Sandra S. Padula

Recent NA35 data on O+Au→π−π− +X at 200 A GeV are shown to be consistent with both a hadronic resonance gas model and a quark-gluon plasma model for this reaction. We show, in addition, that much higher statistics data will be required to differentiate between these models even with the outward and sideward transverse projected correlation functions.

In this communication, we report results of three-dimensional hydrodynamic computations, by using equations of state with a critical end point as suggested by the lattice QCD. Some of the results are an increase of the multiplicity in the mid-rapidity region and a larger elliptic-flow parameter v2. We discuss also the effcts of the initial-condition fluctuations and the continuous emission.

In hadronic reactions, the usual space-time interpretation of pion interferometry often breaks down due to strong correlations between spatial and momentum coordinates. We derive a general interferometry formula based on the Wigner density formalism that allows for arbitrary phase space and multiparticle correlations. Correction terms due to intermediate state pion cascading are derived using semiclassical hadronic transport theory. Finite wave packets are used to reveal the sensitivity of pion interference effects on the details of the production dynamics. The covariant generalization of the formula is shown to be equivalent to the formula derived via an alternate current ensemble formalism for minimal wave packets and reduces in the nonrelativistic limit to a formula derived by Pratt. The final expression is ideally suited for pion interferometric tests of Monte Carlo transport models. Examples involving gaussian and inside-outside phase space distributions are considered.

Bose-Einstein correlation is discussed for particles produced by rapidly expanding sources, when kinematical effects hinder a direct relation between the observed correlations and the source dimensions. Some of these effects are illustrated by considering Landau's hydrodynamical model wherein each space-time point of the fluid with temperature T=${T}_{c}$\ensuremath{\simeq}${m}_{\ensuremath{\pi}}$ is taken as an independent and chaotic emitting center with a Planck spectral distribution. In particular, this model reproduces surprisingly well the observed \ensuremath{\pi}-\ensuremath{\pi} and K-K correlations at the CERN ISR.

The advantages of kaon versus pion interferometry as a probe of quark-gluon plasma formation in high energy nuclear collisions are studied by comparing predictions of Lund resonance gas and plasma hydrodynamic models.

Back-to-back correlations of particle-antiparticle pairs are related to the in-medium mass-modification and squeezing of the quanta involved. They are predicted to appear when hot and dense hadronic matter is formed in high energy nucleus-nucleus collisions. The survival and magnitude of the back-to-back correlations (BBC) of boson-antiboson pairs generated by in-medium mass modifications are studied here in the case of a thermalized, finite-sized, spherically symmetric expanding medium. We show that the BBC signal indeed survives the finite-time emission, as well as the expansion and flow effects, with sufficient intensity to be observed at BNL Relativistic Heavy Ion Collider (RHIC).

Analytical expressions for pion interferometry are derived illustrating the competing effects of various non-ideal aspects of inside-outside cascade dynamics at energies ∼ 200 AGeV.

I review the history of HBT interferometry, since its discovery in the mid 1950's, up to the recent developments and results from BNL/RHIC experiments. I focus the discussion on the contributions to the subject given by members of our Brazilian group.

The hot and dense medium formed in high energy heavy ion collisions may modify some hadronic properties. In particular, if hadron masses are shifted in-medium, it was demonstrated that this could lead to back-to-back squeezed correlations (BBC) of particle-antiparticle pairs. Although well-established theoretically, the squeezed correlations have not yet been discovered experimentally. A method has been suggested for the empirical search of this effect, which was previously illustrated for $\ensuremath{\phi}\ensuremath{\phi}$ pairs. We apply here the formalism and the suggested method to the case of ${K}^{+}{K}^{\ensuremath{-}}$ pairs, since they may be easier to identify experimentally. The time distribution of the emission process plays a crucial role in the survival of the BBC's. We analyze the cases where the emission is supposed to occur suddenly or via a Lorentzian distribution, and compare with the case of a L\'evy distribution in time. Effects of squeezing on the correlation function of identical particles are also analyzed.

