Two-pion Bose-Einstein Correlations Research Articles

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.

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.

Measuring Intensity Interference in a Low Multiplicity System \(\pi \pi X\) with a New Observing Method

Prior proposed observing approaches using event mixing technique for Bose-Einstein correlations (BEC) measurements in exclusive reactions with very low multiplicities are still unsatisfactory due to the problems of sample reduction and introducing extra and unnecessary fitting parameters. We here propose an event mixing method with a new mixing cut, named energy sum range (ESR) cut, to investigate two-pion Bose-Einstein correlations (BEC) in reactions with only two identical pions among three final state particles. This mixing method employs two-pion energy sum characteristic to control the mixing procedures, with no requirement on eliminating any original events. Numerical simulations are performed to show the viability of this new BEC observing method.

Quasi equilibrium state of expanding quantum fields and two-pion Bose-Einstein correlations in pp collisions at the LHC

We argue that the two-particle momentum correlation functions of high-multiplicity $p+p$ collisions at the LHC provide a signal for a ground state structure of a quasi equilibrium state of the longitudinally boost-invariant expanding quantum field which lies in the future light cone of a collision. The physical picture is that pions are produced by the expanding quantum emitter with two different scales approximately attributed to the expanding ideal gas in local equilibrium state and ground-state condensate. Specifically, we show that the effect of suppressing the two-particle Bose-Einstein momentum correlation functions increases with increasing transverse momentum of a like-sign pion pair due to different momentum-dependence of the corresponding particle emission regions.

Sub-regional event mixing constraints for two-pion Bose–Einstein correlations measurements in ππx system

Current BEC measurements in exclusive reactions with very low multiplicities is still a big challenge due to lack of effective observing method. Previously proposed observing approaches using event mixing technique still face problems of sample reduction and introducing extra and unnecessary fitting parameters. Here, we show the viability of a new event mixing approach with sub-regional mixing constraints related to energy hierarchy and energy sum observables. Extensive numerical simulations are performed to test the new mixing technique. Its ability to observe BEC parameters is validated and the systematic bias of the fit BEC parameter [Formula: see text] is improved since this new approach reduces the fitting parameters from 4 to 3 compared to the previously proposed mixing method.

An event-mixing method using energy hierarchy constraint for two-pion Bose–Einstein correlations measurements in ππx system

For the measurement of two-pion Bose–Einstein correlations (BEC) in reactions with [Formula: see text] final state particles, a new event-mixing technique is proposed. The new technique introduces a new mixing constraint, namely energy hierarchy correspondence (EHC) cut, which requires that two bosons being swapped should be equal in energy hierarchy in their original events. Numerical tests are performed to check the validity of the new mixing method. Compared to the previous proposed mixing technique (He et al., Chin. Phys. C 42 (2018) 074004), this new method has smaller systematic uncertainties, improving the accuracy of fit BEC parameters.

Lévy-stable two-pion Bose-Einstein correlations in sNN=200 GeV Au+Au collisions

We present a detailed measurement of charged two-pion correlation functions in 0%-30% centrality $\sqrt{s_{_{NN}}}=200$ GeV Au$+$Au collisions by the PHENIX experiment at the Relativistic Heavy Ion Collider. The data are well described by Bose-Einstein correlation functions stemming from L\'evy-stable source distributions. Using a fine transverse momentum binning, we extract the correlation strength parameter $\lambda$, the L\'evy index of stability $\alpha$ and the L\'evy length scale parameter $R$ as a function of average transverse mass of the pair $m_T$. We find that the positively and the negatively charged pion pairs yield consistent results, and their correlation functions are represented, within uncertainties, by the same L\'evy-stable source functions. The $\lambda(m_T)$ measurements indicate a decrease of the strength of the correlations at low $m_T$. The L\'evy length scale parameter $R(m_T)$ decreases with increasing $m_T$, following a hydrodynamically predicted type of scaling behavior. The values of the L\'evy index of stability $\alpha$ are found to be significantly lower than the Gaussian case of $\alpha=2$, but also significantly larger than the conjectured value that may characterize the critical point of a second-order quark-hadron phase transition.

An energy sum constraint of event mixing for Bose-Einstein correlations in reactions with ππX final states around 1 GeV**Supported by Fundamental Research Funds for the Central Universities (1006-YAH17063, 1006-XAA18059)

We present a new event mixing technique for measuring two-pion Bose-Einstein correlations (BEC) in reactions with only two identical bosons among three final state particles. This new mixing method contains a missing mass consistency (MMC) cut and an energy sum order (ESO) cut. Unlike the previous proposed pion energy cut, which abandons nearly half the original events, the ESO cut does not eliminate any original events and hence improves the statistics of both original events and mixed events. Numerical tests using the γp→π0π0p events around 1 GeV are carried out to verify the validity of the ESO cut. This cut is able to reproduce the relative momentum distribution of the original events in the absence of BEC effects. In addition, its ability to observe BEC effects is tested by an event sample in the presence of BEC effects. Simulation results show the BEC effects can be observed clearly as an enhancement in the correlation function, and the BEC parameters extracted by this event mixing cut are consistent with the input BEC parameters.

