Jet Hadrochemistry in High-Energy Collisions

• Jet hadrochemistry is the study of quantifying hadron species within jets to analyze parton fragmentation and medium-induced modifications.
• Measurement methodologies combine jet reconstruction, particle identification, and background subtraction to accurately isolate hadronic yields.
• Experimental results reveal distinct hadrochemical patterns in proton-proton versus heavy-ion collisions, offering critical constraints on QCD and jet quenching models.

Jet hadrochemistry refers to the measurement, characterization, and interpretation of the hadronic species composition within jets produced in high-energy collisions. This field bridges perturbative quantum chromodynamics (QCD) and nonperturbative hadronization, and is a sensitive probe of the microscopic mechanisms by which energetic partons lose energy and fragment, especially in the presence of a quark–gluon plasma (QGP). Jet hadrochemistry observables, such as the $\pi$, $K$, and $p$ yields and their ratios, provide powerful constraints on models of jet quenching, hadronization, and medium response in both proton–proton and heavy-ion environments (Cantway, 13 Nov 2025, Cantway, 20 Aug 2025, Kang et al., 2016).

1. Definitions and Terminology

Jet hadrochemistry quantifies the differential and integral yields of hadron species (typically pions, kaons, and protons) reconstructed within a QCD jet. The central observable is the single-inclusive fragmentation function $D_i^h(z)$ for a parton $i$ producing hadron $h$, with $z = p_T^h / p_T^{\mathrm{jet}}$ (for $p_T$-selected jets) (Kang et al., 2016, Cantway, 20 Aug 2025). Ratios such as $K/\pi$ or $p/\pi$ inside jets, compared as functions of $z$ or $p_T^h$, directly reflect the hadrochemical composition. Event-level backgrounds, especially in heavy-ion collisions, are disentangled using dedicated underlying-event (UE) estimation and subtraction techniques.

Key mathematical definitions:

• Fragmentation function:

$$D_i^h(z) = \frac{1}{N_{\mathrm{jet}}} \frac{dN^h}{dz}$$

• Jet hadrochemical ratio:

$\frac{dN_{h_1}/dz}{dN_{h_2}/dz}$

where $h_1, h_2$ are hadron species of interest.

In cold QCD matter (e.g., $pp$), jet hadrochemistry probes parton-to-hadron transitions and flavor dependence of hadronization. In hot QCD matter (heavy-ion), modifications in these ratios are indicative of medium-induced fragmentation, recombination, and wake effects (Cantway, 13 Nov 2025, Cantway, 20 Aug 2025).

2. Measurement Methodologies

Experimentally, jet hadrochemistry measurements require:

• Jet Reconstruction: Typically anti-$k_T$ clustering with a defined jet radius ($R=0.4$ is standard in ALICE and SCET-based calculations). Only charged tracks above a low-$p_T$ threshold (e.g., 0.15 GeV/$c$) within a fiducial $\eta$ acceptance are included (Cantway, 13 Nov 2025).
• Particle Identification: Time-of-flight (TOF), d$E$/d$x$, and (where applicable) Cherenkov detectors are used for $\pi$, $K$, $p$ separation, up to $p_T \sim 3-4$ GeV/$c$ (Cantway, 13 Nov 2025, Osborn, 2019). Hadron yields are corrected for tracking and PID efficiencies.
• Background Subtraction in Heavy-Ion Collisions: The large soft background is handled by pedestal (average $\rho$) subtraction, estimation and correction for residual fluctuations ($\delta p_T$), and robust UE estimation via perpendicular cones (PC) at $\Delta\phi=90^\circ$ from each jet (Cantway, 13 Nov 2025, Cantway, 20 Aug 2025).
• Signal Extraction: The per-jet hadronic yield is area-normalized. The pure jet signal is obtained as:

$$\frac{d\rho_{\mathrm{Jet}}}{dp_T} = \frac{d\rho_{\mathrm{Jet+UE}}}{dp_T} - c_{\mathrm{UE}}\,\frac{d\rho_{\mathrm{UE}}}{dp_T}$$

with $c_{\mathrm{UE}}$ correcting for potential UE biases (Cantway, 13 Nov 2025, Cantway, 20 Aug 2025).

• Unfolding: Detector effects and bin migration are removed via iterative unfolding (e.g., Bayesian methods) using MC-based response matrices (Osborn, 2019).

3. Principal Experimental Results

Proton–Proton (Vacuum) Environment

• The $\pi$, $K$, and $p$ spectra inside jets are hard, power-law distributions (Cantway, 13 Nov 2025).
• The $K/\pi$ and $p/\pi$ ratios inside jets rise with hadron $p_T$ but remain below their inclusive (minimum-bias) values by 20–30%, reflecting the dominance of leading-parton fragmentation over soft hadron production (Cantway, 13 Nov 2025, Kang et al., 2016).
• LHCb results further show, for charged hadrons, that jets recoiling against bosons (quark-dominated) have a harder $z$ distribution, narrower $j_T$ profile, and are more collimated in radial distance than inclusive (gluon-enriched) jets (Osborn, 2019).

