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Impact of soft QCD effects over intrajet azimuthal anisotropies

This paper investigates intrajet azimuthal anisotropies in high-energy proton-proton collisions by comparing LHC data with PYTHIA soft QCD model predictions across different jet axis definitions, finding that the QCD-scheme color reconnection tune best reproduces the observed collective signatures and offers new insights into nonperturbative QCD dynamics.

Original authors: Jesus Alberto V. Corral, A. Cota Rodriguez, J. A. Murillo Quijada

Published 2026-09-25

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CC BY 4.0

Original authors: Jesus Alberto V. Corral, A. Cota Rodriguez, J. A. Murillo Quijada

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

In the high-energy world of particle physics, scientists smash protons together at speeds approaching the speed of light to recreate the conditions that existed just moments after the Big Bang. When these collisions happen between heavy atomic nuclei, the debris forms a hot, dense soup of fundamental particles known as a quark-gluon plasma. This state of matter behaves like a nearly perfect fluid, where particles move in a coordinated, collective way rather than bouncing off one another randomly. For years, this collective behavior was thought to require a massive collision system to occur. However, recent observations have suggested that even in much smaller collisions, such as those between single protons, or even within the narrow sprays of particles called jets that emerge from a single high-energy particle, there might be signs of this same collective coordination. The question driving current research is whether these tiny systems can truly form a fluid-like state, or if the patterns we see are simply the result of complex, non-linear interactions between particles that are not yet fully understood.

A team of researchers from the Universidad de Sonora in Mexico has taken a closer look at these subtle patterns within the jets themselves. They focused on energetic jets produced in proton-proton collisions at the Large Hadron Collider, specifically selecting those with a transverse momentum greater than 550 GeV. The team wanted to understand how different theoretical models, which simulate the messy, non-perturbative interactions of particles, could explain the way particles are distributed around the center of these jets. In the language of physics, they were looking for "azimuthal anisotropies," which essentially means checking if the particles prefer to fly out in certain directions more than others, a signature that would hint at collective behavior. To do this, they compared real data from the CMS experiment with predictions from the PYTHIA computer program, testing three different sets of rules, or "tunes," that the program uses to simulate how particles interact and stick together after a collision.

The researchers tested three specific versions of the simulation. The first was the Monash tune, a standard, general-purpose model. The second was the CP5 tune, which has been finely adjusted to match data from the Large Hadron Collider at 13 TeV and is often used as a reference in jet studies. The third was a newer approach called the QCD-scheme CR, which incorporates a more strict set of rules based on the fundamental theory of the strong force, known as Quantum Chromodynamics, to decide how particles reconnect with one another. The team analyzed the number of charged particles inside each jet, looking at both low-multiplicity jets (with fewer particles) and high-multiplicity jets (with many particles, specifically more than 80). They also examined how the results changed depending on how they defined the central axis of the jet. One method, called the standard scheme, calculates the jet's direction based on the sum of all particle momenta. The other, known as the Winner-Take-All scheme, defines the direction based on the single hardest, most energetic particle, effectively ignoring the push from softer, less energetic radiation.

The results showed that the choice of simulation tune mattered significantly. For jets with a moderate number of particles, both the Monash and the QCD-scheme CR tunes provided a much better match to the experimental data than the CP5 tune. The CP5 tune consistently predicted values that were too low compared to what was actually observed. However, the most intriguing findings appeared in the jets with the highest number of particles. In these high-multiplicity events, the experimental data showed a stronger signal of collective behavior than any of the simulations predicted. The QCD-scheme CR tune came the closest to matching the data, with its predictions falling within a 2.3 sigma uncertainty range of the measurements. In statistical terms, this means the agreement is on the very edge of being considered a significant match, suggesting that while the model captures much of the physics, it may still be missing a piece of the puzzle or that the experimental signal is indeed stronger than current theories allow.

The study also revealed that the way the jet is oriented changes the results, particularly for the most extreme cases. When the researchers switched from the standard method of defining the jet axis to the Winner-Take-All method, the predictions from the different tunes began to diverge more noticeably, especially at the highest particle counts. The QCD-scheme CR tune remained the most consistent across both methods, while the CP5 tune showed the largest discrepancies. This suggests that the way soft, low-energy radiation interacts with the core of the jet is a critical factor that current models struggle to describe perfectly. The researchers conclude that while the QCD-scheme CR tune offers the most promising theoretical framework for understanding these phenomena, the slight but persistent gap between the simulation and the real data in the highest-multiplicity jets indicates that the search for collective effects within a single jet is not yet finished. To make a definitive claim about whether these tiny sprays of particles truly behave like a fluid, more precise measurements with larger datasets and finer resolution are needed to determine if the observed excess is a new physical phenomenon or a limitation of our current theoretical tools.

