Quark–Gluon Jet Discrimination

• Quark–gluon jet discrimination is the study of distinguishing jets initiated by quarks from those by gluons using differences in QCD color factors and radiation patterns.
• It employs both counting and shape observables alongside likelihood-based methods and deep learning to optimize background rejection and calibration in collider and heavy-ion settings.
• The approach integrates data-driven calibrations with multi-scale analyses to refine jet-flavor inference, addressing challenges from generator dependence and environmental modifications.

Quark–gluon jet discrimination is the problem of distinguishing jets initiated by quarks from those initiated by gluons through differences in their QCD radiation patterns. Its physical basis is the larger gluon color charge, with $C_F = 4/3$ for quarks and $C_A = 3$ for gluons, which drives broader, softer, and higher-multiplicity gluon showers. The subject is central to collider analyses because it affects background rejection, jet-flavor calibration, precision studies of $\alpha_s$ and parton distribution functions, and the interpretation of jet quenching in heavy-ion collisions. At the same time, it is not only a tagging problem but also a mixture problem: experimentally selected samples are admixtures of quark-like and gluon-like jets, and in heavy-ion collisions both the mixture fractions and the jet substructure are modified by the medium (Andrews et al., 2019, Brewer et al., 2020).

1. QCD origin and discriminating observables

In the soft–collinear limit, gluons radiate more copiously than quarks because the relevant color factors differ by $C_A/C_F = 9/4$. A classic expectation is therefore the relative multiplicity

$n_g / n_q \approx C_A / C_F = 3 / (4/3) = 9/4,$

and this underlies the standard picture that gluon jets have higher particle multiplicities, broader radiation profiles, and softer fragmentation than quark jets. In $e^+e^-$ kinematics, thrust makes this distinction explicit: $$T = \max_{\hat n} \frac{\sum_i |\vec p_i \cdot \hat n|}{\sum_i |\vec p_i|}$$, $\tau = 1-T$, and for $\tau \ll 1$, gluon jets are broader and peaked at larger $\tau$ than quark jets (Mo et al., 2017, Andrews et al., 2019).

The observable basis used in quark–gluon tagging spans both counting and shape information. Common choices include multiplicity $C_A = 3$0, girth $C_A = 3$1, momentum dispersion

$C_A = 3$2

$C_A = 3$3-subjettiness

$C_A = 3$4

energy correlation functions such as

$C_A = 3$5

and angularities

$C_A = 3$6

Within the generalized-angularity family, the IRC-safe sector is $C_A = 3$7, $C_A = 3$8; $C_A = 3$9 corresponds to $\alpha_s$0, and hadron multiplicity to $\alpha_s$1 (Andrews et al., 2019, Larkoski et al., 2014).

Spatial information is structurally important. The detector-level CMS study based on Open Data shows that discrimination performance correlates strongly with spatial resolution, with tracks outperforming ECAL and ECAL outperforming HCAL, and that combining channels improves performance through multi-scale feature extraction. This is consistent with the underlying physics: multiplicity and angular spread are most visible where granularity is highest (Andrews et al., 2019).

2. Optimality, resummation, and information-theoretic structure

A large part of the formal theory is organized by Casimir scaling. For broad classes of IRC-safe observables at leading logarithmic accuracy,

$\alpha_s$2

so the ROC curve becomes universal,

$\alpha_s$3

For QCD, this implies the leading-logarithmic benchmark $\alpha_s$4 for the classifier separation

$\alpha_s$5

and a one-emission AUC of

$\alpha_s$6

The mutual-information analysis sharpens this point: for equal priors, a single LL Casimir-scaling observable captures only about $\alpha_s$7 bits of the available one-bit quark/gluon truth information, which quantifies the intrinsic difficulty of the problem at LL (Gras et al., 2017, Larkoski et al., 2014, Larkoski et al., 2019).

