Subtractive Jet Flavor Techniques

• Subtractive jet flavor is a method that neutralizes soft, wide-angle radiation to secure robust flavor tagging in high-energy jets.
• Dynamic jet charge employs constituent-dependent weighting to downweight low-momentum contributions and enhance quark–gluon separation.
• Modified clustering and explicit perturbative subtraction techniques yield IRC-safe flavor assignments and support flavor-tomographic studies in heavy-ion collisions.

Searching arXiv for recent and foundational papers on subtractive jet flavor, IRC-safe jet flavour, and dynamic jet charge. Subtractive jet flavor denotes a family of jet-flavor constructions in which soft, wide-angle, underlying-event, pileup, or medium-induced contributions are neutralized, downweighted, or analytically removed before they can alter a flavor assignment or a flavor-sensitive observable. In current usage, the term covers several technically distinct strategies: constituent-weighting observables such as dynamic jet charge, flavor-aware clustering and post-clustering dressing algorithms that force opposite-sign soft pairs to recombine before they contaminate hard jets, explicit perturbative subtractions of soft heavy-flavor artefacts and flavor-changing non-global logarithms, and heavy-ion decompositions in which inclusive jet suppression is resolved into gluon-, light-quark-, and heavy-quark-initiated components (Kang et al., 2021, Czakon et al., 2022, Gauld et al., 2022, Generet, 28 Nov 2025, Larkoski, 7 Oct 2025, Zhang et al., 2023).

1. Conceptual basis and scope

The central problem is that naive jet-flavor assignment is generically vulnerable to unresolved radiation. At fixed order, a flavored jet is often defined by the net heavy-flavor number clustered into the jet, but arbitrarily soft gluons can split as $g\to q\bar q$, and if the soft pair is separated by the clustering, one member can be absorbed by a hard jet while the other is not. For standard anti-$k_T$, this produces an infrared-flavor problem: in the double-soft limit, the pair distance does not vanish, so a soft quark can cluster with a hard jet before it clusters with its soft antiquark partner, making naive net-flavor tagging with standard anti-$k_T$ infrared-unsafe for jet flavor at fixed order (Czakon et al., 2022).

A closely related statement appears in all-orders discussions of flavor dressing: constituent-based naive labelling, ghost association of flavoured hadrons or secondary vertices, and similar standard procedures applied to anti-$k_T$ jets are not infrared and collinear safe, and naive subtraction at the constituent level generally fails IRC safety because identifying and removing arbitrarily soft or collinear pairs is itself sensitive to unresolved emissions unless it is driven by an IRC-safe recombination criterion (Gauld et al., 2022). In a complementary language, flavor-changing non-global logarithms arise when a soft $q\bar q$ pair straddles a jet boundary, and they are responsible for the infrared unsafety of a naive definition of jet flavor that is simply the net sum of quark flavors in the jet of interest (Larkoski, 7 Oct 2025).

This suggests that subtractive jet flavor is not a single observable but a methodological class. Its common objective is to prevent zero-net-flavor soft radiation from changing the flavor of hard jets. The subtraction can be implemented implicitly, by modifying constituent weights or clustering distances, or explicitly, by analytic counterterms added to otherwise standard jet definitions.

2. Subtractive weighting with dynamic jet charge

The most direct observable realization is dynamic jet charge. Standard jet charge is defined as

$$Q_\kappa = \sum_{h\in \text{jet}} z_h^\kappa Q_h, \qquad z_h=\frac{p_{T,h}}{p_{T,J}}$$

at hadron colliders, with common practice using $\kappa \approx 0.3$–$0.7$ (Kang et al., 2021). Dynamic jet charge promotes $\kappa$ to a constituent-dependent function,

$Q_{\text{dyn}}=\sum_h z_h^{\kappa(z_h)} Q_h,$

and the specific form studied is

$k_T$0

The default parameters that delivered strong performance in Pythia8 are $k_T$1, $k_T$2, and $k_T$3 (Kang et al., 2021).

The subtractive mechanism is that low-$k_T$4 constituents are strongly downweighted relative to high-$k_T$5 constituents. Since underlying event, pileup, and medium-induced activity populate low $k_T$6, the weighting acts akin to subtraction or filtering of soft contamination without explicitly removing particles or grooming them away. The corresponding soft/hard decomposition,

$k_T$7

produces a characteristic multi-peak distribution: a narrow central peak near $k_T$8 from soft particles and side peaks from hard particles. For the default choice, gluon jets, with more soft fragments, show a higher central peak and smaller side peaks; quark jets show the opposite (Kang et al., 2021).

