Bose-Einstein Correlations Research Articles

Femtoscopy in [formula omitted] p+Pb collisions with ATLAS

Bose-Einstein correlations between identified charged pions are measured for p+Pb collisions at sNN=5.02 TeV with the ATLAS detector using a total integrated luminosity of 28 nb−1. Pions are identified using ionisation energy loss measured in the pixel silicon detector. Two-particle correlation functions and the extracted source radii are presented as a function of collision centrality as well as average transverse pair momentum (kT), rapidity (yππ⋆), and azimuthal angle with respect to the second-order event plane. Pairs are selected with a rapidity −2<yππ⋆<1 and with an average transverse momentum 0.1<kT<0.8 GeV. The effect on the two-particle correlation function from jet fragmentation is studied, and a new method for constraining its contributions to the measured correlations is described. The measured source sizes are substantially larger in more central collisions and are observed to decrease with increasing pair kT. A correlation with the local single-particle multiplicity dNch/dy⋆ is demonstrated. The cross term Rol, which couples radial and longitudinal expansion, is measured as a function of rapidity, and a departure from zero is observed with 5.1σ combined significance for yππ⋆>−1 in the most central events. The azimuthal modulation of the radii in central events is observed to be consistent with that predicted by hydrodynamics and observed in A+A collisions.

A CGC/saturation approach for angular correlations in proton\u2013proton scattering

We generalized our model for the description of hard processes, and calculate the value of the azimuthal angular correlations (Fourier harmonics v_n), for proton–proton scattering. The energy and multiplicity independence, as well as the value of v_n, turns out to be in accord with the experimental data, or slightly larger. Therefore, before making extreme assumptions on proton–proton collisions, such as the production of a quark–gluon plasma in large multiplicity events, we need to understand how these affect the Bose–Einstein correlations, which have to be taken into account since the Bose–Einstein correlations are able to describe the angular correlations in proton–proton collisions, without including final state interactions.

Study of event mixing for Bose–Einstein correlations in reactions with ππ X final states around 1 GeV

We present a new event mixing cut condition, named energy sum (ES) cut, aiming to investigate two-pion Bose–Einstein correlations (BEC) in reaction with only two identical pions among three final state particles. Unlike the previous proposed pion energy cut, which rejects original events with either pion’s energy beyond a given level, this cut does not eliminate any original events and hence improves the statistics of both original events and mixed events. It selects mixed events in terms of a weight proportional to the two-pion energy sum distribution of original events. Numerical tests using the [Formula: see text] events are carried out to verify the validity of the energy sum cut. Simulation results show this cut is able to reproduce the relative momentum distribution of the original events in the absence of BEC effects. Its ability to observe BEC effects and to extract correct BEC parameters is verified using event sample in the presence of BEC effects. It is found that the BEC effects can be obviously observed as an enhancement in the correlation function and the BEC parameters extracted by this event mixing cut are in good agreement with input values.

A study of event mixing for two-pion Bose-Einstein correlations in the γP → π0π0p reaction

A study of event mixing for two-pion Bose-Einstein correlations in the γP → π0π0p reaction

Using the Tsallis distribution for hadron spectra in pp collisions: Pions and quarkonia at s=5−13000 GeV

A thermal model, based on the Tsallis distribution and blast-wave model, is proposed to compute hadron double-differential spectra $d^{2}N/dp_{T}dy$ in $pp$ (also high energy $p\overline{p}$) collisions. It successfully describes the available experimental data on pion and quarkonia ($\phi$, $J/\psi$, $\psi(2S)$, $\Upsilon$ family) production at energies from $\sqrt{s} = 5$ GeV to the LHC ones. Simple parametrizations for the $\sqrt{s}$ dependence of the model parameters are provided allowing predictions for the yields of these particles at new collision energies. The model can be used also for the pion Bose-Einstein correlation studies.

Femtoscopy in = 5.02 TeV p-Pb collisions with ATLAS

Bose-Einstein correlations between identified charged pions are measured for p+Pb collisions at = 5.02 TeV with the ATLAS detector using a total integrated luminosity of 28 nb−1. Pions are identified using ionisation energy loss measured in the pixel detector. Two-particle correlation functions and the extracted source radii are presented as a function of average transverse pair momentum (kT) and rapidity () as well as collision centrality. Pairs are selected with a rapidity −2 < < 1 and with an average transverse momentum 0.1 < kT < 0.8 GeV. The effect on the two-particle correlation function from jet fragmentation is studied, and a new method for constraining its contributions to the measured correlations is described. The measured source sizes are substantially larger in more central collisions and are observed to decrease with increasing pair kT. A correlation with the local single-particle multiplicity dNch/dy* is demonstrated. The scaling of the extracted radii with the mean number of participants is also used to compare a selection of initial-geometry models. The cross term Rol, which couples radial and longitudinal expansion, is measured as a function of rapidity, and a departure from zero is observed with 4.8 σ combined significance for > −1 in the most central events.