Beyond this limit, likelihood-ratio constructions make the optimal structure explicit. In the resolved-emission framework, the optimal classifier is $\alpha_s$8. With $\alpha_s$9 resolved emissions in the strongly ordered limit, the gluon reducibility factor scales as

$C_A/C_F = 9/4$0

while $C_A/C_F = 9/4$1. This explains why observables sensitive to many emissions outperform single-emission shape observables: each additional resolved emission suppresses gluon reducibility and pushes the tagger away from the LL Casimir-scaling ceiling (Larkoski et al., 2019).

This same logic appears in the ratio-of-likelihoods approach based directly on splitting functions. In the strict eikonal limit, the per-emission log-likelihood ratio is constant, proving that multiplicity is the optimal observable at LL. Including sub-eikonal $C_A/C_F = 9/4$2-dependence from the full $C_A/C_F = 9/4$3 splitting kernels promotes the optimal discriminant to a linear combination of weighted multiplicities $C_A/C_F = 9/4$4, with coefficients derived from the analytic likelihood ratio. This provides an interpretable bridge between formal optimality and the empirical success of multiplicity-like observables (Bright-Thonney et al., 2022).

A related development replaces Sudakov-shape observables by IRC-safe counting observables. Iterated Soft Drop defines a soft-drop multiplicity $C_A/C_F = 9/4$5 that is Poisson distributed at LL, with mean proportional to the color factor and with more suppressed tails than Sudakov-resummed observables such as jet mass. In the perturbative optimization discussed in that framework, the best discrimination occurs near $C_A/C_F = 9/4$6, and the resulting ROC curves outperform jet mass and groomed radius while approaching track multiplicity (Frye et al., 2017).

For thrust, an NNLL$C_A/C_F = 9/4$7 analysis in $C_A/C_F = 9/4$8 and $C_A/C_F = 9/4$9 provides a clean benchmark. At $n_g / n_q \approx C_A / C_F = 3 / (4/3) = 9/4,$0, the classifier separation from the NNLL$n_g / n_q \approx C_A / C_F = 3 / (4/3) = 9/4,$1NLL$n_g / n_q \approx C_A / C_F = 3 / (4/3) = 9/4,$2NLO calculations lies around $n_g / n_q \approx C_A / C_F = 3 / (4/3) = 9/4,$3 and $n_g / n_q \approx C_A / C_F = 3 / (4/3) = 9/4,$4, with perturbative and hadronization uncertainties of comparable size. These results agree with modern Pythia 8.223 and Herwig 7.1 within uncertainties, and show that hadronization, not only perturbative resummation, limits precision tagging with thrust (Mo et al., 2017).

3. Likelihood taggers and detector-level calibration

Before deep learning, LHC experiments established quark–gluon tagging through explicitly calibrated likelihood discriminants. ATLAS constructed a data-driven tagger at $n_g / n_q \approx C_A / C_F = 3 / (4/3) = 9/4,$5 TeV using $n_g / n_q \approx C_A / C_F = 3 / (4/3) = 9/4,$6 of $n_g / n_q \approx C_A / C_F = 3 / (4/3) = 9/4,$7 data, based on track multiplicity $n_g / n_q \approx C_A / C_F = 3 / (4/3) = 9/4,$8 and track width. For isolated jets within tracker acceptance, $n_g / n_q \approx C_A / C_F = 3 / (4/3) = 9/4,$9, and $e^+e^-$0 GeV, the headline performance in data was a light-quark efficiency of about $e^+e^-$1 at a gluon mis-tag rate of about $e^+e^-$2, with total uncertainties of about $e^+e^-$3. The same jet properties in Pythia 6 predicted a substantially lower gluon mis-tag rate, about $e^+e^-$4 at $e^+e^-$5 quark efficiency, illustrating the size of generator dependence in realistic detector conditions (Collaboration, 2014).