In proton-proton collisions at $k_T$9 TeV with anti-$k_T$0, $k_T$1, $k_T$2 GeV, $k_T$3, and MPI on, the dynamic observable yields strong quark–gluon separation in the side-peak region. The quoted fractional counts are $k_T$4 for quark jets and $k_T$5 for gluon jets in the $k_T$6 bin, and $k_T$7 for quark jets and $k_T$8 for gluon jets in the $k_T$9 bin (Kang et al., 2021). In PbPb simulations with Angantyr at $k_T$0 TeV, anti-$k_T$1 $k_T$2, $k_T$3 GeV, and $k_T$4, the corresponding dynamic fractions are $k_T$5 for quark jets and $k_T$6 for gluon jets, and $k_T$7 for quark jets and $k_T$8 for gluon jets, demonstrating robustness against enhanced underlying event and soft activity (Kang et al., 2021).

The same study reports that Soft Drop with $k_T$9, $q\bar q$0 produces very little change in either standard or dynamic charge distributions in both pp and PbPb, so the dynamic weighting itself already provides substantial soft resilience (Kang et al., 2021). In that sense, dynamic jet charge is subtractive-like rather than explicitly subtractive.

3. IRC-safe flavored jets through modified clustering and dressing

A more formal subtractive construction modifies the clustering metric so that opposite-sign soft flavored pairs recombine before they can contaminate hard jets. In the flavor-aware anti-$q\bar q$1 proposal, the standard anti-$q\bar q$2 distances

$q\bar q$3

are changed only when both pseudo-jets carry nonzero, opposite-sign flavor (Czakon et al., 2022). The modified pairwise distance is

$q\bar q$4

with

$q\bar q$5

As $q\bar q$6, $q\bar q$7, so $q\bar q$8 and the soft pair clusters first. Flavor is propagated by integer addition of flavor-charge vectors, $q\bar q$9, so opposite-sign unit charges merge to a flavorless pseudo-jet that can no longer contaminate hard jets (Czakon et al., 2022).

This is subtractive in spirit because it neutralizes the potential flavor impact of arbitrarily soft $$Q_\kappa = \sum_{h\in \text{jet}} z_h^\kappa Q_h, \qquad z_h=\frac{p_{T,h}}{p_{T,J}}$$0 pairs before any hard association. The algorithm is verified at NNLO: standard anti-$$Q_\kappa = \sum_{h\in \text{jet}} z_h^\kappa Q_h, \qquad z_h=\frac{p_{T,h}}{p_{T,J}}$$1 shows a logarithmic divergence as the cutoff $$Q_\kappa = \sum_{h\in \text{jet}} z_h^\kappa Q_h, \qquad z_h=\frac{p_{T,h}}{p_{T,J}}$$2 in IR-sensitive channels, whereas the modified flavored anti-$$Q_\kappa = \sum_{h\in \text{jet}} z_h^\kappa Q_h, \qquad z_h=\frac{p_{T,h}}{p_{T,J}}$$3 exhibits flat, cutoff-stable behavior down to small $$Q_\kappa = \sum_{h\in \text{jet}} z_h^\kappa Q_h, \qquad z_h=\frac{p_{T,h}}{p_{T,J}}$$4 (Czakon et al., 2022). Values around $$Q_\kappa = \sum_{h\in \text{jet}} z_h^\kappa Q_h, \qquad z_h=\frac{p_{T,h}}{p_{T,J}}$$5–$$Q_\kappa = \sum_{h\in \text{jet}} z_h^\kappa Q_h, \qquad z_h=\frac{p_{T,h}}{p_{T,J}}$$6 yield robust behavior, and $$Q_\kappa = \sum_{h\in \text{jet}} z_h^\kappa Q_h, \qquad z_h=\frac{p_{T,h}}{p_{T,J}}$$7 is recommended for $$Q_\kappa = \sum_{h\in \text{jet}} z_h^\kappa Q_h, \qquad z_h=\frac{p_{T,h}}{p_{T,J}}$$8-jet–type observables (Czakon et al., 2022).

