Non-identical Particle Research Articles

Femtoscopy analysis of ultrasoft pion trap at energies available at the CERN Large Hadron Collider

Femtoscopy studies of pion radiation in heavy-ion collisions have been conducted extensively at all available collider energies, both theoretically and experimentally. In all these studies special attention is given to mT dependency of pion femtoscopy radii, usually approximated by a power-law function at transverse momenta above 200MeV/c. However, the radii behavior has been much less explored for the ultrasoft pions, possessing transverse momentum comparable to or lower than the pion mass. For many experimental setups this region is difficult to measure. In this work we present theoretical calculations of pion emission in the ultrasoft region in the two hybrid models iHKM and LHYQUID+thERMINATOR2. Along with the particle transverse momentum spectra, we present the calculated femtoscopy radii, in both one-dimensional and three-dimensional representations. We investigate the radii dependence on pair mT and observe, in particular, a departure from the power-law behavior at ultrasoft momenta, potentially reflecting a decoupling of such slow pions from the rest of collectively expanding system. We provide the theoretical interpretation of this result and discuss its significance, in particular, for the ongoing nonidentical particle femtoscopy analysis for pairs consisting of a pion and a baryon (or of a pion and a charmed meson). Published by the American Physical Society 2024

Calculation of momentum correlation functions between π, K , and p for several heavy-ion collision systems at sNN=39 GeV

Momentum correlation functions between π, K, and p are calculated for several heavy-ion collision systems, namely B510+B510, O816+O816, Ca2040+Ca2040, and Au79197+Au79197 in central collisions as well as Au79197+Au79197 collision in different centralities at center-of-mass energy sNN=39 GeV within the framework of a multiphase transport model complemented by the Lednický and Lyuboshitz analytical method. The results present the centrality and system-size dependence of the momentum correlation functions among pairs of π, K, and p, from which the emission source-size can be deduced. It is found that the deduced source sizes increase with the decreasing of centrality for Au + Au system or with the increasing of system size in central collisions with different nuclear size. In addition, through the momentum correlation functions of nonidentical particle pairs gated on velocity, the average emission sequence of nonidentical particles can be indicated. The results illustrate that in the small relative momentum region, protons are emitted in average earlier than π+ and K+, and K+ are emitted averagely earlier than π+. Furthermore, it seems that larger interval of the average emission order among them is exhibited for smaller collision systems. The present study sheds light on the dynamics of light particle emission at RHIC energy. Published by the American Physical Society 2024

Identical Particle and Lepton Mass Effects in the Decay $$H\rightarrow Z^*(\rightarrow \tau ^+\tau ^-)+Z^*(\rightarrow \tau ^+\tau ^-)$$

We consider identical particle and lepton mass effects in the cascade decay $H\to Z^\ast(\to\tau^+\tau^-)+Z^\ast(\to\tau^+\tau^-)$. Since the scale of the problem is set by the off-shellness $p_a^2$ and $p_b^2$ of the respective gauge bosons in the limits ($4m_\tau^2\le p_a^2,p_b^2\le (m_H-2m_\tau)^2$) and not by $m_H^2$, lepton mass effects are nonnegligible in particular close to the threshold of the off-shell decays. We calculate the rates and single angle decay distributions and compare them with the corresponding rates and single angle decay distributions for the nonidentical particle decays $H\to Z^\ast(\to e^+e^-)+Z^\ast(\to\mu^+\mu^-)$ involving negligible lepton masses.

The emission order of hydrogen isotopes via correlation functions in 30 MeV/u Ar+Au reactions

The intensity interferometry is applied as a chronometer of the particle emission of hydrogen isotopes from the intermediate velocity source formed in 40Ar+197Au reactions at 30 MeV/u. The dynamic emission order of τp>τd>τt is evidenced via the correlation functions of nonidentical particle pairs. Assuming the similar source size, the same emission order is inferred from the correlation functions of identical particle pairs, where τp≈100fm/c is extracted by the fit of Koonin-Pratt equation to p-p correlation function. Transport model simulations demonstrate that the dynamic emission order of light charged particles depends on the stiffness of the nuclear symmetry energy.

Taming identical particles for discerning the genuine non-locality

This work provides a comprehensive approach to analyze the entanglement between subsystems generated by identical particles, based on the symmetric/exterior algebra (SEA) and microcausality. Our method amends the no-labeling approach (NLA) to quantify any type of identical particles' entanglement, especially fermions with the parity superselection rule. We can analyze the non-local properties of identical particles' states in a fundamentally equivalent way to those for non-identical particles, which is achieved by the factorizability of the total Hilbert space of identical particles. This formal correspondence between identical and non-identical particle systems turns out to be useful for quantifying the non-locality generated by identical particles, such as the maximal CHSH inequality violation and the GHJW theorem of identical particles.

