distributions are corrected to the particle level using the D'Agostini iterative unfolding method. Transfer matrices are derived from PYTHIA 8.240 (CP1 tune) simulations, accounting for resolution effects, migration between bins, and detector inefficiencies.
Monte Carlo Comparison: Results are compared against PYTHIA 8.240 and PYTHIA 8.310. The latter incorporates a novel treatment of quarkonia production in parton showers (NRQCD fragmentation processes implemented in time-like showers). Both versions utilize the CP1 and CP5 tunes, which differ in the perturbative order of the strong coupling running and the parton distribution functions (PDFs).

Key Contributions

First Measurement: This work presents the first measurement of the fragmentation properties of jets containing $\Upsilon(nS)$ mesons.
Transverse Sensitivity: Unlike previous studies that focused primarily on longitudinal fragmentation, this analysis includes the transverse momentum profile ( $p_{rel}^T$ ), enhancing sensitivity to transverse-momentum-dependent (TMD) distributions and non-perturbative dynamics.
Systematic Evaluation: A comprehensive evaluation of systematic uncertainties is provided, including object reconstruction (jet energy scale/resolution, muon efficiency), event reconstruction (pileup, trigger prefiring), and unfolding model dependence. The model uncertainty, arising from the dependence of the unfolding on the MC generator, is identified as the dominant source, particularly in the collinear region ( $z \approx 1$ ).

Results
The measured distributions at the particle level show significant discrepancies with all tested Monte Carlo predictions:

Longitudinal Profile ( $z$ ): The data indicates that $\Upsilon$ mesons carry a smaller fraction of the jet momentum than predicted by PYTHIA. The MC generators predict more isolated quarkonia (higher $z$ values) than observed.
Transverse Profile ( $p_{rel}^T$ ): The data shows that $\Upsilon$ mesons have a larger transverse momentum relative to the jet axis than predicted by the simulations.
Model Performance: Neither PYTHIA 8.240 nor PYTHIA 8.310 successfully reproduces the data. While PYTHIA 8.310, which includes parton shower fragmentation, predicts less isolated quarkonia (lower $z$ ) compared to 8.240, the prediction remains insufficient to describe the data.
Tune Differences: Small but clear differences are observed between the CP1 and CP5 tunes. The CP1 tune, utilizing a larger value of $\alpha_S$ for radiation, generates more hadronic activity, resulting in slightly less isolated $\Upsilon$ mesons (lower $z$ , higher $p_{rel}^T$ ) compared to CP5, bringing the prediction marginally closer to the data, though still unsatisfactory.

Significance
The paper claims that these measurements provide new and stringent tests for NRQCD. The observed discrepancies, consistent in magnitude with previous $J/\psi$ measurements by LHCb and CMS, indicate that current theoretical models of quarkonium production in parton showers are incomplete. Specifically, the results suggest that the modeling of long-distance matrix elements and the interplay between color-singlet and color-octet mechanisms requires improvement. The simultaneous sensitivity to longitudinal and transverse structures offers additional constraints that may help disentangle the contributions of different Fock states and higher-order angular momentum states. Ultimately, these results are expected to contribute to resolving the quarkonium polarization puzzle by refining the understanding of non-perturbative dynamics in heavy-quark production.

More like this