Nearside Energy-Energy Correlators

• Nearside EEC is the small-angle limit of energy-weighted correlations in e+e- and jet events, probing collinear splitting dynamics.
• It combines fixed-order QCD, resummation, and non-perturbative modeling to bridge perturbative and free-hadron regimes.
• Experimental analyses in pp, p–Pb, and heavy-ion collisions reveal flavor dependence and medium modifications in jet substructure.

Nearside energy-energy correlators are the small-angle limit of energy-weighted angular correlation observables. In $e^+e^-$ annihilation this limit is $\chi\to 0$, equivalently $z=\frac{1-\cos\chi}{2}\to 0$; in jet measurements it is the small intrajet pair separation $R_L\to 0$ inside a reconstructed jet. The near-side region isolates pairs produced within the same collinear system and is therefore sensitive to collinear splitting dynamics, while at sufficiently small transverse scale it also resolves the transition to hadronization and the free-hadron regime. Contemporary treatments combine fixed-order QCD, collinear resummation, di-hadron fragmentation, and non-perturbative transverse-structure modeling, and the observable is now measured in $pp$, $p$–Pb, heavy-flavor-tagged jets, and heavy-ion environments (Neill et al., 2022, Guo et al., 21 Jul 2025, Liang-Gilman, 28 Jun 2025).

1. Definitions and kinematic realizations

In its standard $e^+e^-$ form, the energy-energy correlator is the weighted angular correlation of final-state hadrons,

$$\mathrm{EEC}(\chi)=\sum_{a,b}\int \frac{d\sigma_{ee\to a+b+X}}{\sigma}\, w_{ab}\,\delta(\cos\chi_{ab}-\cos\chi), \qquad w_{ab}=\frac{2E_aE_b}{s},$$

with the angular variable

$$z\equiv \frac{1-\cos\chi}{2}=\sin^2\!\left(\frac{\chi}{2}\right).$$

The near-side region is the collinear endpoint $z\to 0$, while the back-to-back region is $\chi\to 0$0 (Neill et al., 2022).

Jet-based measurements use an intrajet analogue rather than the global $\chi\to 0$1 event shape. In the ALICE formulation, the two-point correlator is built from pairs of constituents inside a reconstructed jet with pair weight

$\chi\to 0$2

and angular distance

$\chi\to 0$3

These are explicitly jet-based correlators for inclusive charged jets in $\chi\to 0$4, $\chi\to 0$5-tagged charged jets in $\chi\to 0$6, inclusive charged jets in $\chi\to 0$7–Pb, and three-point correlators in inclusive jets. The quoted jet definition is anti-$\chi\to 0$8 with $\chi\to 0$9; in the heavy-flavor case, charged particles plus reconstructed neutral $z=\frac{1-\cos\chi}{2}\to 0$0 mesons are clustered and jets containing a reconstructed $z=\frac{1-\cos\chi}{2}\to 0$1 are selected (Liang-Gilman, 28 Jun 2025).

The near-side label therefore has two operational forms. In $z=\frac{1-\cos\chi}{2}\to 0$2, it means $z=\frac{1-\cos\chi}{2}\to 0$3 or $z=\frac{1-\cos\chi}{2}\to 0$4. In jet substructure, it means the leftmost part of the distribution in $z=\frac{1-\cos\chi}{2}\to 0$5, i.e. pairs with very small opening angle inside the same jet. The two descriptions are kinematically analogous but not identical, because the former is a global event-shape definition and the latter is an intrajet observable in $z=\frac{1-\cos\chi}{2}\to 0$6 space (Neill et al., 2022, Liang-Gilman, 28 Jun 2025).

2. Collinear structure and perturbative factorization

The near-side endpoint is singular and requires resummation. A central review-level statement is that the small-angle limit is characterized by a single logarithmic series, in contrast to the back-to-back limit, which has double logarithmic behaviour and a Sudakov-like peak (Neill et al., 2022). Analytically, the fixed-order expansion confirms the collinear enhancement. For the QCD $z=\frac{1-\cos\chi}{2}\to 0$7 EEC, the leading-order coefficient behaves as

$z=\frac{1-\cos\chi}{2}\to 0$8

and the next-to-leading-order coefficient has the collinear expansion

$z=\frac{1-\cos\chi}{2}\to 0$9

with the exact coefficients given in the analytic NLO calculation. That calculation also shows that term-by-term singularities stronger than $R_L\to 0$0 cancel in the full result, and it identifies the leading collinear behaviour with collinear splitting and jet-calculus predictions (Dixon et al., 2018).