Pion–kaon femtoscopy and the lifetime of the hadronic phase in Pb−Pb collisions at [formula omitted] TeV

In this paper, the first femtoscopic analysis of pion–kaon correlations at the LHC is reported. The analysis was performed on the Pb–Pb collision data at sNN=2.76 TeV recorded with the ALICE detector. The non-identical particle correlations probe the spatio-temporal separation between sources of different particle species as well as the average source size of the emitting system. The sizes of the pion and kaon sources increase with centrality, and pions are emitted closer to the centre of the system and/or later than kaons. This is naturally expected in a system with strong radial flow and is qualitatively reproduced by hydrodynamic models. ALICE data on pion–kaon emission asymmetry are consistent with (3+1)-dimensional viscous hydrodynamics coupled to a statistical hadronisation model, resonance propagation, and decay code THERMINATOR 2 calculation, with an additional time delay between 1 and 2 fm/c for kaons. The delay can be interpreted as evidence for a significant hadronic rescattering phase in heavy-ion collisions at the LHC.

Effects of Ptot gates and velocity gates on light-particle momentum correlation in intermediate-energy heavy-ion collisions

Momentum correlation functions at small relative momenta are calculated for light particles $\left(n, p, d, t\right)$ emitted from $^{197}$Au + $^{197}$Au collisions at different impact parameters and beam energies within the framework of the isospin-dependent quantum molecular dynamics model complemented by the $Lednick\acute{y}$ and $Lyuboshitz$ analytical method. We first make sure our model is able to reproduce the FOPI data of proton-proton momentum correlation in a wide energy range from 0.4$A$ GeV to 1.5$A$ GeV. Then we explore more physics insights through the emission times and momentum correlations among different light particles. The specific emphasize is the effects of total pair momentum among different light particles, impact parameters and in-medium nucleon-nucleon cross section. Both two-deuteron and two-triton correlation functions are anti-correlation due to the final state interaction, and they are affected by in-medium nucleon-nucleon cross section for the higher total momentum of the particle pairs, but not for the lower ones. In addition, impact parameter and in-medium nucleon-nucleon cross section dependences of the emission source radii are extracted by fitting the momentum correlation functions. The results indicate that momentum correlation functions gating with total pair momentum is stronger for the smaller in-medium nucleon-nucleon cross section factor $\left(\eta\right)$ or impact parameter $\left(b\right)$. Non-identical particle correlations ($np, pd, pt, $ and $dt$) are also investigated by the velocity-gated correlation functions which can give information of the particles' emission sequence, and the result indicates that heavier ones $\left(deuteron/triton\right)$ are, one the average, emitted earlier than protons, in the small relative momentum region.

Geometry and Dynamics in Heavy-Ion Collisions Seen by the Femtoscopy in the STAR Experiment

The geometry and the dynamics of the particle-emitting source in high-energy heavy-ion collisions can be inferred via femtoscopy measurement. Two-particle correlations at small relative momentum exploit quantum statistics and the final-state interactions which allow one to study the space-time characteristics of the source of the order of 10−15 m and 10−23 s, respectively. The RHIC Beam Energy Scan (BES) program covers a significant part of the QCD Phase Diagram using collisions of Au nuclei at eight beam energies in the range from 7.7 to 200 GeV, covering the baryon-rich region, which can be studied via baryon femtoscopy. Thus, two-baryon measurements together with two-meson and meson-baryon correlations provide complementary information about the source characteristics.In this proceedings, the STAR preliminary results on femtoscopic observables of various particle combinations of protons, pions and kaons from Au+Au collisions at BES energies are presented. Determining how the properties of the particle-emitting source depend on collision energy is an important step towards understanding the physics of heavy-ion collisions. The BES program provides the possibility to study the energy dependence of the source sizes for various collision centralities. In addition to the source size, the measurements of non-identical particle combinations provide information about space-time asymmetries in emission process.