We analyse NA35 data on O + Au → π−π− + X at 200 AGeV including resonance decays and non-ideal dynamical and geometrical effects and find that a rƒ = τ⊥ƒ = 4 fm chaotic source is consistent with the data.

Proceedings of ISMD08

Squeezed correlations of particle-antiparticle pairs were predicted to exist if the hadron masses were modified in the hot and dense medium formed in high energy heavy ion collisions. Although well-established theoretically, they have not yet been observed experimentally. We suggest here a clear method to search for such signal, by analyzing the squeezed correlation functions in terms of measurable quantities. We illustrate this suggestion for simulated phi-phi pairs at RHIC energies.

The effect of the continuous emission hypothesis on the two-pion Bose-Einstein correlation function is discussed and compared with the corresponding results based on the usual freeze-out. Sizeable differences in the correlation function appear in these different descriptions of the decoupling process. This means that, when extracting properties of the hot matter formed in high-energy heavy-ion collisions from the data, completely different conclusions may be reached according to the description of the particle emission process adopted.

Large back-to-back correlations of observable fermion -- anti-fermion pairs are predicted to appear, if the mass of the fermions is modified in a thermalized medium. The back-to-back correlations of protons and anti-protons are experimentally observable in ultra-relativistic heavy ion collisions, similarly to the Andreev reflection of electrons off the boundary of a superconductor. While quantum statistics suppresses the probability of observing pairs of fermions with nearby momenta, the fermionic back-to-back correlations are positive and of similar strength to bosonic back-to-back correlations.

We briefly discuss four different possible types of transitions from quark to hadronic matter and their characteristic signatures in terms of correlations. We also highlight the effects arising from mass modification of hadrons in hot and dense hadronic matter, as well as their quantum statistical consequences: the appearance of squeezed quantum states and the associated experimental signatures, i.e., the back-to-back correlations of particle - anti-particle pairs. We briefly review the theoretical results of these squeezed quanta, generated by in-medium modified masses, starting from the first indication of the existence of surprising particle - anti-particle correlations, and ending by considering the effects of chiral dynamics on these correlation patterns. A prerequisite for such a signature is the experimental verification that these theoretically predicted back-to-back correlation of particle anti-particle pairs are, in fact, observable in high energy heavy ion reactions. Therefore, the experimental observation of back-to-back correlations in high energy heavy ion reactions would be a unique signature, proving the existence of in-medium mass modification of hadronic states. On the other hand, their disappearance at some threshold centrality or collision energy would indicate that the hadron formation mechanism would have qualitatively changed: asymptotic hadrons above such a threshold are not formed from medium modified hadrons anymore, but rather by new degrees of freedom characterizing the medium. Furthermore, the disappearance of the squeezed BBC could also serve as a signature of a sudden, non-equilibrium hadronization scenario from a supercooled quark-gluon plasma phase.

Squeezed correlations of hadron-antihadron pairs are predicted to appear if their masses are modified in the hot and dense medium formed in high energy heavy ion collisions. If discovered experimentally, they would be an unequivocal evidence of in-medium mass shift found by means of hadronic probes. We discuss a method proposed to search for this novel type of correlation, illustrating it by means of D_s-mesons with in-medium shifted masses. These particles are expected to be more easily detected and identified in future upgrades at RHIC.

Squeezed correlations of particle–antiparticle pairs, also called back-to-back correlations (BBC), are predicted to appear if the hadron masses are modified in the hot and dense hadronic medium formed in high energy nucleus–nucleus collisions. Although well established theoretically, the squeezed-particle correlations have not yet been searched for experimentally in high energy hadronic or heavy ion collisions, clearly requiring optimized forms to experimentally search for this effect. Within a non-relativistic treatment developed earlier we show that one promising way to search for the BBC signal is to look into the squeezed correlation function of pairs of ϕ's at RHIC energies, plotted in terms of the average momentum of the pair, . This variable's modulus, 2|K12|, is the non-relativistic limit of the variable Qbbc, introduced herewith. Some squeezing effects on the HBT correlation function are also discussed.