A dedicated nearside factorization theorem was formulated in terms of di-hadron fragmentation. In that framework the correct organizing principle is that, when two measured hadrons become nearly collinear, the EEC is controlled by the fragmentation of a single parent parton into two nearby hadrons. At jet level the small-angle factorization is

$R_L\to 0$1

with $R_L\to 0$2 a hard coefficient and $R_L\to 0$3 an unintegrated EEC jet function built from di-hadron fragmentation (Guo et al., 21 Jul 2025).

The same work derives an all-order $R_L\to 0$4-space solution,

$R_L\to 0$5

and emphasizes several structural features of the near-side limit: there is no separate soft function, no Collins-Soper kernel, and no Sudakov-type double logarithms; the evolution is instead governed by timelike DGLAP, and the resummed formula reproduces the singular fixed-order small-$R_L\to 0$6 terms exactly at the claimed level (Guo et al., 21 Jul 2025).

3. The free-hadron region, the transition region, and non-perturbative modeling

A major development after the purely perturbative collinear treatments is the recognition that the angular variable alone does not determine whether the observable is perturbative. What matters is the transverse scale

$R_L\to 0$7

in $R_L\to 0$8, or the analogous intrajet scale $R_L\to 0$9 in jet measurements. When this scale is only a few GeV or less, the observed pair probes non-perturbative hadron production rather than a purely perturbative partonic splitting (Herrmann et al., 23 Jul 2025, Kang et al., 23 Jul 2025).

One non-perturbative framework introduces the EEC-DiFF, a dihadron-fragmentation object tailored to the near-side observable,

$pp$0

with $pp$1. In the free-hadron and transition regions the EEC factorizes in terms of this object, while in the large-$pp$2 regime it reproduces the perturbative quark EEC jet function,

$pp$3

The same study fitted $pp$4 near-side data in the domain $pp$5 using TASSO, MAC, MARKII, TOPAZ, and OPAL data, obtaining $pp$6 and a model that reproduces the salient peak and scaling features of the free-hadron and transition regions (Kang et al., 23 Jul 2025).

A second unified description works directly in impact-parameter space with a multiplicative non-perturbative jet factor,

$pp$7

A global NNLO+NNLL analysis over $pp$8 and $pp$9 found

$p$0

with $p$1. That analysis interprets $p$2 as a characteristic transition scale, places the transition region around a few GeV, and identifies a dominantly free-hadron regime roughly at $p$3 (Herrmann et al., 23 Jul 2025).

A more phenomenological universality ansatz models the deep near-side region with a non-perturbative TMD kernel,

$p$4

which automatically yields the free-hadron scaling $p$5 as $p$6. Using $p$7, $p$8, $p$9, $e^+e^-$0, and a fit giving $e^+e^-$1, $e^+e^-$2, the model describes near-side shapes and peaks in both $e^+e^-$3 and $e^+e^-$4 jet data over a wide energy range (Liu et al., 2024).

4. Experimental program and measured near-side regimes

Experimentally, the near-side jet EEC is already resolved into multiple angular regimes. At RHIC, STAR measured the two-point correlator in $e^+e^-$5 collisions at $e^+e^-$6 for jets with $e^+e^-$7 and found three regions: a small-angle region that increases linearly with $e^+e^-$8, a transition region around the peak, and a larger-angle perturbative region. The transition scale extracted from the fit parameter $e^+e^-$9 is approximately universal under $$\mathrm{EEC}(\chi)=\sum_{a,b}\int \frac{d\sigma_{ee\to a+b+X}}{\sigma}\, w_{ab}\,\delta(\cos\chi_{ab}-\cos\chi), \qquad w_{ab}=\frac{2E_aE_b}{s},$$0 rescaling,