Emission Asymmetry and Time Delays in Non-identical Particle Femtoscopy

Emission Asymmetry and Time Delays in Non-identical Particle Femtoscopy

Pion-kaon femtoscopy in Pb-Pb collisions at sNN=2.76 TeV modeled in (3+1)D hydrodynamics coupled to the Therminator 2 code, and the effect of delayed kaon emission

Non-identical particle femtoscopy measures the size of the system emitting particles ("radius") in heavy-ion collisions as well as the difference between mean emission space-time coordinates of two particle species ("emission asymmetry"). The system created in such collisions at the LHC behaves collectively and its dynamics is well described by hydrodynamic models. A significant emission asymmetry between pions and kaons, coming from collective flow, enhanced by contribution from flowing resonances is predicted. We present calculations within the (3+1)D viscous hydrodynamic model coupled to statistical hadronization code Therminator 2, corresponding to Pb--Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV. We obtain femtoscopic radii and emission asymmetry for pion-kaon pairs as a function of collision centrality. The radii grow linearly with cube root of particle multiplicity density. The emission asymmetry is negative and comparable to the radius, indicating that pions are emitted closer to the center of the system and/or later than kaons. Recent ALICE Collaboration measurements of identical kaon femtoscopy shows that kaons are emitted, on average, 2.1~fm/$c$ later than pions. We modify our calculation by introducing such delay and find that the system source size is only weakly affected. In contrast the pion-kaon emission asymmetry is directly sensitive to such delays and the modified calculation shows significantly lower values of asymmetry. Therefore we propose the measurement of the pion-kaon femtoscopic correlation function as a sensitive probe of the time delays in particle emission.

Non-identical Particle Correlation Analysis in the Presence of Non-femtoscopic Correlations

Non-identical Particle Correlation Analysis in the Presence of Non-femtoscopic Correlations

Pion-kaon femtoscopy in Au+Au collisions at STAR

In non-identical particle correlations, e.g. pion-kaon femtoscopy, one can obtain information about source size and asymmetry in emission processes of pions and kaons. Such asymmetry give us knowledge of which type of particles is emitted first/second and/or from which region of the source. The studies of non-identical particle femtoscopy for Beam Energy Scan energies give us the opportunity to study how the source size and asymmetry in particle emission depend on the initial conditions of the collision. It also allows one to examine these parameters in the vicinity of the theoretical critical point. In these proceedings, we present STAR results of pion-kaon femtoscopy at mid-rapidity in Au+Au collisions at = 7.7, 19.6 and 39 GeV.

Pion-kaon femtoscopy in Au+Au collisions at STAR

Femtoscopy analysis allows us to extract information about the properties of particle emission source created after collision. From HBT of two correlated pions one can calculate source sizes; in addition, from the non-identical particle correlations, e.g. pion-kaon femtoscopy, one can obtain information not only about source sizes but the asymmetry in the emission processes of particles of different types as well. Such asymmetry gives knowledge of which kind of particles are emitted first/second and/or from which region of the source. The studies of non-identical particle femtoscopy for different collision energies gives us the opportunity to study how the source size and asymmetry in particle emission depend on the initial conditions of the collision. In these proceedings, we will present STAR results of pion-kaon femtoscopy at mid-rapidity in Au + Au collisions from the Beam Energy Scan program.

Digital quantum simulation goes to two fermions

In a recent work, a group of researchers led by Gui-Lu Long of Tsinghua University proposed a digital quantum simulation algorithm for the dynamics of interacting quantum systems in real space. They experimentally implemented the algorithm to simulate the dynamics of two interacting fermions using a nuclear magnetic resonance (NMR) setup [1]. Quantum simulation [2], inspired by the development of quantum computer, is one of the blossoming sub-fields in quantum information science. Efficient simulations of many-body quantum systems are generally difficult on classical computers due to the exponential growth of the required resource with the system size, while quantum computer has been proved to provide intrinsic advantages for such simulation tasks. Quantum simulation can be divided into two categories: analog simulation and digital simulation. An analog quantum simulator must have a sufficiently similar Hamiltonian to that of the target system to be simulated, and thus, on such quantum simulators, universal simulations of quantum systems cannot be realized [3]. In contrast, digital quantum simulation [4, 5] spares the requirement of similarity in Hamiltonians. A digital quantum simulator in principle can perform universal quantum simulations, and a quantum computer can play the role of a digital quantum simulator. A digital quantum simulation algorithm of a single-particle tunneling was proposed in 2012 [6]. Its first experimental realization was completed in 2013 [7]. Digital quantum simulations attract much attention recently. The simulation of real-space evolution of particles is one of the most attracting aspects among various quantum simulation tasks because of the fundamental role of real-space evolution problems in quantum physics. Investigation on the digital simulation of the quantum many-body spatial dynamics is difficult due to the large number of operations and qubits required. In the work of the Tsinghua team [1], they studied digital simulation of interacting quantum many-body dynamics, for both non-identical and identical particle systems. In identical particle systems, second quantization formalism was used. As a representative illustration, they proposed and experimentally realized a small-scale simulation for the temporal– spatial dynamics of a two-fermion system with Coulomb interactions using a three-qubit NMR quantum information processor. The experiment demonstrated the attracting or repelling nature between the particles due to attractive or repulsive interactions. This should be an indication that the simulation of many-body dynamics of small quantum systems is within reach of today’s small-scale quantum simulators with the help of digital quantum simulation algorithm, and quantum computers have promising superior powers in the simulation of complex quantum systems.