The ATLAS analysis also established a template-extraction strategy from quark-enriched and gluon-enriched samples. $e^+e^-$6jet events provided a quark-enriched control region, while dijet and trijet events provided gluon-enriched control regions. The observed distribution of a jet property $e^+e^-$7 in a sample was modeled as a linear mixture of quark, gluon, charm, and bottom components, and high-purity kinematic selections such as $e^+e^-$8 in trijet events and $e^+e^-$9 in $$T = \max_{\hat n} \frac{\sum_i |\vec p_i \cdot \hat n|}{\sum_i |\vec p_i|}$$0-jet events were used to validate the extracted templates (Collaboration, 2014).

CMS implemented a related likelihood discriminant at $$T = \max_{\hat n} \frac{\sum_i |\vec p_i \cdot \hat n|}{\sum_i |\vec p_i|}$$1 TeV using particle-flow inputs. The three discriminating variables were the total PF multiplicity $$T = \max_{\hat n} \frac{\sum_i |\vec p_i \cdot \hat n|}{\sum_i |\vec p_i|}$$2, the energy-sharing variable

$$T = \max_{\hat n} \frac{\sum_i |\vec p_i \cdot \hat n|}{\sum_i |\vec p_i|}$$3

and the minor axis $$T = \max_{\hat n} \frac{\sum_i |\vec p_i \cdot \hat n|}{\sum_i |\vec p_i|}$$4 obtained from the $$T = \max_{\hat n} \frac{\sum_i |\vec p_i \cdot \hat n|}{\sum_i |\vec p_i|}$$5-weighted covariance matrix of constituent directions in the $$T = \max_{\hat n} \frac{\sum_i |\vec p_i \cdot \hat n|}{\sum_i |\vec p_i|}$$6 plane. In each $$T = \max_{\hat n} \frac{\sum_i |\vec p_i \cdot \hat n|}{\sum_i |\vec p_i|}$$7 bin and separately for central and forward jets, CMS formed factorized per-flavor likelihoods and defined

$$T = \max_{\hat n} \frac{\sum_i |\vec p_i \cdot \hat n|}{\sum_i |\vec p_i|}$$8

The overall discriminator shape in simulation was then corrected with a data-driven smearing map

$$T = \max_{\hat n} \frac{\sum_i |\vec p_i \cdot \hat n|}{\sum_i |\vec p_i|}$$9

with $\tau = 1-T$0 obtained by minimizing a $\tau = 1-T$1 between data and simulation in quark-enriched and gluon-enriched control samples (Cornelis, 2014).

These early likelihood taggers established two persistent lessons. First, multiplicity and angular spread are consistently among the strongest single inputs. Second, data-driven calibration is indispensable, because generator-level quark/gluon differences are not reliably transported to detector-level analysis without dedicated correction (Collaboration, 2014, Cornelis, 2014).

4. Deep learning, end-to-end detectors, and weak supervision

Jet-image CNNs reframed quark–gluon tagging as a computer-vision problem. In the “deep learning in color” study, jets were mapped to $\tau = 1-T$2 images in $\tau = 1-T$3, with color channels defined by charged-particle $\tau = 1-T$4, neutral-particle $\tau = 1-T$5, and charged-particle counts. On simulated dijet samples, the deep CNN matched or outperformed hand-engineered observables and their BDT combinations. At $\tau = 1-T$6 GeV in Pythia, the deep color CNN achieved $\tau = 1-T$7 at fixed $\tau = 1-T$8, compared with $\tau = 1-T$9 for the BDT of five observables and $\tau \ll 1$0 for charged-particle multiplicity alone; in Herwig at the same $\tau \ll 1$1, the corresponding numbers were $\tau \ll 1$2, $\tau \ll 1$3, and $\tau \ll 1$4. The same work also found surprisingly good cross-generator robustness: a CNN trained on Pythia and tested on Herwig performed comparably to a CNN trained and tested on Herwig, suggesting that the network was extracting robust physical structure rather than generator-specific artifacts (Komiske et al., 2016).