$$\mathrm{EEC}(\chi)=\sum_{a,b}\int \frac{d\sigma_{ee\to a+b+X}}{\sigma}\, w_{ab}\,\delta(\cos\chi_{ab}-\cos\chi), \qquad w_{ab}=\frac{2E_aE_b}{s},$$1

for the three $$\mathrm{EEC}(\chi)=\sum_{a,b}\int \frac{d\sigma_{ee\to a+b+X}}{\sigma}\, w_{ab}\,\delta(\cos\chi_{ab}-\cos\chi), \qquad w_{ab}=\frac{2E_aE_b}{s},$$2 intervals with $$\mathrm{EEC}(\chi)=\sum_{a,b}\int \frac{d\sigma_{ee\to a+b+X}}{\sigma}\, w_{ab}\,\delta(\cos\chi_{ab}-\cos\chi), \qquad w_{ab}=\frac{2E_aE_b}{s},$$3, summarized as $$\mathrm{EEC}(\chi)=\sum_{a,b}\int \frac{d\sigma_{ee\to a+b+X}}{\sigma}\, w_{ab}\,\delta(\cos\chi_{ab}-\cos\chi), \qquad w_{ab}=\frac{2E_aE_b}{s},$$4. STAR also measured like-sign and opposite-sign EECs and found that both PYTHIA and HERWIG under-predict the relative contribution of like-charge correlations for angles smaller than the transition region (Collaboration, 21 Feb 2025).

ALICE reports a complementary LHC program based on anti-$$\mathrm{EEC}(\chi)=\sum_{a,b}\int \frac{d\sigma_{ee\to a+b+X}}{\sigma}\, w_{ab}\,\delta(\cos\chi_{ab}-\cos\chi), \qquad w_{ab}=\frac{2E_aE_b}{s},$$5, $$\mathrm{EEC}(\chi)=\sum_{a,b}\int \frac{d\sigma_{ee\to a+b+X}}{\sigma}\, w_{ab}\,\delta(\cos\chi_{ab}-\cos\chi), \qquad w_{ab}=\frac{2E_aE_b}{s},$$6, predominantly charged-particle jets. In inclusive $$\mathrm{EEC}(\chi)=\sum_{a,b}\int \frac{d\sigma_{ee\to a+b+X}}{\sigma}\, w_{ab}\,\delta(\cos\chi_{ab}-\cos\chi), \qquad w_{ab}=\frac{2E_aE_b}{s},$$7 jets, the left side of the EEC distribution is identified with smaller-angle pairs and interpreted as the non-perturbative region where free-hadron scaling becomes relevant, the peak marks the transition region sensitive to hadronization, and the right side corresponds to wider-angle pairs associated with early-time perturbative splittings. In scaled presentations involving $$\mathrm{EEC}(\chi)=\sum_{a,b}\int \frac{d\sigma_{ee\to a+b+X}}{\sigma}\, w_{ab}\,\delta(\cos\chi_{ab}-\cos\chi), \qquad w_{ab}=\frac{2E_aE_b}{s},$$8, the distributions in different jet-$$\mathrm{EEC}(\chi)=\sum_{a,b}\int \frac{d\sigma_{ee\to a+b+X}}{\sigma}\, w_{ab}\,\delta(\cos\chi_{ab}-\cos\chi), \qquad w_{ab}=\frac{2E_aE_b}{s},$$9 intervals align approximately, suggesting approximate universality of the underlying jet dynamics (Liang-Gilman, 28 Jun 2025).