Heavy-Ion Collisions

• After robust UE subtraction, the $\pi$ spectrum in jets in central Pb–Pb ($\sqrt{s_{NN}}=5.02$ TeV) exhibits a possible enhancement at $p_T \lesssim 2$ GeV/$c$ and a mild suppression at intermediate $p_T$ (2–5 GeV/$c$) relative to a smeared $pp$ reference (Cantway, 13 Nov 2025).
• Both $K$ and $p$ show a $\sim$10–20% enhancement over smeared-$pp$ in the intermediate $p_T$ range (Cantway, 13 Nov 2025).
• $K/\pi$ and $p/\pi$ in jets are systematically higher in Pb–Pb than in vacuum by $\lesssim 20\%$ at $p_T \sim$ 2–4 GeV/$c$, but this is significantly less than the $K/\pi$ and $p/\pi$ enhancement observed in the UE (bulk) (Cantway, 13 Nov 2025, Cantway, 20 Aug 2025).
• The ALICE data also show that, after subtraction, baryon/meson enhancement is significantly reduced inside jets compared to the underlying event, disfavoring strong wake/coalescence scenarios (Cantway, 20 Aug 2025).

Table: Summary of Key Jet Hadrochemical Ratios (ALICE, Pb–Pb)

$p_T^h$ (GeV/$c$)	$K/\pi$ (in-jet)	$p/\pi$ (in-jet)	$K/\pi$ (UE)	$p/\pi$ (UE)
2–4	$0.2$–$0.3$	$0.25$–$0.3$	$0.3$–$0.35$	$0.35$–$0.4$

(Editor's term: Values rounded; see (Cantway, 13 Nov 2025, Cantway, 20 Aug 2025) for systematic uncertainties.)

4. Theoretical Framework and Interpretation

Jet hadrochemistry is quantitatively interpreted using fragmentation functions and the semi-inclusive fragmenting jet function (FJF) approach within Soft Collinear Effective Theory (SCET) (Kang et al., 2016). The jet fragmentation function is defined as the probability for a hadron $h$ to carry a fraction $z$ of the initiating parton's energy. The SCET-based semi-inclusive FJF, $\mathcal{G}_i^h(z, z_h, \omega_J, R, \mu)$, incorporates dependence on jet energy, radius, and hadron momentum fraction; its renormalization group evolution follows timelike DGLAP equations, with resummation of logarithms of $R$ up to NLL$_R$ accuracy (Kang et al., 2016).

Hadronization in-vacuum is described via factorization to standard fragmentation functions, with species-sensitive effects governed by parton flavor, color factors, and hadron mass.

In heavy-ion environments, jet quenching models predict both suppression at high $z$ (leading hadrons) and possible enhancement of softer species from medium-induced splittings and jet–medium coupling. Coalescence (e.g., in AMPT/wake models) can enhance baryons and strangeness at intermediate $z$, but data suggest only a moderate effect inside jets (Cantway, 13 Nov 2025, Cantway, 20 Aug 2025).

Medium-induced effects are also reflected in the hadron nuclear modification factor,

$$R_{\mathrm{AA}}^h(p_T) = \frac{(1/\langle T_{\mathrm{AA}} \rangle)\, dN_h^{\mathrm{AA}}/dp_T}{d\sigma_h^{pp}/dp_T}$$

and in the jet fragmentation nuclear modification, $R_{\mathrm{AA}}^{h,\mathrm{jet}}(z)$ (Cantway, 13 Nov 2025, Cantway, 20 Aug 2025).

5. Constraints on QCD and Jet Quenching Models

Jet hadrochemistry observables tightly constrain models of jet quenching, hadronization, and QGP response:

• The enhancement of $K/\pi$ and $p/\pi$ ratios inside Pb–Pb jets over $pp$ is significant but much smaller than in the bulk, indicating that pure modification of quark/gluon fractions is insufficient to explain baryon–meson species effects (Cantway, 13 Nov 2025).
• The data require both softening of fragmentation inside jets (possibly via increased $g \rightarrow q\bar{q}$ splitting) and a partial contribution from the medium response at the jet periphery (wake), but do not support large coalescence-induced baryon enhancement inside the jet cone (Cantway, 13 Nov 2025, Cantway, 20 Aug 2025).
• The SCET FJF formalism reproduces LHC $K/\pi$ and $p/\pi$ yields in jets at the 10–20% level, consistent with perturbative expectations and standard fragmentation functions at NLO+NLL$_R$ accuracy (Kang et al., 2016).
• The observed differences in hadrochemistry between quark-enriched (e.g., $Z$+jet) and gluon-enriched jets quantitatively reflect color-factor scaling, and can anchor nonperturbative parameter extractions in MC event generators (Osborn, 2019).

6. Outlook and Future Directions

Open directions include:

• Unfolding full $pp$ and Pb–Pb jet spectra to correct for detector and background effects robustly, enabling direct $R_{\mathrm{AA}}^{h,\mathrm{jet}}(z)$ extractions (Cantway, 13 Nov 2025).
• Extending particle identification to higher $p_T$ and broader rapidity acceptance, to probe larger $z$ and better separate quark/gluon jet origins (Cantway, 13 Nov 2025, Cantway, 20 Aug 2025).
• Radial ($\Delta R$) dependence of hadronic species composition in jets, which can disentangle jet-core (fragmentation-dominated) versus periphery (wake-dominated) effects (Cantway, 13 Nov 2025, Cantway, 20 Aug 2025).
• Incorporation of heavy-flavor hadrons and identified neutral species for a more complete flavor-resolved jet hadrochemistry (Osborn, 2019).
• High-precision phenomenology using the semi-inclusive FJF formalism and improved fragmentation functions, as experimental uncertainties continue to diminish (Kang et al., 2016).

The paper of jet hadrochemistry directly constrains the interplay between perturbative and nonperturbative QCD dynamics and is essential for elucidating the fundamental mechanisms of parton energy loss and hadronization in the QGP. Recent measurements by ALICE and LHCb set the stage for comprehensive, differential tests of both baseline QCD and in-medium modification models (Cantway, 13 Nov 2025, Cantway, 20 Aug 2025, Osborn, 2019).