Technical Summary: Impact of Soft QCD Effects over Intrajet Azimuthal Anisotropies

Problem Statement
Recent observations at the Large Hadron Collider (LHC) have identified collective signatures within high-multiplicity jets in proton-proton ($pp$) collisions, suggesting the potential formation of a Quark-Gluon Plasma (QGP) or collective-like phenomena even in "small systems." These signatures challenge the traditional distinction between heavy-ion and $pp$ collisions. However, the interpretation of these effects is complicated by non-perturbative Quantum Chromodynamics (QCD) dynamics, specifically soft QCD effects such as multiparton interactions (MPI) and color reconnection (CR). The paper addresses the need to quantify how different soft QCD model tunes in Monte Carlo event generators affect the measurement of intrajet azimuthal anisotropies, particularly the elliptic flow coefficient ( $v_2$ ), to determine if observed enhancements are genuine collective effects or artifacts of modeling choices.

Methodology
The study utilizes the PYTHIA8 Monte Carlo event generator (version 8.309) to simulate $pp$ collisions at $\sqrt{s} = 13$ TeV. The analysis focuses on energetic jets with transverse momentum $p_T^{jet} > 550$ GeV and pseudorapidity $|\eta_{jet}| < 1.6$ , reconstructed using the anti- $k_t$ algorithm with a cone size $R=0.8$ .

Three specific soft QCD tunes are compared:

Monash: The original PYTHIA8 scheme incorporating MPI and CR models.
CP5: A tune optimized for 13 TeV LHC data, known for improved descriptions of underlying soft physics.
QCD-scheme CR: A tune incorporating specific color rules based on SU(3) QCD theory, minimizing string length according to simplified color algebra.

The analysis investigates intrajet azimuthal anisotropies as a function of the charged particle multiplicity within the jet ( $N_{ch}^j$ ), specifically in the high-multiplicity region ( $N_{ch}^j > 80$ ). Two distinct jet reference frames are employed:

E-scheme (Standard): The jet axis is defined by the vector sum of all particle momenta.
Winner-Take-All (WTA): The jet axis aligns with the hardest particle, recursively recombining pairs to minimize the effect of soft radiation recoils.

Two-particle angular correlation functions are calculated for charged particles within the jet ( $0.3 < p_T < 3.0$ GeV/c). These are projected onto the long-range region ( $|\Delta\eta^*| > 2$ ) and fitted to a Fourier decomposition series to extract coefficients $V_{n\Delta}$ , which are then factorized to obtain single-particle anisotropy coefficients $v_n$ (specifically $v_2$ ).

Key Results

Tune Dependence: Significant differences are observed between the predictions of the three tunes. The QCD-scheme CR and Monash tunes generally show better agreement with experimental data (from CMS-HIN-21-013) for $V_{n\Delta}$ and $v_2$ coefficients in the region $N_{ch}^j < 80$ . The CP5 tune consistently underestimates the data, showing larger discrepancies, particularly at high multiplicities.
High Multiplicity Region ( $N_{ch}^j \ge 80$ ): Experimental data exhibits an enhancement in $v_2$ compared to all PYTHIA8 tune predictions. However, the QCD-scheme CR tune prediction remains consistent with the data measurements within a 2.3 $\sigma$ uncertainty level. The Monash tune also shows consistency at this level, while CP5 deviates more significantly.
Frame Dependence (E-scheme vs. WTA):
- For $N_{ch}^j < 80$ , predictions from the WTA and E-scheme frames are largely consistent across all tunes, though WTA yields slightly smaller anisotropy magnitudes at the lowest multiplicities.
- At the highest multiplicities ( $N_{ch}^j \ge 80$ ), significant discrepancies emerge between the two frames. The QCD-scheme CR tune demonstrates the smallest variation between frames. In contrast, the Monash tune shows a significantly larger $v_2$ value in the WTA frame compared to its E-scheme prediction, and CP5 shows the largest discrepancy.
Statistical Comparison: Chi-squared ( $\chi^2$ ) tests confirm that the QCD-scheme CR tune provides the best fit to data for $N_{ch}^j < 80$ ( $\chi^2/ndof = 0.32$ ), outperforming Monash (2.28), CP5 (4.69), and the Sherpa reference (1.02).

Significance and Claims
The paper claims that the choice of soft QCD tune has a substantial impact on the modeling of intrajet azimuthal anisotropies. The results suggest that the QCD-scheme CR tune, which incorporates specific SU(3) color algebra rules, provides a more robust theoretical framework for describing non-perturbative QCD dynamics in high-multiplicity jets compared to the CP5 tune.

The authors conclude that while an enhancement in $v_2$ is observed in data at high multiplicities, the QCD-scheme CR tune is consistent with this observation at the 2.3 $\sigma$ level. This places the claim of a significant "excess" (indicative of new collective physics) at the very edge of statistical significance. Consequently, the paper argues that current differences between tunes and data may be attributed to variations in color reconnection mechanisms and soft QCD effects rather than definitive evidence of intrajet collectivity.

The study emphasizes the importance of the WTA frame in minimizing soft radiation recoil effects and calls for future experimental probes with finer $N_{ch}^j$ resolution and WTA frame measurements to definitively distinguish between non-perturbative QCD modeling artifacts and genuine collective phenomena. The work provides new guidance for understanding the origin of collective effects and non-perturbative dynamics originating from a single parton.

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