A later ALICE proceedings summary makes the scaling statement more explicit. In inclusive $$z\equiv \frac{1-\cos\chi}{2}=\sin^2\!\left(\frac{\chi}{2}\right).$$0 and $$z\equiv \frac{1-\cos\chi}{2}=\sin^2\!\left(\frac{\chi}{2}\right).$$1–Pb charged jets, the EEC peak shifts to smaller $$z\equiv \frac{1-\cos\chi}{2}=\sin^2\!\left(\frac{\chi}{2}\right).$$2 as jet $$z\equiv \frac{1-\cos\chi}{2}=\sin^2\!\left(\frac{\chi}{2}\right).$$3 increases, but when plotted versus $$z\equiv \frac{1-\cos\chi}{2}=\sin^2\!\left(\frac{\chi}{2}\right).$$4 the distributions collapse onto a common curve with a peak near $$z\equiv \frac{1-\cos\chi}{2}=\sin^2\!\left(\frac{\chi}{2}\right).$$5. The same summary states that the very-small-$$z\equiv \frac{1-\cos\chi}{2}=\sin^2\!\left(\frac{\chi}{2}\right).$$6 region agrees with linear scaling for free hadrons, while the very-large-$$z\equiv \frac{1-\cos\chi}{2}=\sin^2\!\left(\frac{\chi}{2}\right).$$7 region agrees with a pQCD calculation; neither limiting description works near the peak, indicating a broad transition rather than a sharp boundary (Nambrath, 17 Oct 2025).

Measurement class	Near-side result	Reference
STAR $$z\equiv \frac{1-\cos\chi}{2}=\sin^2\!\left(\frac{\chi}{2}\right).$$8, $$z\equiv \frac{1-\cos\chi}{2}=\sin^2\!\left(\frac{\chi}{2}\right).$$9	Linear small-$z\to 0$0 rise; transition scale $z\to 0$1	(Collaboration, 21 Feb 2025)
ALICE inclusive $z\to 0$2 jets	Small-angle side interpreted as non-perturbative/free-hadron; peak marks hadronization-sensitive transition	(Liang-Gilman, 28 Jun 2025)
ALICE scaled $z\to 0$3 and $z\to 0$4–Pb summaries	Collapse versus $z\to 0$5, peak near $z\to 0$6	(Nambrath, 17 Oct 2025)

These measurements make the near-side EEC unusual among jet observables: the same distribution exposes a perturbative collinear tail, a hadronization-sensitive transition, and an ultra-small-angle free-hadron regime within a single self-normalized shape (Collaboration, 21 Feb 2025, Liang-Gilman, 28 Jun 2025).

5. Flavor dependence and nuclear-medium modifications

Heavy flavor introduces an intrinsically near-side effect through the dead cone. In ALICE $z\to 0$7-tagged $z\to 0$8 jets, the EEC is suppressed relative to inclusive jets, and the collaboration states that “the reduced yield corresponds to a reduction of the number of pairs, which is consistent with the expectations of suppressed radiation due to the dead cone.” At the same time, “the peak position of the inclusive jet EEC is consistent within $z\to 0$9 of the peak position of the $\chi\to 0$00-tagged jet EEC,” so the measured effect is primarily a yield suppression rather than a resolved peak displacement (Liang-Gilman, 28 Jun 2025).

Model studies of heavy-flavor-tagged jets sharpen this point by decomposing the jet EEC into three ingredients: the average number of particle pairs per jet, the normalized pair-angular distribution, and the average energy weight per pair. In that decomposition, the low-$\chi\to 0$01 behaviour is not controlled by angular suppression alone. In the $\chi\to 0$02 baseline, $\chi\to 0$03-tagged jets show the strongest low-$\chi\to 0$04 suppression and the broadest distribution, while the $\chi\to 0$05-tagged case is complicated by possible $\chi\to 0$06 contributions at very small angle. This suggests that dead-cone interpretations of the near-side yield must be read together with multiplicity and energy-weight effects (Shen et al., 2024).

The first system-to-system near-side modification reported experimentally is the ALICE comparison of $\chi\to 0$07–Pb to $\chi\to 0$08. Only the lowest jet-$\chi\to 0$09 range, $\chi\to 0$10–$\chi\to 0$11, shows a visible change: an approximately $\chi\to 0$12 suppression in the small-angle region and an approximately $\chi\to 0$13 enhancement in the large-angle region. The underlying cause is explicitly stated to remain undetermined. A later summary adds that current pure initial-state descriptions do not explain the small-angle effect: a CGC model fails, Angantyr reproduces the small-angle suppression qualitatively, and higher-twist final-state calculations can reproduce the trend qualitatively (Liang-Gilman, 28 Jun 2025, Nambrath, 17 Oct 2025).