Bose-Einstein correlations of two identically charged $Q$ bosons are derived considering these particles to be confined in finite volumes. Boundary effects on single $Q$-boson spectrum are also studied. We illustrate the effects on the spectrum and on the two-$Q$-boson correlation function by means of two toy models. We also derive a generalized expression for the Wigner function depending on the deformation parameter $Q$, which is reduced to its original functional form in the limit of $Q\ensuremath{\rightarrow}1$.

The Bose-Einstein correlations of two identically charged pions are derived when these particles, the most abundantly produced in relativistic heavy ion collisions, are confined in finite volumes. Boundary effects on single pion spectrum are also studied. Numerical results emphasize that conventional formulation usually adopted to describe two-pion interferometry should not be used when the source size is small, since this is the most sensitive case to boundary effects. Specific examples are considered for better illustration.

We study the sensitivity of pion interferometry in pp and pp collisions at ISR energies to the resonance abundance. We show that those data are not compatible with the full resonance fractions predicted by the Lund model. The preliminary S+S and O+Au data at 200 A GeV are, however, not incompatible with the Lund predictions, although their sensitivity to resonances is significantly weaker than in the pp/pp case.

The two-photon correlation of the light pulse emitted from a sonoluminescence bubble is discussed. It is shown that several important information about the mechanism of light emission, such as the time-scale and the shape of the emission region could be obtained from the HBT interferometry. We also argue that such a measurement may serve to reject one of the two currently suggested emission mechanisms, i.e., thermal process versus dynamical Casimir effect.

We suggest that pion and kaon interlerometry are complementary probes that help differentiate hadronic resonance gas from plasma dynamical models. We also discuss how interferometry could be used to test the presence of resonances at AGS energies. Finally, we study the A dependence of interferometry in the resonance model at 200 A GeV.

Effects of lattice-QCD-inspired equations of state and continuous emission on some observables are discussed, by solving a 3D hydrodynamics. The particle multiplicity as well as v2 are found to increase in the mid-rapidity. We also discuss the effects of the initial-condition fluctuations.

Back-to-Back Correlations (BBC) of particle-antiparticle pairs are predicted to appear if hot and dense hadronic matter is formed in high energy nucleus-nucleus collisions.The BBC are related to in-medium mass-modification and squeezing of the quanta involved.Although the suppression of finite emission times were already known, the effects of finite system sizes and of collective phenomena had not been studied yet.Thus, for testing the survival and magnitude of the effect in more realistic situations, we study the BBC when mass-modification occurs in a finite sized, thermalized medium, considering a non-relativistically expanding fireball with finite emission time, and evaluating the width of the back-to-back correlation function.We show that the BBC signal indeed survives the expansion and flow effects, with sufficient magnitude to be observed at RHIC.

One of the most dramatic results from the first RHIC run are the STAR results for pi+- pi+- interferometry. They showed that the ratio of the so-called R_{out} and R_{sid} radii seem to decrease below unity for increasing transverse momentum of the pair (K_T). This was subsequently confirmed by PHENIX, which also extended the K_T range of the measurements. We consider here the effects of opacity of the nuclei on this ratio, and find that such a small value is consistent with surface emission from an opaque source.

The hadronic correlation among particle-antiparticle pairs was highlighted in the late 1990's, culminating with the demonstration that it should exist if the masses of the hadrons were modified in the hot and dense medium formed in high energy heavy ion collisions. They were called Back-to-Back Correlations (BBC) of particle-antiparticle pairs, also known as squeezed correlations. However, even though they are well-established theoretically, such hadronic correlations have not yet been experimentally discovered. Expecting to compel the experimentalists to search for this effect, we suggest here a clear way to look for the BBC signal, by constructing the squeezed correlation function of phi-phi and K+K- pairs at RHIC energies, plotted in terms of the average momentum of the pair, K12=(k1+k2)/2, inspired by procedures adopted in Hanbury-Brown & Twiss (HBT) correlations.