A complementary route is flavor dressing, which factorizes flavor assignment from jet finding. One begins with any IRC-safe set of flavor-agnostic jets, especially anti-$$Q_\kappa = \sum_{h\in \text{jet}} z_h^\kappa Q_h, \qquad z_h=\frac{p_{T,h}}{p_{T,J}}$$9 jets, and a set of flavored particles such as quarks, heavy-flavor hadrons, or reconstructed secondary vertices. The dressing algorithm iteratively compares particle–particle, particle–jet, and beam distances using

$\kappa \approx 0.3$0

with default parameters $\kappa \approx 0.3$1 and $\kappa \approx 0.3$2, and merges soft or collinear flavored pairs before association to jets (Gauld et al., 2022). The jets themselves are unchanged: flavor is post-processed onto the original anti-$\kappa \approx 0.3$3 kinematics. In $\kappa \approx 0.3$4, the “bad tag” cross section tends to zero as $\kappa \approx 0.3$5 at order $\kappa \approx 0.3$6 and $\kappa \approx 0.3$7, whereas naive assignments do not (Gauld et al., 2022). In pp $\kappa \approx 0.3$8-jet, the dressed definition gives good agreement between NNLO fixed order and NLO+PS and preserves standard anti-$\kappa \approx 0.3$9 jet kinematics (Gauld et al., 2022).

The distinction between these two strategies is structural. Modified flavored anti-$0.7$0 changes the clustering metric itself, whereas dressing leaves the jet definition intact and constructs an IRC-safe recombination graph for flavor only. Both accomplish subtraction by forcing the cancellation of soft opposite-sign flavor before flavor is attached to hard jets.

4. Explicit perturbative subtraction and flavor-changing non-global logarithms

A third strand makes the subtraction fully explicit at the level of fixed-order perturbation theory. One approach restores IRC safety for standard anti-$0.7$1 jets and conventional flavor tags without changing either the jet algorithm or the observable (Generet, 28 Nov 2025). In this formulation, the flavor modulo-2 tag removes collinear $0.7$2 sensitivity at NLO but remains IRC-unsafe at NNLO because of double-soft $0.7$3 pairs. The remedy is to reintroduce the heavy-quark mass at leading power only in the soft heavy-flavor sector and to add and subtract local counterterms built from universal double-soft kernels (Generet, 28 Nov 2025).

Schematically, the counterterm acts through the unchanged measurement function $0.7$4 as

$0.7$5

so only the flavor-changing soft contribution is removed. The construction is renormalization-like: it preserves exact anti-$0.7$6 kinematics, introduces no extra clustering or tagging step, and yields small NNLO corrections with good regulator independence and explicit $0.7$7-pole cancellation (Generet, 28 Nov 2025).

A more direct subtractive definition appears in the analysis of flavor-changing non-global logarithms. There, the naive flavor vector of a jet is regulated with a transverse-momentum threshold,

$0.7$8

and the subtractive jet flavor cross section is defined by

$0.7$9

The problematic soft logarithm is therefore removed analytically rather than by modifying the jet definition (Larkoski, 7 Oct 2025). The same work calculates the exact coefficient of the leading flavor-changing non-global logarithm through quadratic order in $\kappa$0 and shows that the truncation is within $\kappa$1 of the complete result for radii up to $\kappa$2 (Larkoski, 7 Oct 2025).

These perturbative constructions clarify a common misconception. The obstacle is not the existence of soft flavor pairs as such, but the fact that naive bookkeeping lets zero-net-flavor soft radiation alter a flavor label. Subtractive jet flavor, in this explicit sense, removes precisely that artefact and leaves the rest of the observable unchanged.

5. Heavy-ion and flavor-tomographic interpretations

In heavy-ion phenomenology, subtractive jet flavor acquires a second meaning: observed quenching is decomposed into flavor-tagged pieces so that color-charge, mass, path-length, and spectrum effects can be separated. A Bayesian analysis combining inclusive jets, $\kappa$3+jet events, and $\kappa$4-jets in Pb+Pb at $\kappa$5 TeV extracts flavor-dependent jet energy loss distributions and finds the hierarchy

$\kappa$6

across $\kappa$7 and centrality (Zhang et al., 2023). The channel logic is itself subtractive: inclusive jets are a quark–gluon mixture, $\kappa$8+jet is approximately quark-dominated, and $\kappa$9-jets constrain the heavy-flavor sector, so the combination allows one to solve for the gluon component (Zhang et al., 2023).

A minimal-model parametric analysis of inclusive-jet, $Q_{\text{dyn}}=\sum_h z_h^{\kappa(z_h)} Q_h,$0-jet, and $Q_{\text{dyn}}=\sum_h z_h^{\kappa(z_h)} Q_h,$1-jet suppression reaches an analogous conclusion about path length. With

$Q_{\text{dyn}}=\sum_h z_h^{\kappa(z_h)} Q_h,$2

the best-fit inclusive-jet parameters are $Q_{\text{dyn}}=\sum_h z_h^{\kappa(z_h)} Q_h,$3, $Q_{\text{dyn}}=\sum_h z_h^{\kappa(z_h)} Q_h,$4 GeV, and $Q_{\text{dyn}}=\sum_h z_h^{\kappa(z_h)} Q_h,$5 GeV, and the path-length dependence