A study of event mixing for two-pion Bose–Einstein correlations in the γp→π0π0p reaction

We develop an event mixing technique with a missing mass consistency (MMC) cut and a pion energy (PE) cut for the measurement of two-pion Bose-Einstein correlations (BEC) in reactions with only two identical pions produced in the final state. A multi mixing mode that allows one event to be mixed with multiple other events is proposed for the purpose of improving the statistics of mixed samples, and compared with the single mixing mode which requires one original event can be mixed only once. Numerical tests using the {\gamma}p -> {\pi}^0 {\pi}^0 p events are used to testify its ability to measure two-pion correlations. To improve the mixing speed, the optimal MMC cut window is also explored via simulations.

Bose-Einstein correlations andv2nandv2n−1in hadron and nucleus collisions

We show that Bose-Einstein correlations of identical particles in hadron and nucleus high energy collisions, lead to long range rapidity correlations in the azimuthal angle. These correlations are inherent features of the CGC/saturation approach, however, their origin is more general than this approach. In framework of the proposed technique both even and odd $v_n$ occur naturally, independent of the type of target and projectile. We are of the opinion that it is premature to conclude that the appearance of azimuthal correlations are due to the hydrodynamical behaviour of the quark-gluon plasma.

Perturbative QCD and beyond: Azimuthal angle correlations in deuteron-deuteron scattering from Bose-Einstein correlations

In this paper, we found within the framework of perturbative QCD, that in deuteron-deuteron scattering the Bose-Einstein correlations due to two parton showers production, induce azimuthal angle correlations, with three correlation lengths: the size of the deuteron ($R_D$), the proton radius ($R_N$), and the size of the BFKL Pomeron which, is closely related to the saturation momentum ($R_c \sim 1/Q_s$). These correlations are independent of the values of rapidities of the produced gluons (long range rapidity correlations), for large rapidities ($\bas |y_1 - y_2| \geq 1$), and have no symmetry with respect to $\phi \to \pi - \phi$ ($ \vec{p}_{T1} \to - \vec{p}_{T1}$). Therefore, they give rise to $v_n$ for all values of $n$, not only even values. The contributions with the correlation length $R_D$ and $R_N$ crucially depend on the non-perturbative contributions, and to obtain estimates of their values, requiries a lot of modeling, while the correlations with $R_c \sim 1/Q_s$ have a perturbative QCD origin, and can be estimated in the ColorGlass Condensate (CGC) approach.

Glauber theory and the quantum coherence of curvature inhomogeneities

The curvature inhomogeneities are systematically scrutinized in the framework of the Glauber approach. The amplified quantum fluctuations of the scalar and tensor modes of the geometry are shown to be first-order coherent while the interference of the corresponding intensities is larger than in the case of Bose–Einstein correlations. After showing that the degree of second-order coherence does not suffice to characterize unambiguously the curvature inhomogeneities, we argue that direct analyses of the degrees of third- and fourth-order coherence are necessary to discriminate between different correlated states and to infer more reliably the statistical properties of the large-scale fluctuations. We speculate that the moments of the multiplicity distributions of the relic phonons might be observationally accessible thanks to new generations of instruments able to count the single photons of the Cosmic Microwave Background in the THz region.

Event mixing constraints for Bose-Einstein correlations in reactions with three particles in the final state

