Beam Energy ScanEdit

The Beam Energy Scan (BES) is a major program at the Relativistic Heavy Ion Collider (RHIC) designed to chart the phase structure of strongly interacting matter by colliding heavy ions at a wide range of center-of-mass energies. The core aim is to explore how quark-gluon plasma (QGP) emerges from hadronic matter and to search for features in the QCD phase diagram that would signal a phase transition or a critical point. By varying the collision energy, BES probes different temperatures and baryon densities, effectively scanning the region of the phase diagram where the transition between confined hadrons and deconfined quarks and gluons is expected to change its character. The program has involved multiple detectors at RHIC, notably the STAR collaboration and the PHENIX collaboration, with later developments extending into the sPHENIX era. The BES program complements theoretical work in lattice QCD and phenomenological modeling to connect experimental signals with the properties of hot, dense QCD matter.

The BES approach centers on measuring fluctuations, correlations, and collective behavior of particles produced in heavy-ion collisions as a function of energy. Near a critical point or within a first-order transition region, correlation lengths are expected to grow and non-Gaussian fluctuations can become enhanced. Observables include higher moments of conserved-charge distributions (such as net-proton, net-electric charge, and net-strangeness), as well as anisotropic flow and particle yields. These measurements aim to infer the temperature (T) and baryochemical potential (μB) conditions at chemical freeze-out and to connect them to the hypothesized features of the QCD phase diagram. The BES program thus serves as a bridge between experimental data and the theoretical landscape of QCD matter, including connections to the physics of compact stars and the early universe.

Goals and scope

Map the QCD phase diagram in the T–μB plane by varying the collision energy in Au+Au collisions at RHIC.
Search for a QCD critical point and for a possible first-order phase transition boundary at high μB.
Extract properties of the created matter, including transport coefficients and the relative degrees of freedom, through energy-dependent observables.
Constrain theoretical models and lattice QCD predictions with experimental data, and connect findings to related areas such as neutron-star physics and heavy-ion phenomenology.

Key concepts linked to this program include the QCD phase diagram QCD phase diagram and the idea of a critical point in the transition from hadronic matter to a quark-gluon plasma critical point.

Experimental setup and methodology

The BES program is conducted at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory, a facility designed to collide heavy ions over a broad energy range. RHIC enables Au+Au collisions at center-of-mass energies per nucleon pair from roughly 7.7 GeV up to 200 GeV, accessing a wide span of μB values.
The STAR detector and the PHENIX detector have played central roles, with STAR providing broad phase-space coverage and excellent particle identification that are crucial for fluctuation analyses, and PHENIX contributing complementary measurements. In the subsequent sPHENIX era, upgraded instrumentation continued to refine precision measurements.
BES data-taking has proceeded in phases: BES-I established the basic energy scan and initial fluctuation measurements, while BES-II expanded the dataset with higher statistics, improved detector performance, and, in some runs, fixed-target configurations to extend the energy reach toward higher μB.
Measurements emphasize centrality selection and careful treatment of detector acceptance, efficiency corrections, and background contributions (from resonance decays, baryon stopping, and hadronic rescattering) that can affect fluctuation signals.

Within the theoretical framework, the observed signals are interpreted through connections to the QCD phase diagram and to models for chemical freeze-out and hadronization. The experimental program also links to the broader context of high-energy nuclear physics, including the study of QGP properties and the behavior of matter under extreme conditions Quark–gluon plasma.

Observables and data analysis

Fluctuations of conserved charges: The fluctuations in net-baryon number (often proxied by net-protons), net-electric charge, and net-strangeness are quantified through moments of the distributions, such as mean (M), variance (σ^2), skewness (S), and kurtosis (κ). Products like κσ^2 and Sσ are used to reduce sensitivity to volume fluctuations and to highlight potential critical behavior.
Energy dependence: The BES program looks for non-monotonic energy dependence of these fluctuation measures as a signature of critical phenomena or phase-change dynamics in the hot medium.
Flow and spectra observables: Anisotropic flow coefficients (for example, v2) and identified-particle spectra offer complementary information about the equation of state and the evolution of the medium, helping distinguish critical-related signals from non-critical hadronic effects.
Hadronization and freeze-out: Hadron resonance gas modeling provides a framework to relate measured particle yields and fluctuations to freeze-out conditions, offering a way to compare experimental results with theoretical expectations for the QCD phase diagram.
The data analysis recognizes the importance of controlling systematic uncertainties, such as detector acceptance, efficiency, centrality determination, and non-critical background processes, to ensure robust interpretation of potential signals.

