Bose-Einstein Correlations Research Articles

Effect of an Expanding Charged Cloud on two-particle Bose-Einstein Correlations

Effect of an Expanding Charged Cloud on two-particle Bose-Einstein Correlations

Principles and prospects of Bose-Einstein correlation study at BESIII* *This study was supported by the National Key R&D Program of China (2020YFA0406403) and the National Natural Science Foundation of China (11275211, 11335008, 12035013)

One method for determining the characteristic parameters of a hadron production source is to measure the Bose-Einstein correlation functions. In this study, we present fundamental concepts and formulas related to the Bose-Einstein correlations, focusing on the measurement principles and the Lund model from an experimental perspective. We perform Monte Carlo simulations using the Lund model generator in the 2–3 GeV energy range. Through these feasibility studies, we identify key features of the Bose-Einstein correlations that offer valuable insights for experimental measurements. Utilizing data samples collected at BESIII, we perform measurements of the Bose-Einstein correlation functions, with an expected experimental precision of a few percent for the hadron source radius and incoherence parameter.

The maximal frequency of cosmic gravitons

We show that the maximal frequency of cosmic gravitons must not exceed the THz domain. From a classical viewpoint, both in conventional inflationary scenarios and in bouncing models the largest frequency of the spectrum overshoots the MHz band even if its specific signature is model dependent. According to a quantum mechanical perspective the maximal frequency is instead associated with the range of energies where a single pair of gravitons with opposite (comoving) three-momenta is produced. The upper limit on the largest frequency determines the minimal chirp amplitude [typically O(10−32)] required for a direct detection of a cosmic signal in the THz band. Below this limiting frequency the minimal chirp amplitude can be enhanced so that the optimal range ultimately depends on the physical properties of the diffuse backgrounds. In case a hypothetical instrument (at present just a figment of a hopeful imagination) would reach chirp amplitudes down to O(10−30) in the MHz or GHz bands, the Bose-Einstein correlations could be used to probe the properties of cosmic gravitons and their super-Poissonian statistics.

Two-Pion Bose–Einstein Correlations in Au+Au Collisions at sNN = 3 GeV in the STAR Experiment

The correlation femtoscopy technique makes it possible to estimate the geometric dimensions and lifetime of the particle emission region after the collision of ions. Measurements of the emission region characteristics not only at midrapidity but also at backward (forward) rapidity can provide new information about the source and make it possible to impose constraints on the heavy-ion collision models. This work is devoted to revealing the dependence of the spatial and temporal parameters of the emission region of identical pions in Au+Au collisions at sNN = 3 GeV from the fixed-target program of the STAR experiment. The extracted femtoscopic radii, Rout, Rside, Rlong, Rout−long2, and the correlation strength, λ, are presented as a function of collision centrality, pair rapidity, and transverse momentum. Physics implications will be discussed.

Bulk flow and correlation measurements at LHCb

Particle correlations are a powerful tool to study the properties of the bulk nuclear matter produced in relativistic heavy ion collisions. The momentum correlations between identical particles originating from the same particleemitting source, referred to as the Bose-Einstein correlations, measure scales that are related to the geometrical size of the source. The two-particle azimuthal angular correlations measure the spatial anisotropy of produced particles, providing information on collective phenomena arising in the dense nuclear medium. This contribution will discuss new LHCb measurements of Bose- Einstein correlations and, for the first time, the collective flow coefficients in the far forward rapidity region.

A novel method for calculating Bose–Einstein correlation functions with Coulomb final-state interaction

Measurements of Bose–Einstein correlations played a crucial role in the discovery and the subsequent detailed exploration of the Quark-Gluon-Plasma (QGP) created in high-energy collisions of heavy nuclei. Such measurements gave rise to femtoscopy, a flourishing sub-field of high-energy physics, and there are important new directions to explore and discoveries to be made in the near future. One of these important current topics is the precise investigation of the shape of the correlation functions utilizing Lévy-stable sources. In this paper, we utilize Lebesgue’s dominated convergence theorem and Fubini’s theorem to present a novel method of calculating the shape of the two-particle correlation functions, including the Coulomb final-state interaction. This method relies on an exact calculation of a large part of the necessary integrals of the Coulomb wave function and can be utilized to calculate the correlation function for any source function with an easily accessible Fourier transform. In this way, it is eminently applicable to Lévy-stable source functions. In this particular case, we find that the new method is more robust and allows the investigation of a wider parameter range than the previously utilized techniques. We present an easily applicable software package that is ready to use in experimental studies.

