In-Jet Baryon to Meson Ratios

• In-jet baryon to meson ratios are defined as the comparative yields of baryons relative to mesons within reconstructed jets, offering insights into jet fragmentation and hadronization processes.
• Experimental studies at RHIC and LHC show that in-jet ratios follow fragmentation baselines like PYTHIA, contrasting with enhanced inclusive ratios observed in heavy-ion collisions.
• Theoretical models including quark coalescence, statistical approaches, and colour reconnection explicate how medium effects and jet dynamics differentially impact baryon and meson production.

In-jet baryon to meson ratios refer to the relative yields of baryons and mesons measured within reconstructed jets, typically as a function of jet $p_\mathrm{T}$, hadron $p_\mathrm{T}$, and other kinematic variables. This observable serves as a probe of the microscopic hadronization mechanisms inside jets and their modification in different collision environments. It is particularly sensitive to the interplay between fragmentation, recombination (coalescence), and medium-induced effects, such as those arising in the quark-gluon plasma (QGP) created in high-energy nuclear collisions.

1. Definition, Motivation, and Historical Context

The in-jet baryon to meson ratio quantifies the relative probability for a jet parton shower to hadronize into baryons versus mesons within the jet cone. Expressed generically as

$$R_{B/M}(p_\mathrm{T}) = \frac{N_{\mathrm{baryon}}(p_\mathrm{T})}{N_{\mathrm{meson}}(p_\mathrm{T})}$$

where $N_\mathrm{baryon}$ and $N_\mathrm{meson}$ denote the yields of identified baryons and mesons associated with a reconstructed jet as a function of transverse momentum.

Early studies of inclusive baryon/meson ratios in heavy-ion collisions revealed a strong enhancement at intermediate $p_\mathrm{T}$ (2–6 GeV/c), often reaching values of $p/\pi$ or $\Lambda/K_S^0$ approaching unity or higher, compared to much lower ratios in $pp$ collisions. This enhancement was attributed to medium effects such as coalescence and hydrodynamic flow. The measurement of in-jet ratios—where only particles originating within jets are counted—aims to disentangle effects from jet fragmentation and those from the underlying soft event (bulk).

2. Experimental Measurements and Comparative Results

Direct measurements of in-jet baryon to meson ratios have been performed across RHIC and the LHC, focusing on both light-flavor ($p/\pi$, $\Lambda/K_S^0$) and heavy-flavor ($\Lambda_c/D^0$) channels.

ALICE (LHC) in p–Pb and Pb–Pb:

• In both collision systems, the $\Lambda/K_S^0$ ratio within jets is significantly lower than the inclusive ratio, especially at intermediate $p_\mathrm{T}$ (Kučera, 2015). The in-jet ratio matches the PYTHIA simulation baseline and shows negligible sensitivity to the jet resolution parameter $R$ or the jet $p_\mathrm{T}$ threshold.
• In Pb–Pb, the convergence of the in-jet and inclusive ratios at high hadron $p_\mathrm{T}$ indicates fragmentation dominance at high momenta.

STAR (RHIC) in Au+Au and $pp$:

• The first fully reconstructed in-jet $p/\pi$ ratio at RHIC shows that in-jet baryon/meson ratios from Au+Au coincide with those in $pp$ for leading jets (high $p_\mathrm{T}$, narrow $R$), even though the inclusive Au+Au baryon/meson ratio is much higher at intermediate $p_\mathrm{T}$ (Dale-Gau, 2023).

Charm Sector (ALICE):

• The in-jet $\Lambda_c^+/D^0$ ratio in $pp$ and $p$–Pb is large at low $p_\mathrm{T}$ (0.4–0.5) but falls with increasing $p_\mathrm{T}$, showing remarkably similar shapes to the light-flavor $\Lambda/K_S^0$ ratio (Collaboration, 2020).

These consistent findings establish that in-jet baryon/meson ratios do not reflect the strong enhancement seen in the inclusive spectra of heavy-ion collisions.

System	Inclusive Ratio (intermediate $p_\mathrm{T}$)	In-jet Ratio (same $p_\mathrm{T}$)
Pb–Pb (ALICE)	$\Lambda/K_S^0 \sim 1$	$\Lambda/K_S^0 \lesssim 0.3$
Au+Au (STAR)	$p/\pi \sim 1$	$p/\pi \approx$ $pp$ value

3. Theoretical Frameworks and Model Interpretations

Quark Coalescence and Statistical Models

In-medium hadronization models, such as the quark coalescence approach, predict that enhanced baryon production (relative to mesons) is driven by the recombination of thermal or moderate $p_\mathrm{T}$ quarks (0901.1382, Cuautle et al., 2013). These models explain the inclusive baryon enhancement as a bulk medium (soft) effect, peaked at intermediate $p_\mathrm{T}$. The baryon/meson ratio from coalescence can be parametrically much higher than expected from fragmentation.