Bose-Einstein correlations (BEC) are widely used to gain an insight into the spatiotemporal characteristics of boson emitters. It was used for the first time in the 1950s by R. Hanbury-Brown and R. Q. Twiss[Hanbury-Brown R, Twiss R Q 1954 Phil. Mag. 45 663] in astronomy to measure the dimension of distant astronomical objects emitting photons, and hence is also known as Hanbury-Brown-Twiss effect (HBT). In nuclear and particle physics field, BEC also has important applications in the investigation of the space-time properties of subatomic reaction region, especially in elementary-particle collisions and relativistic heavy-ion collisions with large multiplicity at high energies. Its potential application in exclusive reactions with low multiplicity in the non-perturbative QCD energy region may offer complementary information like duration and size of nucleon resonances, which are generally excited by hadronic or electromagnetic probes and usually decay into the ground states accompanied by emission of identical mesons. However, the event mixing technique, which is highly adopted for BEC observations in inclusive reactions at high energies with large multiplicity cannot be directly applied to the BEC measurement in exclusive reactions with very limited multiplicity at low energies. The event mixing method produces un-correlated samples from original sample through making mixed events by randomly selecting the momenta of two bosons from different original events. It works well for the high multiplicity case because the degree of freedom of final state particles is large compared with that of the low multiplicity case. In exclusive reactions with a very limited number of identical bosons in the final state, this method is however strongly interfered by non-BEC factors such as global conservation laws and decays of resonances. Appropriate constraints are required to control the event mixing process in order to eliminate the influence of those non-BEC factors. In this study, we are trying to develop an event mixing method for BEC measurement in reactions having only three final state particles and only two identical bosons among them. For this end, five constraint modes for the event mixing are proposed and investigated via Monte Carlo simulation. Each mode employs one or a combination of the following cut conditions:1) missing mass cut (MM) that requires the missing mass of the mixed event to be equal to that of the original event; 2) polar angle consistency cut (PAC) that requires that the swapping particles should come from the same polar angle bin; 3) azimuthal angle consistency cut (AAC); 4) momentum consistency cut (MC); 5) energy upper limit cut (EU) that requires that any boson energy should not exceed a given upper limit. The double neutral pion photoproduction on the proton around 1 GeV is taken for example to demonstrate the effects of these constraints on the event mixing. In the simulation, one event sample free of BEC effects and four samples in the presence of BEC effects are generated for testing the ability for these constraints to extract BEC parameters. It is found the constraint mode using the MM and PAC cuts, and the mode employing the MM and AAC cuts, and the mode adopting the MM and the EU cuts can be used to observe BEC effects and extract BEC parameters. Among them, optimum results can be achieved by the combination of the MM and EU cuts.

Lévy Distributions for One-Dimensional Analysis of the Bose–Einstein Correlations

A general study of relations between the parameters of two centrally symmetric Lévy distributions, often used for one-dimensional investigation of Bose–Einstein correlations, is given for the first time. These relations of the strength of correlations and of the radius of the emission region take into account possible various finite ranges of the Lorentz invariant four-momentum difference for two centrally symmetric Lévy distributions. In particular, special cases of the relations are investigated for Cauchy and normal (Gaussian) distributions. The mathematical formalism is verified using the recent measurements given that a generalized centrally symmetric Lévy distribution is used. The reasonable agreement is observed between estimations and experimental results for all available types of strong interaction processes and collision energies.

Femtoscopy in √SNN= 5.02 TeVp-Pb collisions withATLAS

Bose-Einstein correlations between identified charged pions are measured for p +Pb collisions at √S NN = 5.02 TeV with the ATLAS detector using a total integrated luminosity of 28 nb−1 . Pions are identified using ionisation energy loss measured in the pixel detector. Two-particle correlation functions and the extracted source radii are presented as a function of average transverse pair momentum (k T ) and rapidity (y ππ *) as well as collision centrality. Pairs are selected with a rapidity −2 ππ * T T . A correlation with the local single-particle multiplicity dN ch /dy * is demonstrated. The scaling of the extracted radii with the mean number of participants is also used to compare a selection of initial-geometry models. The cross term R o1 , which couples radial and longitudinal expansion, is measured as a function of rapidity, and a departure from zero is observed with 4.8 σ combined significance for y ππ * > −1 in the most central events.

Detrended analysis of shower track distribution in nucleus-nucleus interactions at CERN SPS energy

We have studied the charged particle density fluctuations in 16O+Ag(Br) and 32S+Ag(Br) interactions at 200A GeV incident energy in the laboratory frame by using the detrended methods. These methods can extract (multi)fractal properties of the underlying distributions after filtering out the average trend of fluctuations associated. Multifractal parameters obtained from data analysis are systematically compared with event samples generated by the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model, where Bose–Einstein correlation (BEC) effect is mimicked via a charge reassignment algorithm implemented as an after burner. Both the experimental and the simulated data are subjected to two different statistical techniques namely the multifractal detrended fluctuation analysis (MFDFA) and multifractal detrended moving average (MFDMA) analysis. The results indicate that for both the interactions considered the pseudorapidity distributions of the shower tracks are multifractal in nature. Qualitatively, both methods of analysis and both interactions considered, result in similar behavior of multifractal parameters. We do however notice significant quantitative differences in certain cases.

An event mixing technique for Bose-Einstein correlations of two pions in photoproduction around 1 GeV**Supported by Ministry of Education and Science of Japan (19002003) and JSPS KAKENHI (24244022, 26400287)

We have developed an event mixing technique to observe Bose-Einstein correlations (BEC) between two identical neutral pions produced in photo-induced reactions in the non-perturbative QCD energy region. It is found that the missing-mass consistency cut and the pion-energy cut are essential for the event mixing method to effectively extract BEC observables. A Monte Carlo (MC) simulation is used to validate these constraints and confirms the efficiency of this method. Our work paves the way for similar BEC studies at lower energies where the multiplicity of emitted bosons is limited.