A broader detector-level CNN comparison using DELPHES PF-like reconstruction evaluated VGGNet, ResNet, Inception variants, DenseNet, Xception, SENet-enhanced models, and a custom Vanilla ConvNet. At $\tau \ll 1$5 GeV, the best reported detector-level performance came from SE-Inception-ResNet-v2 with 10 channels, yielding $\tau \ll 1$6 at $\tau \ll 1$7 and $\tau \ll 1$8 at $\tau \ll 1$9, compared with $\tau$0 and $\tau$1 for the CMS-like five-variable BDT. The study also found that performance saturated with modest parameter counts and that moving from three to six or ten channels improved AUC, with diminishing returns beyond the six-channel setup (Lee et al., 2020).

The CMS Open Data end-to-end study pushed this program to detector realism by bypassing particle-flow reconstruction and learning directly from high-fidelity low-level detector responses. A ResNet-15 processed three-channel jet-view images built from tracks, ECAL, and HCAL. On the test set, the full end-to-end jet classifier reached $\tau$2 and $\tau$3, compared with $\tau$4 and $\tau$5 for the particle-based QCD-aware RecNN baseline. Event-level extensions for dijet classification reached $\tau$6 and $\tau$7 with the unified full-detector-image classifier. Cross-evaluation between full images and “zeroed” images, in which pixels outside the two jet windows were masked, showed only minimal losses, indicating that the classifier was largely insensitive to UE and pile-up outside the jet regions of interest (Andrews et al., 2019).

Weak supervision addresses the dependence on Monte Carlo truth labels. The CWoLa study trained CNN, RNN, and BDT classifiers on mixed $\tau$8jet and dijet samples rather than on pure quark/gluon labels. Its central observation was that realistically simulated mixed samples can produce effective quark–gluon classifiers, but only if domain shifts are controlled. In particular, restricting the training to central jets, $\tau$9, dramatically improved weakly supervised deep-learning performance and reduced the gap to fully supervised training, because otherwise the networks exploited $C_A = 3$00 differences and production-specific color-flow effects between the two mixtures rather than learning pure quark–gluon structure (Lee et al., 2020).

Graph-based representation learning has since become part of this landscape. A recent graph-contrastive study using a Quantum Rationale Generator on the Pythia8 quark–gluon jet dataset reported an AUC of $C_A = 3$01 with a rationale module containing only $C_A = 3$02 trainable quantum parameters. The reported advantage was not merely numerical compression but rationale-aware augmentation that preserved discriminative substructure while respecting infrared and collinear constraints (Jahin et al., 2024).

5. Mixture models and heavy-ion modifications

In both $C_A = 3$03 and heavy-ion collisions, quark–gluon discrimination is fundamentally a problem of latent mixtures. The topic-modeling formulation makes this explicit: $C_A = 3$04 with reducibility factors

$C_A = 3$05

From these one extracts mutually irreducible topics,

$C_A = 3$06

and corresponding quark fractions as functions of $C_A = 3$07. In the heavy-ion proof of concept, constituent multiplicity $C_A = 3$08 was the preferred observable because counting observables have strong theoretical support for quark/gluon separability. Using $C_A = 3$09jet as a quark-enriched sample and dijet/inclusive events as a gluon-enriched sample, the extracted quark-like and gluon-like multiplicity distributions in both $C_A = 3$10 and HI agreed qualitatively with the MC-defined topics, and the HI study showed medium-induced changes to both the fractions and the topic shapes (Brewer et al., 2020).

A complementary heavy-ion line of work used JEWEL together with physics-motivated observables, jet images, and telescoping deconstruction. In that setting, quark–gluon discrimination worsened in heavy-ion collisions because significant soft radiation affected soft jet substructures. Telescoping deconstruction organized jet information through subjets at multiple angular scales, while Lund diagrams showed enhanced soft, wide-angle branches in AA relative to $C_A = 3$11. The same studies found that pixel multiplicity was the dominant observable for discriminating $C_A = 3$12 from AA jets, but that it was also highly sensitive to soft event activity, which made quark–gluon separation less robust in the medium (Chien et al., 2018, Chien, 2018).