Fragmentation-based event generators (e.g. PYTHIA8), which use parton shower evolution followed by string fragmentation, systematically underpredict the inclusive baryon yield at intermediate $p_\mathrm{T}$. However, they accurately describe the in-jet baryon/meson ratios, aligning with the data from $pp$ and in-jet LHC/RHIC measurements (Kučera, 2015, Dale-Gau, 2023).

Effects of QGP and Medium Modification

Hydrodynamic flow and parton recombination enhance the inclusive baryon/meson ratio in the QGP, but have negligible impact on the in-jet ratio for leading, high-$p_\mathrm{T}$ jets. Instead, medium response and jet-induced excitation can enhance baryon/meson ratios around, but not inside, the jet cone, as predicted by transport models including coalescence of jet-excited medium partons (Luo et al., 2021).

Some studies propose that survivor bias—jets minimally affected by the medium are more likely to be reconstructed—explains the similarity in in-jet baryon/meson ratios between Au+Au and $pp$ (Dale-Gau, 2023).

4. Multiplicity and Event Activity Dependence

Recent high-multiplicity $pp$ studies at the LHC reveal a pronounced multiplicity dependence of the $\Lambda_c/D^0$ ratio (Collaboration, 2021, Chen et al., 2020):

• In $pp$ collisions at $\sqrt{s} = 13$ TeV, $\Lambda_c^+/D^0$ increases significantly with event multiplicity at $1 < p_\mathrm{T} < 12$ GeV/c.
• This effect is reproduced in models invoking canonical suppression in the statistical hadronization ensemble (where exact conservation of quantum charges like baryon number and charm is enforced in small volumes) (Chen et al., 2020).
• Colour reconnection models (beyond the leading-colour approximation) also enhance baryon yields in both light and heavy flavor sectors.

Table: Summary of Model Behavior for In-jet Ratios

Model	Inclusive Bulk	In-jet (Jets)	Multiplicity Dependence
PYTHIA (fragment.)	Underpredicts	Matches data	None (default tunes)
Coalescence	Overpredicts	Only if coalescence inside jet cone is significant	Yes (if tuned)
Statistical (CE-SH)	Predicts trend	Not directly modelled, but suppression effects may translate	Yes
Colour reconnection	Can reproduce	Yes	Yes

5. Angular Correlations and Production Mechanisms

Analysis of two-particle angular correlations, specifically $\Delta\eta$–$\Delta\varphi$ correlation maps, reveals that:

• Mesons from jets display a near-side peak reflecting clustering in jet fragmentation.
• Baryon pairs show an anti-correlation at the near-side, i.e., same-sign baryons are suppressed when emitted close together in phase space (Janik, 2023).

Standard fragmentation and hadronization models, including modern Monte Carlo generators, do not quantitatively reproduce this anti-correlation phenomenon for baryon pairs, indicating incomplete understanding of baryon production mechanisms within jets.

This anti-correlation contributes to the observed reduction in in-jet baryon/meson ratios and signals the need for fundamental improvements in jet hadronization modeling.

6. Flavor and Heavy-Flavor Dependence

The in-jet baryon/meson ratio exhibits substantial species dependence:

• For light flavors, $p/\pi$ and $\Lambda/K_S^0$ show moderate and similar ratios inside jets in $pp$ and central $A+A$ (Kučera, 2015, Dale-Gau, 2023).
• For heavy flavor, the $\Lambda_c^+/D^0$ ratio is notably large at low $p_\mathrm{T}$ in both $pp$ and $p$–Pb, with a decreasing trend at higher $p_\mathrm{T}$ (Collaboration, 2020).

This behavior points to potentially common mechanisms governing baryon formation across flavors, but with quantitative differences traceable to constituent quark content, resonance feed-down, and mass effects.

7. Implications for Hadronization, QGP Studies, and Future Directions

In-jet baryon to meson ratios serve as a crucial discriminant between fragmentation-dominated hadron (jet) production and medium-driven (bulk) recombination or flow effects:

• Consistency between in-jet $p/\pi$, $\Lambda/K_S^0$ ($pp$, $A+A$) and PYTHIA baselines suggests that jet fragmentation remains largely unmodified, as opposed to inclusive hadron spectra dominated by medium effects.
• Enhanced baryon/meson ratios around but not inside the jet cone (radial or angular distributions) have been predicted as a signature of jet-induced energy diffusion and coalescence-driven medium response (Luo et al., 2021).
• Further systematic studies—varying jet reconstruction parameters, broadening to wider cones, and advanced particle identification—are necessary to identify possible regimes where the QGP could impact in-jet particle content.

In summary, in-jet baryon to meson ratios remain a sensitive observable for testing jet-medium interactions, hadronization universality, and the consequences of baryon production mechanisms inside and outside jets. They consistently show that fragmentation dominates inside jets under standard selection criteria, while the bulk baryon enhancement arises from collective medium-driven physics, as corroborated by both experimental data and leading theoretical models.