Baryon-Baryon Anticorrelation in Collider Data

• The paper shows that like-sign baryon pairs exhibit a near-side dip with a 10–30% suppression, contrary to the meson–meson enhancement.
• Methodologies involve two-particle correlation functions using strict PID cuts in ALICE and STAR experiments, highlighting deficiencies in current models.
• Results indicate that standard event generators fail to reproduce the anticorrelation, suggesting the need for revised baryon production mechanisms and local conservation effects.

Near-side anticorrelation in baryon–baryon measurements refers to the pronounced suppression of like-sign baryon pairs (for example, proton–proton and Λ–Λ) detected at similar azimuthal angles and pseudorapidities in high-energy hadronic or nuclear collisions. Contrary to the expected near-side enhancement (peak) characteristic of mini-jet fragmentation observed for meson–meson correlations, baryon–baryon correlation functions exhibit a distinctive near-side dip (anticorrelation), with the conditional yield of a second baryon significantly reduced in the vicinity of an existing one. This phenomenon has been robustly established in proton–proton collisions at the LHC (ALICE) and heavy-ion collisions at RHIC (STAR), and is not reproduced by contemporary event generators, indicating a gap in the modeling of baryon production and hadronization.

1. Experimental Definition and Measurement

In collider experiments such as ALICE and STAR, the two-particle correlation function $C(\Delta\eta,\Delta\varphi)$ is constructed as the ratio:

$$C(\Delta\eta, \Delta\varphi) = \frac{S(\Delta\eta, \Delta\varphi)}{B(\Delta\eta, \Delta\varphi)}$$

where $S$ is the distribution of pair counts from the same event and $B$ is a mixed-event reference constructed to account for detector acceptance and efficiency effects, normalized so that $C=1$ in the absence of correlations. For baryon–baryon studies, particles are identified by specific ionization ($dE/dx$) in the TPC and TOF detectors for protons, and topological and invariant-mass reconstruction for strange baryons like $\Lambda$ (Janik, 2017, Janik, 2023).

Selection criteria typically require both particles within $|\eta|<0.8$ and $p_T$ in the range $0.5$–$2.5$ GeV/$c$, with strict PID cuts for purity (>99% for protons, >95% for $\Lambda$). The measurement is performed separately for like-sign (pp, $\Lambda\Lambda$) and unlike-sign pairs; the near-side ($\Delta\eta\approx0,\Delta\varphi\approx0$) structure in the correlation function is the focus.

2. Empirical Findings: Near-side Anticorrelation Phenomenon

ALICE measurements of $pp$ collisions at $\sqrt{s}=7$ TeV and $13$ TeV show that the near-side region for like-sign baryon–baryon pairs exhibits a pronounced dip in $C(\Delta\varphi)$ (integrated over $|\Delta\eta|$), with values $C(0)\approx 0.75$–$0.9$—a $10$–$30$\% suppression below unity—with significance $>5\sigma$ (Janik, 2017, Janik, 2023, Collaboration, 2016). The anticorrelation extends over $\Delta\varphi\lesssim0.6$ rad. Qualitatively similar anticorrelations are observed in $\Lambda\Lambda$ and $p\Lambda$ pairs and are absent in meson–meson ($\pi\pi$, $KK$) or baryon–antibaryon pairs, which show the canonical near-side enhancement (jet/Bose–Einstein/strangeness correlations).

In heavy-ion collisions at STAR (Au–Au, $\sqrt{s_{NN}}=200$ GeV), two-baryon femtoscopy using $C(Q_\mathrm{inv})$ as a function of relative momentum shows a depression at small $Q_\mathrm{inv}$ (down to $C\sim0.8$–$0.9$ at $Q_\mathrm{inv}\lesssim0.1$ GeV/$c$ for $\Lambda\Lambda$ and $\Xi\Xi$), confirming that the suppression is not exclusive to $pp$ collisions and persists across system size and energy (Isshiki, 2021).

3. Model Comparisons and Inadequacy of Standard Event Generators

General-purpose Monte Carlo event generators (PYTHIA6, PYTHIA8, PHOJET, HERWIG, EPOS) reproduce meson–meson peaks but fail to describe the observed baryon–baryon anticorrelation. These generators predict either a featureless $C(\Delta\varphi\approx0)\approx1$ (no correlation) or a residual near-side peak (enhancement) for like-sign baryons, in qualitative and quantitative disagreement with data (Janik, 2017, Janik, 2023, Collaboration, 2016, Demazure et al., 2022).

The standard Lund string-fragmentation mechanism imposes local baryon number conservation but allows multiple baryons to be produced in close phase-space via repeated diquark–antidiquark "popcorn" popping, which results in positive, not negative, near-side correlations. The observed anticorrelation implies a much stronger local exclusion: once a baryon is produced at a given $(\eta,\varphi)$, subsequent same-sign baryon production is significantly suppressed in the immediate vicinity.