Energy–energy correlators provide a more differential medium probe. In a Pb+Pb study at $C_A = 3$13 TeV, the jet EEC was defined as an energy-weighted pair distribution in the $C_A = 3$14 plane with an ALICE-style ring-area factor. The main reported flavor-dependent patterns were that pure quark jets showed mild suppression at small $C_A = 3$15 and monotonic enhancement at larger $C_A = 3$16, whereas pure gluon jets exhibited a bimodal enhancement, with increases at both small and large $C_A = 3$17. The same work proposed photon-tagged jets as quark proxies and inclusive charged-hadron jets as gluon proxies, and found that these proxies reproduced the respective flavor-specific quenching patterns. Its central conclusion was that the observed flavor dependence in the EEC ratio was driven more by intrinsic quark–gluon jet-structure differences than by medium-induced mechanisms alone (Chen et al., 2024).

Taken together, these heavy-ion results reframe quark–gluon discrimination as a coupled inference problem. One must separate “who is in the sample” from “how each category is modified,” and methods that work in $C_A = 3$18 only as pure taggers become, in HI, tools for deconvolving composition and medium response (Brewer et al., 2020, Chen et al., 2024).

6. Ambiguities, systematics, and current directions

The main conceptual ambiguity is the definition of jet flavor itself. Several papers adopt the pragmatic view that a quark jet is the result of showering a quark parton and a gluon jet the result of showering a gluon parton, which is adequate in the resummation region, but the literature also emphasizes that this becomes subtle beyond NLL, in the presence of flavor-changing splittings, color interference, and nonperturbative effects. In practice, parton-level labels, detector-level taggers, and operational topic-model definitions are not identical objects, and much of the systematic complexity of the subject follows from that mismatch (Larkoski et al., 2014, Larkoski et al., 2019).

A second long-standing issue is generator dependence, especially for gluon jets. Earlier studies found factor-of-two spreads in discrimination performance across parton showers. The NNLL$C_A = 3$19 thrust comparison showed that this spread has narrowed, largely because Herwig 7.1 substantially improved its gluon-jet modeling relative to Herwig 7.0.4. Even so, the LHC detector-level studies remain clear that data show quark and gluon jets to be more similar than some Monte Carlo setups predict, and this is precisely why ATLAS and CMS relied on data-driven templates, smearing functions, and control-sample calibration rather than on uncorrected simulated shapes (Mo et al., 2017, Collaboration, 2014, Cornelis, 2014).

A third issue concerns robustness under pile-up, underlying event, and domain shift. End-to-end detector learning on CMS Open Data showed that a minimally processed image-based classifier can learn pile-up mitigation intrinsically, but the same study also noted that calibration and uncertainty propagation become more involved for unified event-level classifiers. Weak supervision exposed a complementary failure mode: if $C_A = 3$20jet and dijet mixtures differ in $C_A = 3$21 or in production-specific color flow, a classifier can violate the CWoLa assumption and learn sample identity rather than quark–gluon structure. In heavy-ion topic modeling, the analogous caveat is that mutual irreducibility may degrade in the medium, and that the proof-of-concept generator lacks several ingredients of real data, including underlying event and full detector effects (Andrews et al., 2019, Lee et al., 2020, Brewer et al., 2020).

The present outlook is therefore dual. On the theory side, the literature points toward higher-order resummation, improved nonperturbative modeling, and more systematic likelihood constructions based on resolved emissions, weighted multiplicities, and topic extraction. On the analysis side, it points toward calibrated detector-level or end-to-end classifiers, weakly supervised and data-driven methods that avoid fragile truth labels, and multi-scale observables such as EECs, Lund-plane coordinates, and higher-point correlators in environments where composition and modification are entangled. This suggests that quark–gluon discrimination is evolving from a single tagger into a broader framework for jet-flavor inference across $C_A = 3$22, detector-level, and heavy-ion settings (Bright-Thonney et al., 2022, Brewer et al., 2020, Chen et al., 2024).