⚛️ phenomenology

Charmed baryon-to-meson ratios inside jets as a discriminator of hadronization mechanisms: from color reconnection in p+p to coalescence in Pb+Pb

This paper proposes that the sign of the modification in the in-jet charmed baryon-to-meson ratio ( $\Lambda_c^+/D^0$ ) serves as a key discriminator between hadronization mechanisms, where color reconnection in p+p collisions enhances the ratio while coalescence in Pb+Pb collisions suppresses it, offering distinct predictions for future jet-tagged measurements.

Original authors: Zi-Xuan Xu, Wei Dai, Ben-Wei Zhang, Enke Wang

Published 2026-10-23

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CC BY 4.0

Original authors: Zi-Xuan Xu, Wei Dai, Ben-Wei Zhang, Enke Wang

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

When particles smash together at nearly the speed of light, they create a fleeting, super-hot soup of fundamental building blocks called quarks and gluons. As this soup cools and expands, these particles must stick together to form the matter we see in the universe today, such as protons and neutrons. Physicists have long observed a curious pattern in these collisions: at certain speeds, the universe seems to prefer making heavy, three-part particles called baryons over lighter, two-part particles called mesons. This "baryon enhancement" happens in massive collisions between heavy atomic nuclei, where a large, long-lived soup forms, but it also appears in tiny, high-speed crashes between single protons. The mystery lies in whether this preference comes from the same cause in both cases. In the large collisions, the answer is likely a process where particles merge like droplets of water. In the tiny ones, the cause is less clear, with some theories suggesting it arises from the complex ways particles reconnect their internal color charges before they even form.

To solve this puzzle, a team of researchers turned their attention to jets. When a collision occurs, it often sprays out a narrow, focused beam of particles called a jet, which acts like a spotlight on the original, high-energy crash. By looking only at the particles caught inside these jets, scientists can separate the direct products of the crash from the messy background noise of the rest of the event. The researchers focused on a specific type of heavy particle containing a charm quark, comparing how often they form a three-part baryon versus a two-part meson. They simulated these events using powerful computer models to see how different theories of particle formation would behave when forced into a jet. Their goal was to see if the behavior of these particles inside a jet could reveal whether they were formed by merging with the surrounding soup or by reconfiguring their internal connections in a vacuum.

The team ran simulations for two very different scenarios: collisions between single protons and collisions between heavy lead nuclei. In the proton collisions, they modeled a mechanism where particles rearrange their internal color connections, a process known as color reconnection. They found that when they looked inside the jets, the ratio of baryons to mesons actually increased at lower speeds compared to the overall average. This happened because the particles formed by this color reconnection stayed tightly linked to the original jet, surviving the selection process. In contrast, when they simulated the heavy lead collisions, where a hot, dense soup of matter is created, they used a model where particles form by merging with the surrounding thermal particles. Here, the result was the opposite. Inside the jets, the ratio of baryons to mesons dropped at intermediate speeds. This occurred because the particles formed by merging with the soup carried no memory of the jet's direction; they were scattered randomly and were often filtered out when the researchers selected only those particles moving in line with the jet.

This reversal in behavior provides a powerful tool for distinguishing between the two mechanisms. The researchers found that the sign of the change—whether the ratio goes up or down inside a jet—acts as a fingerprint. If the ratio rises, it suggests the particles formed through color reconnection, staying correlated with the jet. If it falls, it points to coalescence, where the particles formed from the surrounding medium and were largely discarded by the jet selection. The study also examined how these particles are distributed around the center of the jet. In both scenarios, the extra baryons were found further away from the central axis than the mesons, but the specific speed ranges where this effect was strongest differed between the two types of collisions. In the proton collisions, the effect was most visible at the lowest speeds, while in the heavy ion collisions, it peaked at intermediate speeds.

The researchers also looked at how much of the jet's total momentum the heavy particles carried. In both cases, the formation of baryons tended to shift the particles toward carrying a smaller fraction of the jet's momentum, a signature of the merging or reconnection processes. However, the study emphasized that this momentum shift alone could not tell the two mechanisms apart, as both produced a similar trend. It was the combination of the momentum shift with the direction of the ratio change inside the jet and the spatial distribution of the particles that allowed the team to separate the theories. The simulations showed that while the overall number of baryons increases in both systems, the way they are organized inside a jet tells a different story.

These findings offer a clear path forward for experimental physicists. By measuring the ratio of these specific heavy particles inside jets in future experiments, scientists can determine which mechanism is at work without needing to rely on complex, indirect inferences. The study provides a baseline prediction for what should be seen in proton collisions at specific energy levels, which can then be compared with data from heavy ion collisions. If future measurements confirm that the ratio drops inside jets for heavy collisions but rises for light ones, it would confirm that the baryon enhancement in small systems comes from color reconnection, while the enhancement in large systems comes from the merging of particles in a hot medium. This distinction would finally settle the question of whether the same physical laws govern the formation of matter in the smallest and largest cosmic collisions.

Technical Summary: Charmed Baryon-to-Meson Ratios Inside Jets as a Discriminator of Hadronization Mechanisms

Problem Statement
The enhancement of the baryon-to-meson yield ratio at intermediate transverse momentum ( $p_T$ ) is a well-established phenomenon observed in both heavy-ion (Pb+Pb) and high-multiplicity small-system (p+p, p+A) collisions. While quark coalescence is the dominant explanation in heavy-ion collisions, the origin of this enhancement in small systems remains debated, with competing hypotheses involving vacuum-like mechanisms (such as color reconnection and rope hadronization) versus the formation of small quark-gluon plasma (QGP) droplets where coalescence occurs. Inclusive measurements of the charmed baryon-to-meson ratio ( $\Lambda_c^+/D^0$ ) cannot distinguish between these scenarios, as both mechanisms enhance the ratio. The paper addresses the need for a discriminator that can separate hadronization mechanisms based on their correlation with the initiating hard scattering (the jet).