Centrality Dependent Lévy-Stable Two-Pion Bose-Einstein Correlations in \( {\sqrt{s_{NN}}} \) = 200 GeV Au+Au Collisions at the PHENIX Experiment

Investigation of femtoscopic correlation functions in relativistic heavy ion reactions is an important tool to access the space-time structure of particle production in the sQGP. The shape of the correlation functions is often assumed to be Gaussian, but a detailed analysis reveals that the statistically correct assumption could be the so-called L\'evy distribution. The detailed analysis of correlation functions in various systems may shed light on the location of the critical endpoint on the QCD phase diagram. It could also reveal if there is partially coherent pion production or could indicate the possible in-medium mass modification of the $\eta'$ meson due to the (partial) restoration of the $U_A(1)$ axial symmetry. In this paper we present the status of the centrality dependent measurements of two-pion L\'evy Bose-Einstein correlation functions in Au+Au collisions at PHENIX.

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

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.

A Comparison of HBT Measurements for d + Au and Au + Au collision systems at = 200 GeV

Two-pion Bose-Einstein correlations are a valuable tool for studying the space-time extent of emission sources in p + A, d + A, and A + A collisions. In recent work, PHENIX has extracted the 3-D HBT radii as a function of centrality and transverse-pair mass (mT) for the d + Au and Au + Au collision systems. A comparison of the radii for both systems indicate strong similarities in the detailed dependencies on centrality and mT, suggestive of important final-state re-scattering effects in the reaction dynamics for the d + Au and Au + Au systems. The measurements also point to a smaller freeze-out size and system lifetime in d + Au as compared to Au + Au.

Pion femtoscopy measurements in ALICE at the LHC

We present the results of two-pion Bose-Einstein correlations measured in Pb--Pb collisions at a center-of-mass energy sqrt(s_NN) = 2.76 TeV recorded by ALICE at the Large Hadron Collider. These types of correlations allow to extract, using the technique of femtoscopy (also known as Hanburry-Brown Twiss interferometry, or shortly HBT), the space-time characteristics of the source from the correlation calculated as a function of the pair momentum difference. The femtoscopic analysis was performed using both the Spherical Harmonics decomposition and the standard 3D Cartesian representation of the correlation function. The source sizes in three dimensions, the HBT radii, were extracted by fitting the experimental correlation functions. The resulting dependencies of the radii as a function of centrality and pair transverse momentum are shown. The results indicate the existence of a flowing medium and provide constraints on existing dynamical models. The ALICE Pb-Pb HBT radii are also compared to the pp analysis and other heavy-ion experiments in order to test the multiplicity scaling between different systems.

Measurement of two-particle correlations in pp collisions at √s = 900 GeV with the ALICE detector

ALICE is the experiment at the CERN Large Hadron Collider dedicated to study high-energy nuclear collisions which is also carrying out a proton-proton physics program, thanks to its wide phase-space coverage and good momentum and spatial resolution. We present first results on two-pion Bose-Einstein correlations in pp collisions at √s = 900 GeV measured with ALICE. An increase of the HBT radius with increasing event multiplicity is observed, in agreement with previous measurements. However, a strong decrease of the radius with increasing transverse momentum, as observed at RHIC and at Tevatron, is not evident in our analysis.

Two-pion Bose–Einstein correlations in Pb–Pb collisions at 2.76 TeV with ALICE

We present the first measurement of pion source radii in Pb–Pb collisions at the Large Hadron Collider. The radii were obtained by analyzing the Bose–Einstein enhancement in two-pion correlation functions. Like at lower energies, the radii drop with increasing transverse momentum, indicating the presence of collective expansion. In absolute terms, all three radii (Rout, Rside, Rlong) are larger than at RHIC, roughly consistent with a linear scaling with the cube root of the particle multiplicity.

Effects of source opacity and expansion on two-pion Bose-Einstein correlations

We examine two-pion Bose-Einstein correlations for partially coherent particle-emitting sources within quantum statistical formalism, where the sources are treated as classical currents with chaotic and coherent components. The two-pion correlation functions of the partially coherent sources contain a phase which is sensitive to the asymmetry of the source emission function. We investigate the influence of source opacity and expansion in high energy heavy ion collisions on the phase by Monte Carlo calculations. We find that these two physical effects shift the phase from zero. The Gaussian-formula fit results to the simulated two-pion correlation functions indicate that the opaque and expansion effects lead to a smaller interferometry radius R out and a larger λ parameter.

Two-pion Bose–Einstein correlations in central Pb–Pb collisions at [formula omitted

The first measurement of two-pion Bose–Einstein correlations in central Pb–Pb collisions at sNN=2.76 TeV at the Large Hadron Collider is presented. We observe a growing trend with energy now not only for the longitudinal and the outward but also for the sideward pion source radius. The pion homogeneity volume and the decoupling time are significantly larger than those measured at RHIC.

Detection of source inhomogeneity through event-by-event two-pion Bose–Einstein correlations

We develop a method for detecting the inhomogeneity of the pion-emitting sources produced in ultra-relativistic heavy ion collisions, through event-by-event two-pion Bose–Einstein correlations. The root-mean-square of the error-inverse-weighted fluctuations between the two-pion correlation functions of single and mixed events are useful observables for the detection. By investigating the root-mean-square of the weighted fluctuations for different impact parameter regions people may hopefully determine the inhomogeneity of the particle-emitting in the coming Large Hadron Collider (LHC) heavy ion experiments.

Signals in single-event pion interferometry for granular sources of quark-gluon plasma droplets

We investigate two-pion Bose-Einstein correlations of quark-gluon plasma droplet sources in single-event measurements. We find that the distribution of the fluctuation between correlation functions of the single- and mixed-events provide useful signals to detect the granular structure of the source.