A first-principles in-medium analysis pushes the discussion into the genuinely asymptotic near-side regime. In a thin medium, the small-angle jet EEC remains factorized, but for

$\chi\to 0$14

the anomalous dimensions themselves are modified,

$\chi\to 0$15

and the non-contact term contains a screened Coulomb logarithm. In that picture, medium effects do not merely broaden the distribution at fixed order; they alter the collinear RG evolution of the near-side EEC below the LPM angle (Ke et al., 12 Dec 2025).

In central Pb+Pb, an additional issue is that the experimentally reconstructed near-side EEC is biased upward by jet-induced medium response inside the jet cone. A recent heavy-ion study formulates an augmentation method that uses momentum conservation between the near side and the away side in $\chi\to 0$16-jet events to reconstruct a shower-dominated near-side EEC. In CoLBT-hydro simulations of $\chi\to 0$17–$\chi\to 0$18 Pb+Pb collisions at $\chi\to 0$19, the augmented reconstruction improves agreement with the correlator built from hadrons originating predominantly from jet-parton splittings, and comparisons under different matching conditions are proposed as tests of the scenario of jet energy loss followed by fragmentation outside the QGP (Saraswat et al., 29 Apr 2026).

6. Universality, higher-point extensions, and conceptual tensions

Near-side EECs now sit at the intersection of several lines of thought that were once treated separately. One line emphasizes universality. The TMD-based phenomenology of the free-hadron region describes both global $\chi\to 0$20 EEC and leading-jet EEC in $\chi\to 0$21 collisions with a common non-perturbative structure and only two fitted effective parameters, while also predicting a small-angle constant limit for the ratio $\chi\to 0$22,

$\chi\to 0$23

for the fitted value $\chi\to 0$24 (Liu et al., 2024).

A second line emphasizes that higher-point correlators probe different dynamics in different limits. ALICE notes that the three-point correlator $\chi\to 0$25 “probes higher order energy flow correlations,” and in its wide-angle regime the slope of the ratio $\chi\to 0$26 is expected to be proportional to $\chi\to 0$27, with sensitivity to the running of the strong coupling (Liang-Gilman, 28 Jun 2025). This does not make the three-point correlator a near-side observable in the same sense as the two-point EEC, but it situates near-side studies within a broader correlator program.

A recurring conceptual tension concerns the status of the small-angle limit itself. In the precision-QCD literature, the near-side region is the collinear singular endpoint, governed by a single-logarithmic series and requiring resummation (Neill et al., 2022). In several jet measurements, however, the experimentally accessible leftmost part of the distribution is described as a non-perturbative or free-hadron region (Liang-Gilman, 28 Jun 2025). These statements are not contradictory. They refer to different transverse scales inside the same angular endpoint. When $\chi\to 0$28 or $\chi\to 0$29 is perturbative, the near-side EEC is a collinear QCD observable. When that scale drops to a few GeV or below, the same endpoint becomes dominated by non-perturbative fragmentation and hadronization (Herrmann et al., 23 Jul 2025).

This scale-based reading clarifies several open problems. A fully unified description across the free-hadron, transition, and perturbative regions is now plausible but not yet closed. The dihadron-fragmentation framework suggests a formal bridge between EEC-DiFFs and perturbative jet functions (Kang et al., 23 Jul 2025). The NNLO+NNLL global analysis shows that a single position-space framework can describe the full near-side region in $\chi\to 0$30 (Herrmann et al., 23 Jul 2025). Experimental jet measurements, meanwhile, continue to expose flavor sensitivity, charge-dependent hadronization effects, and possible cold- and hot-nuclear-matter distortions that are not yet fully understood (Collaboration, 21 Feb 2025, Liang-Gilman, 28 Jun 2025).

The near-side EEC has therefore evolved from a limiting angular singularity into a precision multiscale observable. It is simultaneously a probe of collinear splitting, di-hadron fragmentation, hadronization, flavor dependence, and medium response. The main unresolved issue is no longer whether the near side is perturbative or non-perturbative, but how the observable interpolates between those regimes in a quantitatively controlled way across processes and environments.