Key terms and concepts connected to these observables include conserved-charge fluctuations, higher moments, and the idea of a critical point in the QCD phase diagram Conserved charge Higher moments (statistics) Hadron resonance gas model.

Key findings

BES-I indicated intriguing features in fluctuation observables, particularly for net-proton distributions, where certain moments and their combinations showed energy dependences that were not entirely monotonic across the scanned range. These results generated interest in the possibility of a critical region, but statistical limitations and model dependencies left room for alternative explanations.
Other observables, such as net-charge fluctuations and flow measurements, generally pointed to a complex interplay of hadronic transport, finite-size effects, and non-equilibrium dynamics that can complicate the extraction of a clean critical-point signal.
BES-II, with higher statistics and improved detectors, sought to sharpen these measurements, extend the energy reach, and reduce systematic uncertainties. The overall interpretation remains cautious: no unambiguous, model-independent discovery of a QCD critical point has been reported, but the data provide important constraints on where such a point could lie in the phase diagram.
The results are often compared with lattice QCD expectations (where feasible) and with phenomenological models that incorporate critical fluctuations, hydrodynamic evolution, and hadronic afterburners to reproduce measured observables.

These findings are part of an ongoing effort to connect experimental signals with the underlying phase structure of QCD, while recognizing the challenges posed by finite-size systems, non-equilibrium dynamics, and the need for complementary data from other facilities and energy regimes QCD phase diagram quark–gluon plasma.

Theoretical context and interpretation

Lattice QCD provides robust results for zero or small μB, indicating a crossover transition near the critical temperature at low baryon density. Extending these results to the higher μB region accessed by BES is technically challenging due to the sign problem, which motivates reliance on effective theories and phenomenological models for interpretation.
The QCD phase diagram is expected to feature a crossover at small μB and a possible first-order transition at larger μB, with a critical point marking the boundary between these regimes. The precise location and even its existence are topics of active debate, with experimental BES results contributing essential constraints.
The experimental signatures being pursued—non-Gaussian fluctuations, non-monotonic behavior with energy, and correlated flow patterns—are interpreted within frameworks that combine critical phenomena, non-equilibrium dynamics, and hadronic transport. Disentangling true critical signals from backgrounds remains a central theoretical challenge.
The BES program intersects with broader physics goals, including the understanding of dense QCD matter relevant to neutron stars and other astrophysical environments, where the equation of state under high baryon density plays a crucial role Neutron star.

Controversies and debates

Existence and location of a QCD critical point: While BES searches for a critical point, there is no consensus on whether such a point exists in the accessible region of the phase diagram, or precisely where it would lie if it does.
Interpretation of fluctuation signals: Non-monotonic fluctuations could arise from critical dynamics, but they can also emerge from non-critical processes such as baryon transport, resonance decays, hadronic rescattering, and finite-size effects. Establishing a robust, model-independent interpretation remains debated.
Role of theoretical limitations: Lattice QCD faces challenges at finite μB, which affects the ability to make definitive predictions that experiments can confirm. This has led to reliance on indirect methods and model-assisted interpretations, which some critics argue reduce the conclusiveness of claims.
Complementarity of energy regimes: Some researchers emphasize the importance of combining BES results with higher-energy data (e.g., from LHC heavy-ion programs) and with low-energy programs at other facilities to obtain a fuller picture of the QCD phase diagram, while others caution against overinterpreting localized signals without a coherent global framework.

These debates reflect the healthy scientific tension around probing the fundamental phases of strongly interacting matter, rather than a settled consensus, and they guide ongoing improvements in both experimental technique and theoretical modeling.

History and timeline

Concept and planning: The idea of scanning a range of collision energies to explore the QCD phase structure emerged in the 2000s as a way to extend the phenomenology of heavy-ion collisions beyond the highest-energy regime.
BES-I data-taking: Conducted in the early 2010s, establishing the basic energy scan and enabling initial comparisons between measurements and theoretical expectations.
BES-II enhancements: In the mid-to-late 2010s and early 2020s, BES-II incorporated higher-statistics datasets, detector upgrades, and additional running modes (including extended energy reach and fixed-target configurations) to improve sensitivity to critical fluctuations and phase-change signals.
Ongoing analysis and synthesis: Researchers continue to analyze BES-II data, integrate results with lattice QCD progress and transport-model studies, and plan future measurements to refine the map of the QCD phase diagram and to tighten constraints on possible critical phenomena.