Bose–Einstein Correlations of Charged Pions in Au $${+}$$ Au Collisions at $$\sqrt{{s_{NN}}}{=3}$$ GeV from UrQMD

Bose–Einstein Correlations of Charged Pions in Au $${+}$$ Au Collisions at $$\sqrt{{s_{NN}}}{=3}$$ GeV from UrQMD

Study of the Bose-Einstein correlations of same-sign pions in proton-lead collisions

Correlations of same-sign charged pions are analysed using proton-lead collision data collected by the LHCb experiment at a nucleon-nucleon centre-of-mass energy of 5.02 TeV, corresponding to an integrated luminosity of 1.06 nb−1. Bose-Einstein correlations are observed in the form of an enhancement of pair production for same-sign charged pions with a small four-momentum difference. The dependence of the correlation radius and the intercept parameter on the reconstructed charged-particle multiplicity is investigated. The measured correlation radii scale linearly with the cube root of the reconstructed charged-particle multiplicity, being compatible with predictions of hydrodynamic models on the collision system evolution.

Coulomb Corrections for Bose–Einstein Correlations from One- and Three-Dimensional Lévy-Type Source Functions

In the study of femtoscopic correlations in high-energy physics, besides Bose–Einstein correlations, one has to take final-state interactions into account. Amongst them, Coulomb interactions play a prominent role in the case of charged particles. Recent measurements have shown that in heavy-ion collisions, Bose–Einstein correlations can be best described by Lévy-type sources instead of the more common Gaussian assumption. Furthermore, three-dimensional measurements have indicated that, depending on the choice of frame, a deviation from spherical symmetry observed under the assumption of Gaussian source functions persists in the case of Lévy-type sources. To clarify such three-dimensional Lévy-type correlation measurements, it is thus important to study the effect of Coulomb interactions in the case of non-spherical Lévy sources. We calculated the Coulomb correction factor numerically in the case of such a source function for assorted kinematic domains and parameter values using the Metropolis–Hastings algorithm and compared our results with previous methods to treat Coulomb interactions in the presence of Lévy sources.

Particle interferometry in a moat regime

Dense strongly interacting matter can exhibit regimes with spatial modulations, akin to crystalline phases. In this case particles can have a moat spectrum with minimal energy at nonzero momentum. We show that particle interferometry is a sensitive probe of such a regime in heavy-ion collisions. To this end, we develop a field-theoretical formalism that relates particle spectra to in-medium real-time correlation functions of quantum fields on curved hypersurfaces of spacetime. This is then applied to the study of Bose-Einstein correlations in a moat regime in heavy-ion collisions. The resulting two-particle spectra exhibit peaks at nonzero average pair momentum, in contrast to the two-particle spectra in a normal phase, which peak at zero momentum. These peaks lead to nontrivial structures in the ratio of two-particle correlation functions, which should be experimentally measurable if the resolution in the direction of average pair momentum is sufficiently large. We propose these structures in the correlation-function ratios as clear signature of a moat regime and spatially modulated phases in quantum chromodynamics (QCD).