Efforts to reconcile PYTHIA with data have used ad hoc "veto-and-retry" fragmentation policies, such as allowing at most one baryon (plus one antibaryon) per string ("one-baryon policy") or always requiring one such pair per string ("always-baryon policy"). These artificial modifications flip the near-side peak into a dip, but at the expense of distorting global baryon yields unless both constraints are combined (Demazure et al., 2022). Neither real event generators nor such hacks implement a physical quantum statistical suppression at the quark level (Pauli exclusion); the experimental trend suggests a missing ingredient related to such effects.

Model/Scenario	Near-side bb $C(0)$	Meson–meson $C(0)$	Qualitative Behavior
ALICE data	0.75–0.9 (suppression)	1.3–1.5 (enhance)	bb "dip", mm "peak"
PYTHIA/PHOJET/HERWIG/EPOS	1.0–1.1 (flat or peak)	1.2–1.4	bb "peak" (incorrect)
PYTHIA with "always-baryon" policy	0.8 (dip, matches data)	—	Recovers "dip"

4. Theoretical Interpretations and Underlying Mechanisms

Multiple hypotheses have been advanced to account for the anticorrelation:

• Local baryon number conservation beyond standard string fragmentation: The suppression magnitude and breadth suggest more stringent local baryon number compensation, possibly requiring a re-tuning of diquark–antidiquark “popcorn” production or new mechanisms that further restrict same-sign baryon production in a single string segment (Janik, 2017, Janik, 2023).
• Baryon junction dynamics: If baryon number is carried by a “string junction” (as in some QCD-inspired models), its migration in rapidity could inhibit two baryons of the same sign from being produced near each other in a single jet (Janik, 2017).
• Color-reconnection or collective effects: Modifications of string topology during fragmentation or reorganization of color flow at low $p_T$ may generate repulsive-like correlations among same-sign baryons (Janik, 2017).
• Flux-tube models: The Polyakov-loop dual description leads to alternating baryon–antibaryon (vertex–antivertex) patterns at hadronization, producing oscillatory two-point baryon-number correlations with a negative near-side component—typically a few-percent dip in $C(\Delta\varphi)$ (Patel, 2012).

No current generator has a fully satisfactory implementation reproducing both the suppression depth and its angular/rapidity scale.

5. Role of Conservation Laws and Statistical Effects

Canonical ensemble (CE) approaches demonstrate that exact baryon number conservation within a finite phase-space window creates intrinsic anticorrelation among baryons at small separation. For an event with fixed total baryon number $B$, the two-particle correlator $G_{BB}(\Delta y)$ is negative at $\Delta y=0$, reflecting that an excess at one rapidity must be balanced by a deficit elsewhere. For realistic rapidity profiles, the Cholesky-factorized covariance or Metropolis sampling reproduces the observed magnitude and width of the ALICE near-side dip when the constraint is enforced over a correlation length $\Delta y_{\mathrm{corr}}\gtrsim5$ (Braun-Munzinger et al., 2023). However, purely statistical conservation models do not account for the full dip amplitude unless “local” conservation on the scale of a string/cluster is invoked.

6. Femtoscopy, Quantum Statistics, and Dynamical Interactions

In femtoscopic analyses, anticorrelation at small relative momentum $k$ ($Q_{\mathrm{inv}}$) for baryon–baryon pairs is an established effect of Fermi–Dirac statistics for identical baryons, further modified by strong and Coulomb interactions (Liu et al., 2022, Haidenbauer et al., 2022, Isshiki, 2021). The general Koonin–Pratt formalism yields

$$C(k) = 1 + \int d^3r\, S(r)[|\psi(k,r)|^2 - |j_0(kr)|^2]$$

where $S(r)$ is the pair source probability and $\psi(k, r)$ the wavefunction including all final-state effects.

For baryons with weak or repulsive S-wave interactions (e.g., $\Xi^-\Xi^-$ or $\Sigma^+\Sigma^+$), quantum statistics and Coulomb repulsion combine to create a significant suppression $C(0)\lesssim0.7$–$0.9$. For $\Lambda\Lambda$ or $\Xi\Lambda$, the effect is weaker or even compensated by attractive strong interactions. The main finding from these studies is that the depth, width, and shape of the near-side dip in $C(k)$ serve as direct probes of the underlying scattering parameters (scattering length, effective range) as well as quantum-statistical effects (Haidenbauer et al., 2022, Liu et al., 2022).

7. Open Questions and Outlook

Despite extensive phenomenological and theoretical efforts, the origin of the near-side suppression in baryon–baryon angular correlations—particularly its scale, magnitude, and universality across baryon species—remains unresolved. Pauli suppression at the quark level, local baryon number compensation beyond present fragmentation models, and the possible role of junction or color topologies are under active investigation (Demazure et al., 2022, Janik, 2017). Forthcoming high-precision measurements of two-baryon momentum correlations (especially for multi-strange baryons) in heavy-ion and $pp$ collisions are critical for constraining effective field theories (EFT) and flux-tube models (Liu et al., 2022, Haidenbauer et al., 2022, Patel, 2012).

The near-side baryon–baryon anticorrelation is now established as a diagnostic signature for baryon production mechanisms and hadronization dynamics. Its quantitative modeling is an outstanding challenge for QCD event generators and hadronic phenomenology, with implications reaching from collider experiments to the equation of state of dense baryonic matter.