After five years of running at RHIC, and on the eve of the LHC heavy-ion program, we highlight the status of femtoscopic measurements.We emphasize the role interferometry plays in addressing fundamental questions about the state of matter created in such collisions, and present an enumerated list of measurements, analyses and calculations that are needed to advance the field in the coming years.

Back-to-Back Correlations (BBC) of particle-antiparticle pairs are predicted to appear if hot and dense hadronic matter is formed in high energy nucleus-nucleus collisions. The BBC correlations are related to in-medium mass-modification and squeezing of the quanta involved. The formalisms are analogous in the bosonic (bBBC) and in the fermionic (fBBC) cases. Both the bBBC and the fBBC are positive and unlimited correlations of similar strength. For testing the survival and the intensity of the effect in a more realistic situation, we study the back-to-back correlations for mass-modification occurring in a finite sized, thermalized medium. For illustration, we consider a non-relativistically expanding fireball with finite emission time. We show that the BBC signal indeed survives the expansion and flow effects, with sufficient magnitude to be observed at RHIC.

Bose‐Einstein correlations of two identically charged Q‐bosons are derived considering those particles to be confined in finite volumes. Boundary effects on single Q‐boson spectrum are also studied. We illustrate these effects by two examples: a toy model (one‐dimensional box) and a confining sphere. We also derive a generalized expression for the Wigner function depending on the deformation parameter Q, which is reduced to its original functional form in the limit Q → 1.

We show results from an analysis performed to test the resolving power of a two-dimensional ${\ensuremath{\chi}}^{2}$ method proposed previously when applied to the case of kaon interferometry, where no significant contribution from long-lived resonances is expected. For that purpose, use is made of the preliminary E859 ${K}^{+}{K}^{+}$ interferometry data from Si+Au collisions at $14.6A\mathrm{GeV}/c.$ Although less sensitivity is achieved in the present case, this analysis seems to favor scenarios with no resonance formation at the AGS energy range. The possible compatibility of data with zero decoupling proper time interval, conjectured by the three-dimensional experimental analysis, is also investigated and is ruled out when considering more realistic dynamical models with expanding sources. Furthermore, these results strongly emphasize that the static Gaussian parametrization cannot be trusted under more realistic conditions, leading to a distorted or even wrong interpretation of the source parameters.

The effects of opacity of the nuclei together with a blackbody type of emission along the system history are considered as a means to explain the ratio Rout/Rsid observed by STAR and PHENIX collaborations at RHIC. Within our model, no flow is required to explain the data trend of this ratio for large surface emissivities.

We perform an extensive study of the role played by the equation of state in the hydrodynamic evolution of the matter produced in relativistic heavy ion collisions. By using the same initial conditions and freeze-out scenario, the effects of different equations of state are compared by calculating their respective hydrodynamical evolution, particle spectra, harmonic flow coefficients $v_2$, $v_3$ and $v_4$ and two-pion interferometry radius parameters. The equations of state investigated contain distinct features, such as the nature of the phase transition, as well as strangeness and baryon density contents, which are expected to lead to different hydrodynamic responses. The results of our calculations are compared to the data recorded at two RHIC energies, 130 GeV and 200 GeV. The three equations of state used in the calculations are found to describe the data reasonably well. Differences can be observed among the studied observables, but they are quite small. In particular, the collective flow parameters are found not to be sensitive to the choice of the equation of state, whose implications are discussed.

Multidimensional two-particle Bose-Einstein correlation functions of charged hadrons are reported for pp collisions at 2.76 and 7 TeV in terms of different components of the pair relative momentum, extending the previous one-dimensional (1-D) analyses of CMS. This allows for investigating the extension of the source accessible to the femtoscopic correlation technique in different directions, revealing a more detailed picture of the emitting source in these collisions at increasing energies. The measurements are performed for different intervals of the pair average transverse momentum, kT, and for increasing charged particle multiplicitiy, Nch. Results in 1-D, 2-D and 3-D show a decrease of the fit radius parameters with kT, whereas a clear rise with Nch is observed in all cases. In addition, the fit radius parameters at both energies show close similarity in size and behavior within the same intervals of (Nch,kT).