Centrality Dependent Lévy Analysis of two-pion BEC Functions at PHENIX

We present most recent PHENIX preliminary data on centrality dependence of two-pion Bose-Einstein correlation functions measured in √SNN = 200 GeV Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC). The data are well described by assuming the source to be a Lévy-stable distribution. The Lévy parameters, R, α, λ are measured in 18 bins of transverse mass (mT) for 4 centrality intervals. The Lévy scale parameter R(mT) decreases with mT and exhibits a clear centrality ordering which supports its geometrical interpretation. The Lévy exponent α(mT) is independent of mT in every centrality bin but shows some centrality dependence. At all centralities α is significantly different from that of a Gaussian (α = 2) or Cauchy (α = 1) source distribution. The Lévy strength parameter λ was also investigated. We observed that λ(mT) decreases at low mT and saturates around mT = 0.6 GeV/c2. In the already published 0-30% centrality class, Monte Carlo simulations are found to be inconsistent with the measurements, unless a significant reduction of the in-medium mass of the η′ meson is included.

Measurements of collectivity in the forward region at LHCb

Due to its unique pseudorapidity coverage (2 < 77 < 5) and excellent performance at low pT, the LHCb detector provides measurements of two-particle correlation in a complementary region to other LHC experiments. Ongoing studies in flow at different collision systems and energies, pPb collisions at √SNN = 8 TeV, PbPb collisions at √SNN = 5 TeV, and Bose-Einstein correlations of identical pions for pPb collisions at √SNN = 5 TeV, are summarised.

Results on Bose–Einstein Correlations of Charged Hadrons in pp Collisions at 13 TeV in CMS

Results on Bose–Einstein Correlations of Charged Hadrons in pp Collisions at 13 TeV in CMS

Analysis of OPAL Bose–Einstein correlation at Z0-pole by the second conventional formula

In this paper, we can obtain a second conventional formula ([Formula: see text]) with two components by extending the conventional formula [Formula: see text] with one component for Bose–Einstein Correlation (BEC). We used [Formula: see text] to analyze the BEC at [Formula: see text]-pole as part of the OPAL collaboration. [Formula: see text] fm ([Formula: see text]) and [Formula: see text][Formula: see text]fm ([Formula: see text]) are the estimated interaction region, where [Formula: see text] and [Formula: see text] are the degrees of coherence, and G is the Gaussian distribution, respectively. Long-range correlation (LRC) is also studied.

Two-particle Bose–Einstein correlations in { pp } collisions at mathbf {sqrt{s} = 13} TeV measured with the ATLAS detector at the LHC

This paper presents studies of Bose–Einstein correlations (BEC) in proton–proton collisions at a centre-of-mass energy of 13 TeV, using data from the ATLAS detector at the CERN Large Hadron Collider. Data were collected in a special low-luminosity configuration with a minimum-bias trigger and a high-multiplicity track trigger, accumulating integrated luminosities of 151 upmu b^{-1} and 8.4 nb^{-1}, respectively. The BEC are measured for pairs of like-sign charged particles, each with |eta | < 2.5, for two kinematic ranges: the first with particle p_{mathrm {T}} > 100 MeV and the second with particle p_{mathrm {T}} > 500 MeV. The BEC parameters, characterizing the source radius and particle correlation strength, are investigated as functions of charged-particle multiplicity (up to 300) and average transverse momentum of the pair (up to 1.5 GeV). The double-differential dependence on charged-particle multiplicity and average transverse momentum of the pair is also studied. The BEC radius is found to be independent of the charged-particle multiplicity for high charged-particle multiplicity (above 100), confirming a previous observation at lower energy. This saturation occurs independent of the transverse momentum of the pair.

QUANTUM STATISTICAL PERSPECTIVE TO EXAMINE THE SOURCE CHAOS FRACTION THROUGH BOSON FEMTOSCOPY

Bose–Einstein correlations of identical particles reveal the shape and size of the particle emitting source of the given boson. These correlations are pivotal for a better understanding of the source dynamics and developing techniques to examine the propagation of quantum chaos in the presence of coherence at a certain temperature and momentum. Femtoscopy is of the utmost importance during this transformation for data processing and coherence-chaos analysis discrepancies. We introduced an evolving source to describe chaotic information inside quantum entanglement and the impact of the coherence order is discussed in this research. We also investigate the role of source size parameter and particle number in the dynamics of the temperature profiles with the function of momentum variation. The influences of the modeling factors on the correlations with their normalized correlator in the perspective of source coherence have been evaluated and the orientation of the source has an effect on the diffusivity of the fluid under consideration. Such consequences can cause an increase or decrease the genuine correlations due to the distributions of velocity and temperature. The main findings of the paper have been illustrated using the graphical representations of the considered correlations according to the geometry of the expanding source. Such results reveal the lucrativeness in the field of engineering applications.