$Q_{\text{dyn}}=\sum_h z_h^{\kappa(z_h)} Q_h,$6

yields $Q_{\text{dyn}}=\sum_h z_h^{\kappa(z_h)} Q_h,$7, consistent with radiative energy loss (Ogrodnik et al., 2024). The same study finds that energy-loss fluctuations are necessary for a good description of inclusive $Q_{\text{dyn}}=\sum_h z_h^{\kappa(z_h)} Q_h,$8 and that $Q_{\text{dyn}}=\sum_h z_h^{\kappa(z_h)} Q_h,$9-jet suppression in central collisions is compatible with an effective path length smaller than for inclusive jets, with $k_T$00 in $k_T$01–$k_T$02 centrality (Ogrodnik et al., 2024).

Transport-based flavor tomography makes the same subtraction at the hadron level. In the Linear Boltzmann Transport framework, parton-level quenching obeys the robust ordering $k_T$03, but the hadron-level similarity between prompt $k_T$04 mesons and charged hadrons at the LHC emerges once gluon contributions to both channels are accounted for consistently (Cao et al., 2017, Xing et al., 2019). CUJET phrased this program as jet flavor tomography: differences and double ratios of $k_T$05 for $k_T$06, $k_T$07, $k_T$08, and heavy-flavor electrons cancel common normalization and geometry systematics and foreground color-charge and dead-cone effects (Buzzatti et al., 2012).

This heavy-ion usage is conceptually distinct from IRC-safe flavor labelling, yet the logic is again subtractive: the measured suppression is treated as a superposition of flavor components, and comparison across flavor-sensitive channels removes common medium effects to isolate the flavor dependence.

6. Medium-induced flavor conversion, phenomenology, and open issues

A more literal medium-induced subtraction of gluon dominance is proposed in studies of quenched jets in the quark–gluon plasma. In static-medium simulations for a $k_T$09 GeV gluon jet at $k_T$10 GeV, the combined conversion rate

$k_T$11

is about twice the reverse quark-to-gluon rate, and the conversion probability exceeds $k_T$12–$k_T$13 for path lengths of $k_T$14–$k_T$15 fm (Sirimanna et al., 2022). Together with the color-factor scaling

$k_T$16

this produces an intermediate-$k_T$17 sector, roughly $k_T$18–$k_T$19 GeV and at angles of order $k_T$20–$k_T$21 rad, in which quarks and antiquarks can outnumber gluons (Sirimanna et al., 2022). The paper explicitly interprets this as the medium subtracting gluon dominance from the jet’s semi-hard sector.

Experimentally, several observable classes have been proposed as probes of subtractive jet flavor across these contexts. Dynamic jet charge and standard jet charge binning can be used to enhance flavor fractions, including at the EIC, where restricting to $k_T$22 or $k_T$23 increases the fractional $k_T$24 contribution relative to $k_T$25, and kaon-only jet charge amplifies the negative-charge bin fraction for $k_T$26-quark jets by approximately a factor of $k_T$27 relative to $k_T$28 (Kang et al., 2020). Heavy-flavor-tagged substructure provides an orthogonal route: ALICE charm-tagged jets with anti-$k_T$29, $k_T$30 show a reduced energy–energy correlator integral, near-perfect WTA–$k_T$31 alignment of $k_T$32 in the smallest $k_T$33 bin, and a steeper groomed $k_T$34 than inclusive jets, all consistent with dead-cone-suppressed radiation and with template-based subtraction of $k_T$35 and $k_T$36 contamination (Yeats, 16 Jun 2025).

Several limitations recur across the literature. Parton-level net-flavor definitions differ from experimental hadron-level tags and generally require unfolding (Czakon et al., 2022). In heavy-ion applications, Angantyr and related simulations do not include fully quenched medium dynamics, and dedicated JEWEL or JETSCAPE studies are identified as necessary to quantify robustness in fully quenched environments (Kang et al., 2021). More generally, the optimal constituent-weight function $k_T$37, the optimal damping function $k_T$38, and the systematic treatment of detector thresholds and tracking remain open optimization problems (Kang et al., 2021, Czakon et al., 2022).

The unifying lesson is that subtractive jet flavor is a control strategy for flavor ambiguity. Whether implemented through constituent reweighting, flavor-aware recombination, soft-kernel counterterms, non-global-logarithm subtraction, or multi-channel quenching inference, its purpose is to ensure that flavor information is carried by the hard, physically informative part of the jet rather than by unresolved radiation or background.