Multidimensional two-particle Bose-Einstein correlation functions of charged hadrons are reported for pp collisions at 2.76 and 7 TeV in terms of different components of the pair relative momentum, extending the previous one-dimensional (1-D) analyses of CMS. This allows for investigating the extension of the source accessible to the femtoscopic correlation technique in different directions, revealing a more detailed picture of the emitting source in these collisions at increasing energies. The measurements are performed for different intervals of the pair average transverse momentum, kT , and for increasing charged particle multiplicitiy, Nch. Results in 1-D, 2-D and 3-D show a decrease of the fit radius parameters with kT , whereas a clear rise with Nch is observed in all cases. In addition, the fit radius parameters at both energies show close similarity in size and behavior within the same intervals of (Nch; kT ).

In high energy heavy ion collisions a hot and dense medium is formed, where the hadronic masses may be shifted from their asymptotic values. If this mass modification occurs, squeezed back-to-back correlations (BBC) of particle-antiparticle pairs are predicted to appear, both in the femionic (fBBC) and in the bosonic (bBBC) sectors. Although they have unlimited intensity even for finite-size expanding systems, these hadronic squeezed correlations are very sensitive to their time emission distribution. Here we discuss results in case this time emission is parameterized by a Lévy-type distribution, showing that it reduces the signal even more dramatically than a Lorentzian distribution, which already reduces the intensity of the effect by orders of magnitude, as compared to the sudden emission. However, we show that the signal could still survive if the duration of the process is short, and if the effect is searched for lighter mesons, such as kaons. We compare some of our results to recent PHENIX preliminary data on squeezed correlations of K + K − pairs.

A χ2 analysis is performed to test the resolving power of two-dimensional pion interferometry using for illustration the preliminary E802 data on Si+Au at 14.6 A GeV/c. We find that the resolving power to distinguish two decoupling geometries of different dynamical models is enhanced by studying the variation of the mean χ2 per degrees of freedom with respect to the range of the analysis in the qT,qL plane. The preliminary data seem to rule out dynamical models with significant ω, η resonance formation yields.

In high energy heavy ion collisions a hot and dense medium is formed, where the hadronic masses may be shifted from their asymptotic values. If this mass modification occurs, squeezed back-to-back correlations (BBC) of particle-antiparticle pairs are predicted to appear, both in the femionic (fBBC) and in the bosonic (bBBC) sectors. Although they have unlimited intensity even for finite-size expanding systems, these hadronic squeezed correlations are very sensitive to their time emission distribution. Here we discuss results in case this time emission is parameterized by a Levy-type distribution, showing that it reduces the signal even more dramatically than a Lorentzian distribution, which already reduces the intensity of the effect by orders of magnitude, as compared to the sudden emission. However, we show that the signal could still survive if the duration of the process is short, and if the effect is searched for lighter mesons, such as kaons. We compare some of our results to recent PHENIX preliminary data on squeezed correlations of K^+K^- pairs.

Many aspects of anisotropic collective flow in ultra relativistic heavy-ion collisions have been studied extensively in the past years using two or more particle correlations.An overview of collective flow and particle correlation measurements at CMS as a function of transverse momentum, pseudorapidity, event multiplicity, for both charged hadrons or identified particles will be presented.These results will be compared among pp, pPb and PbPb systems.Latest results of pp and PbPb data from 2015 run will also be discussed.

The hadronic correlation among particle-antiparticle pairs was highlighted in the late 1990's, culminating with the demonstration that it should exist if the masses of the hadrons were modified in the hot and dense medium formed in high energy heavy ion collisions. They were called Back-to-Back Correlations (BBC) of particle-antiparticle pairs, also known as squeezed correlations. However, even though they are well-established theoretically, such hadronic correlations have not yet been experimentally discovered. Expecting to compel the experimentalists to search for this effect, we suggest here a clear way to look for the BBC signal, by constructing the squeezed correlation function of phi-phi and K+K- pairs at RHIC energies, plotted in terms of the average momentum of the pair, K12=(k1+k2)/2, inspired by procedures adopted in Hanbury-Brown & Twiss (HBT) correlations.