Probing Gluon Bose Correlations in Deep Inelastic Scattering.

We study correlations originating from the quantum nature of gluons in a hadronic wave function. Bose-Einstein correlation between identical particles lead to the enhancement in the number of pairs of gluons with the same quantum numbers and small relative momentum. We show that these preexisting correlations can be probed in deep inelastic scattering experiments at high energy. Specifically, we consider diffractive dijet plus a third jet production. The azimuthal dependence displays a peak at the zero relative angle between the transverse momentum imbalance of the photon-going dijet and the transverse momentum of the hadron-going jet. Our calculations explicitly show that the peak originates from Bose enhancement. Comparing electron-proton to electron-nucleus collisions, we demonstrate that the nuclear target enhances the relative strength of the peak. With the future high luminosity electron-ion collider the proposed measurements of gluon Bose enhancement become experimentally feasible.

Bose-Einstein momentum correlations at fixed multiplicities: Lessons from an exactly solvable thermal model for pp collisions at the LHC

Two-particle momentum correlations of $N$ identical bosons are studied in the quantum canonical ensemble. We define the latter as a properly selected subensemble of events associated with the grand canonical ensemble which is characterized by a constant temperature and a harmonic-trap chemical potential. The merits of this toy model are that it can be solved exactly, and that it demonstrates some interesting features revealed recently in small systems created in $p+p$ collisions at the LHC. We find that partial coherence can be observed in particle emission from completely thermal ensembles of events if instead of inclusive measurements one studies the two-boson distribution functions related to the events with particle numbers selected in some fixed multiplicity bins. The corresponding coherence effects increase with the multiplicity.

Probing granular inhomogeneity of a particle-emitting source by imaging two-pion Bose–Einstein correlations

Using the source imaging technique in two-pion interferometry, we study the image of the hydrodynamic particle-emitting source with the HIJING initial conditions for relativistic heavy-ion collisions on an event-by-event basis. It is shown that the initial-state fluctuations may give rise to bumpy structures of the medium during hydrodynamical evolution, which affects the two-pion emission space and leads to a visible two-tiered shape in the source function imaged using the two-pion Bose–Einstein correlations. This two-tiered shape can be understood within a similar but more analytic granular source model and is found to be closely related to the introduced quantity $$\xi$$ , which characterizes the granular inhomogeneity of the source. By fitting the imaged source function with a granular source parametrization, we extract the granular inhomogeneity of the hydrodynamic source, which is found to be sensitive to both the Gaussian smearing width of the HIJING initial condition and the centrality of the collisions.

Analyses of multi-pion Bose-Einstein correlations for granular sources with coherent pion-emission droplets * *Supported by the National Natural Science Foundation of China (11675034, 11275037)

The ALICE Collaboration measured three- and four-pion Bose-Einstein correlations (BECs) for Pb-Pb collisions at the Large Hadron Collider (LHC). It is speculated that the observed significant suppression of multi-pion BECs is owing to a considerable degree of coherent pion emission in these collisions. Here, we study multi-pion BEC functions for granular sources with coherent pion-emission droplets. We find that the intercepts of the multi-pion correlation functions at the relative momenta near zero are sensitive to the number of droplets in the granular source. They decrease with the droplet number. The three-pion correlation functions for evolving granular sources with momentum-dependent partially coherent pion-emission droplets basically agree with the experimental data for Pb-Pb collisions at TeV at the LHC. However, the model results for the four-pion correlation function are inconsistent with the experimental data. Investigations into normalized multi-pion correlation functions of granular sources suggest an interesting enhancement of the normalized four-pion correlation function in the moderate relative-momentum region.