Methodology
The authors employ a comparative theoretical framework to analyze $\Lambda_c^+/D^0$ ratios within jets in p+p and Pb+Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV.

p+p Baseline: Events are simulated using PYTHIA8. Two hadronization setups are compared: the standard 4C tune (Lund string fragmentation) and the CR-BLC Mode 2 tune, which implements color reconnection beyond the leading-color approximation (allowing string junctions and baryonic configurations). The CR-BLC Mode 2 is adopted as the representative scenario for vacuum-like mechanisms.
Pb+Pb Framework: The SHELL model is utilized, incorporating a modified Langevin transport approach for parton evolution in the QGP (including both collisional and radiative energy loss) and a coalescence-plus-fragmentation hybrid model for charm quark hadronization.
Jet Reconstruction: Charged-particle jets are reconstructed using the anti- $k_T$ algorithm ( $R=0.4$ ). A jet is retained only if it contains at least one prompt charmed hadron within $R < 0.4$ .
Observables: The study focuses on three key observables:
1. The inclusive and in-jet $\Lambda_c^+/D^0$ ratio as a function of hadron $p_T$ .
2. The radial profile of this ratio relative to the jet axis.
3. The parallel jet momentum fraction ( $z_{||}^{ch}$ ) distributions for $\Lambda_c^+$ and $D^0$ .

Key Contributions and Results

Opposite Signs of In-Jet Modification:
- In p+p (Color Reconnection): The in-jet $\Lambda_c^+/D^0$ ratio is enhanced at low-to-intermediate $p_T$ relative to the inclusive ratio. This occurs because the color-reconnection mechanism generates an excess of baryons that remains correlated with the color flow of the hard partons. Consequently, these baryons survive the jet selection, whereas uncorrelated hadrons are discarded. The fragmentation-only baseline shows no such enhancement.
- In Pb+Pb (Coalescence): Conversely, the in-jet ratio is suppressed at intermediate $p_T$ relative to the inclusive ratio. Coalescence hadrons are assembled from soft thermal partons that are uncorrelated with the jet direction. The jet selection preferentially discards these soft, uncorrelated partners, driving the in-jet ratio back toward the fragmentation-only value.
- Significance: The sign of the in-jet modification (enhancement vs. suppression) serves as a direct discriminator between color reconnection (vacuum-like) and coalescence (medium-like) mechanisms.
Radial Profiles:
- In both systems, the in-jet $\Lambda_c^+/D^0$ ratio increases with the distance from the jet axis.
- p+p: The enhancement is displaced farthest outward for the lowest- $p_T$ interval. This reflects that color-reconnection products remain associated with the jet only when emitted at larger angles.
- Pb+Pb: The enhancement is most pronounced for the intermediate- $p_T$ interval. This aligns with the coalescence mechanism where soft thermal partners are uncorrelated with the jet axis.
Parallel Momentum Fraction ( $z_{||}^{ch}$ ):
- Both color reconnection (in p+p) and coalescence (in Pb+Pb) shift charmed hadrons toward smaller values of $z_{||}^{ch}$ , with a stronger effect on $\Lambda_c^+$ than on $D^0$ .
- This results in a decreasing $\Lambda_c^+/D^0$ ratio as a function of $z_{||}^{ch}$ .
- Crucially, the shape of the $z_{||}^{ch}$ spectrum is found to be insensitive to parton energy loss when compared against a fragmentation-only baseline. Thus, the $z_{||}^{ch}$ spectrum acts as a clean probe of recombination-type hadronization, independent of energy loss effects.
Decomposition of Mechanisms:
- The authors introduce a $PbPb/pp$ ratio of $z_{||}^{ch}$ distributions as a model decomposition tool. By comparing a Pb+Pb calculation (with and without coalescence) against a p+p reference, they isolate the specific effects of energy loss (which cancels out in the ratio) and coalescence (which shifts the distribution to lower $z_{||}^{ch}$ ).
- The study highlights that the magnitude and $z_{||}^{ch}$ dependence of this ratio depend on the choice of the p+p reference (fragmentation-only vs. CR-BLC), emphasizing the need for a measured p+p reference at 5.02 TeV for experimental extraction.

Significance and Claims
The paper claims to provide the necessary theoretical baseline and predictions for future jet-tagged charmed-hadron measurements in both p+p and Pb+Pb collisions. Its primary significance lies in demonstrating that inclusive observables are insufficient to distinguish between vacuum-like and medium-like hadronization mechanisms for heavy flavors. By utilizing jet-constrained observables, the authors show that:

The sign of the in-jet ratio modification distinguishes the mechanism (enhancement for color reconnection, suppression for coalescence).
The radial profile and $z_{||}^{ch}$ spectrum provide complementary spatial and momentum-space constraints that further resolve the mechanism identity.
The $z_{||}^{ch}$ spectrum offers a unique probe of recombination physics that is robust against uncertainties in parton energy loss modeling.

The authors conclude that these results enable a direct test of hadronization scenarios: if future measurements in p+p reveal an in-jet enhancement, it supports color reconnection; if a suppression is observed (or if the enhancement is uncorrelated with the jet axis), it would suggest the presence of a small-system medium and coalescence. The paper does not claim to have solved the problem experimentally but provides the specific predictions required to do so.

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