CGC/saturation approach for high energy soft interactions: ‘soft’ Pomeron structure and $$v_{n}$$ v n in hadron and nucleus collisions from Bose–Einstein correlations

In the framework of our model of soft interactions at high energy based on CGC/saturation approach,we show that Bose-Einstein correlations of identical gluons lead to large values of $v_n$. We demonstrate how three dimensional scales of high energy interactions: hadron radius, typical size of the wave function in diffractive production of small masses (size of the constituent quark), and the saturation momentum, influence the values of BE correlations, and in particular, the values of $v_n$. Our calculation shows that the structure of the `dressed' Pomeron leads to values of $v_n$ which are close to experimental values for proton-proton scattering, 20\% smaller than the observed values for proton-lead collisions, and close to lead-lead collisions for 0-10\% centrality. Bearing this result in mind, we conclude that it is premature to consider, that the appearance of long range rapidity azimuthal correlations are due only to the hydrodynamical behaviour of the quark-gluon plasma.

An analytic hydrodynamical model of rotating 3D expansion in heavy-ion collisions

A new exact and analytic solution of non-relativistic fireball hydrodynamics is presented. It describes an expanding three-axis ellipsoid that rotates along one of its principal axes. The observables are calculated using simple analytic formulas. Following earlier works, it is pointed out that azimuthal oscillation of the off-diagonal Bertsch-Pratt radii of Bose-Einstein correlations as well as rapidity dependent directed and third flow measurements provide means to determine the magnitude of the rotation of the fireball. It is argued that observing this rotation and its dependence on collision energy may lead to new information on the equation of state of the strongly interacting quark gluon plasma produced in high energy heavy ion collisions.

PHENIX results on fluctuations and Bose–Einstein correlations in Au + Au collisions from the RHIC Beam Energy Scan

The RHIC Beam Energy Scan focuses on mapping the QCD phase diagram and pinpointing the location of a possible critical end point. Bose-Einstein correlations and event-by-event fluctuations of conserved quantities, measured as a function of centrality and collision energy, are promising tools in these studies. Recent lattice QCD and statistical thermal model calculations predict that higher-order cumulants of the fluctuations are sensitive indicators of the phase transition. Products of these cumulants can be used to extract the freeze-out parameters [A. Bazavov et al., Phys. Rev. Lett. 109, 192302 (2012)] and to locate the critical point [M. A. Stephanov, K. Rajagopal and E. V. Shuryak, Phys. Rev. D 60, 114028 (1999)]. Two-pion interferometry measurements are predicted to be sensitive to potential softening of the equation of state and prolonged emission duration close to the critical point [S. Pratt, Phys. Rev. Lett. 53, 1219 (1984)]. We present recent PHENIX results on fluctuations of net-charge using high-order cumulants and their products in Au+Au collisions at sNN=7.7–200 GeV, and measurement of two-pion correlation functions and emission-source radii in Cu+Cu and Au+Au collisions at several beam energies. The extracted source radii are compared to previous measurements at RHIC and LHC in order to study energy dependence of the specific quantities sensitive to expansion velocity and emission duration. Implications for the search of a critical point and baryon chemical potentials at various collision energies are discussed.

Recent highlights from the ATLAS heavy-ion program

These proceedings report on recent measurements performed with the ATLAS Detector at the LHC presented at the Quark Matter 2015 Conference. These include measurements of two-particle correlations in pp collisions at s=2.76 and 13 TeV. These results are the first to show a second harmonic modulation in the azimuthal dependence of the particle yields in pp collisions, a signature closely associated with collective flow in ion-ion collisions. Measurements of p+Pb collisions at sNN=5.02 TeV are presented including charged particle multiplicities, Bose-Einstein correlations and yields of jets and electroweak bosons that provide insight into the initial stages of these collisions including the nuclear geometry. Finally, measurements of dijet asymmetry and jet structure in Pb+Pb and pp collisions at sNN=2.76 TeV are presented that further illuminate the phenomenon of partonic energy loss.

Multipion correlations induced by isospin conservation of coherent emission

Recent measurements have revealed a significant suppression of multipion Bose-Einstein correlations in heavy-ion collisions at the LHC. The suppression may be explained by postulating coherent pion emission. Typically, the suppression of Bose-Einstein correlations due to coherence is taken into account with the coherent state formalism in quantum optics. However, since charged pion correlations are most often measured, the additional constraint of isospin conservation, which is absent in quantum optics, needs to be taken into account. As a consequence, correlations emerge between pions of opposite charge. A calculation of the correlations induced by isospin conservation of coherent emission is made for two, three- and four-pion correlation functions and compared to the data from the LHC.