A novel type of correlation involving particle-antiparticle pairs was found out in the 1990's. Currently known as Squeezed or Back-to-Back Correlations (BBC), they should be present if the hadronic masses are modified in the hot and dense medium formed in high energy heavy ion collisions. Although well-established theoretically, such hadronic correlations have not yet been observed experimentally. In this phenomenological study we suggest a promising way to search for the BBC signal, by looking into the squeezed correlation function of phi phi and K^+ K^- pairs at RHIC energies, as function of the pair average momentum, K_{12}=(k_1+k_2)/2. The effects of in-medium mass-shift on the identical particle correlations (Hanbury-Brown & Twiss effect) are also discussed.

A novel type of correlation involving particle-antiparticle pairs was found out in the 1990's. Currently known as Squeezed or Back-to-Back Correlations (BBC), they should be present if the hadronic masses are modified in the hot and dense medium formed in high energy heavy ion collisions. Although well-established theoretically, such hadronic correlations have not yet been observed experimentally. In this phenomenological study we suggest a promising way to search for the BBC signal, by looking into the squeezed correlation function of phi phi and K^+ K^- pairs at RHIC energies, as function of the pair average momentum, K_{12}=(k_1+k_2)/2. The effects of in-medium mass-shift on the identical particle correlations (Hanbury-Brown & Twiss effect) are also discussed.

A novel type of correlation involving particle-antiparticle pairs was found out in the 1990's. Currently known as Squeezed or Back-to-Back Correlations (BBC), they should be present if the hadronic masses are modified in the hot and dense medium formed in high energy heavy ion collisions. Although well-established theoretically, such hadronic correlations have not yet been observed experimentally. In this phenomenological study we suggest a promising way to search for the BBC signal, by looking into the squeezed correlation function of phi phi and K^+ K^- pairs at RHIC energies, as function of the pair average momentum, K_{12}=(k_1+k_2)/2. The effects of in-medium mass-shift on the identical particle correlations (Hanbury-Brown & Twiss effect) are also discussed.

In this article we write a biographical note about Yogiro Hama. It is quite an amazing life story, as you will read in the pages below. In the second part of this article we include many messages and letters sent by several of his friends and collaborators for the celebration of his 70th birthday.

The quark-gluon plasma created in high energy collisions of large nuclei exhibits strong anisotropic collective behavior as a nearly perfect fluid, flowing with little frictional resistance or viscosity. It has been investigated extensively over the past years employing two or more particle correlations. An overview of collective flow and particle correlation measurements at CMS as a function of transverse momentum, pseudorapidity, event multiplicity, for both charged hadrons or identified particles will be presented. These results are compared among pp, pPb and PbPb systems and several aspects of their intriguing similarities are discussed.

The back‐to‐back correlations (BBC) of particle‐antiparticle pairs, signalling in‐medium mass modification, are studied in a finite size thermalized medium. The width of BBC function is explicitly evaluated in the case of a nonrelativistic spherically symmetric expanding fireball. The effect of the flow is to reduce the BBC signal as compared to the case of non flow. Nevertheless, a significant signal survives finite‐time emission plus expansion effects.

The effects of opacity of the nuclei together with a blackbody type of emission along the system history are considered as a means to explain the ratio R{sub out}=R{sub sid} observed by STAR and PHENIX collaborations at RHIC. Within our model, no flow is required to explain the data trend of this ratio for large surface emissivities.

Abstract We study the sensitivity of pion interferometry in pp and p p collisions at ISR energies to the resonance abundance. We show that those data are not compatible with the full resonance fractions predicted by the Lund model. The preliminary S+S and O+Au data at 200 A GeV are, however, not incompatible with the Lund predictions, although their sensitivity to resonances is significantly weaker than in the pp/ p p case.