Prediction of non-identical particle correlations for the Beam Energy Scan program

Femtoscopy of two non-identical particles in heavy ion collisions enables one to study the space-time asymmetry in the particle's emission process. Theoretical studies based on EPOS model performed for collision energies from the Beam Energy Scan program in STAR allow us to investigate the dependence of source sizes and dynamics effects. Obtained information will enable us to predict the collective behaviour of femtoscopic particle's source.

Heine-Stieltjes correspondence and a new angular momentum projection for many-particle systems

A new angular momentum projection for systems of particles with arbitrary spins is formulated based on the Heine-Stieltjes correspondence, which can be regarded as the solutions of the mean-field-plus -pairing model in the strong-pairing interaction $G\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. Properties of the Stieltjes zeros of the extended Heine-Stieltjes polynomials, whose roots determine the projected states, and the related Van Vleck zeros are discussed. An electrostatic interpretation of these zeros is presented. As examples, applications to $n$ nonidentical particles of spin $1/2$ and to identical bosons or fermions are made to elucidate the procedure and properties of the Stieltjes zeros and the related Van Vleck zeros. It is shown that the new angular momentum projection for $n$ identical bosons or fermions can be simplified with the branching multiplicity formula of U$(N)\ensuremath{\downarrow}\mathrm{O}(3)$ and the special choices of the parameters used in the projection. Especially, it is shown that the solutions for identical bosons can always be expressed in terms of zeros of Jacobi polynomials. However, unlike nonidentical particle systems, the $n$-coupled states of identical particles are nonorthogonal with respect to the multiplicity label after the projection.

Non-Born–Oppenheimer nuclear and electronic densities for a three-particle Hooke–Coulomb model

Non-Born–Oppenheimer, nBO, one-particle nuclear and electron densities for a Hooke–Coulomb model of a three-body system are presented. These densities are obtained using exact closed-form analytic solutions to this problem as well as variational solutions. Moreover, the densities are calculated using different reference points, such as the global center of mass [cm], the geometric centers between both identical [gc12] and non-identical particles [cm13], and the location of the non-identical particle [p3]. It is shown that the topology of these nBO densities depends upon the choice of the reference points. This result is in turn used to argue that in a nBO regime the topological properties of the one-particle density cannot be univocally correlated with molecular structure, in the way it is done for the Born–Oppenheimer approximation.

Plans for correlation studies for BES program at RHIC

We present an overview of the main concepts concerning correlation studies for the Beam Energy Scan Program at STAR. QGP signatures at higher RHIC energies are the most obvious example of the creation of a new state of matter. In order to learn more about the transition to this state and to find a possible location of a critical point between a first-order transition and cross-over area, a new program dedicated to such analyses is formulated. Correlation studies are one of the most important obervables of the scanning of unknown region of the phase diagram. Measurements of elliptic flow, local parity violation in strong interactions, azimuthally-sensitive correlations as well as two-proton femtoscopy and nonidentical particle correlations are discussed in this paper.

Femtoscopy of the system shape fluctuations in heavy-ion collisions

Dipole, triangular and higher harmonic flows that have an origin in the initial density fluctuations have gained a lot of attention as they can provide additional important information about the dynamical properties (e.g. viscosity) of the system. The fluctuations in the initial geometry should also be reflected in the detailed shape and velocity field of the system at freeze-out. In this talk, I discuss the possibility of measuring such fluctuations by means of identical and non-identical particle interferometry.

Nonidentical-particle femtoscopy atsNN=200GeV in hydrodynamics with statistical hadronization

Non-identical particle femtoscopy probes not only the size of the emitting system, but also the emission asymmetries between particles of different mass, which are intimately related with the collective behavior of matter. We apply the technique to the simulations from the {\tt THERMINATOR}+Lhyquid model of the heavy-ion collisions at sqrt{s_{NN}}=200 AGeV. We present predictions for all common pair combinations and discuss their interpretation. Emphasis is put on extracting unique information about collective behavior of matter from the non-identical particle correlations and understanding the role of particles coming from decays of hadronic resonances. We also present, in detail, the technical aspects of the non-identical particle femtoscopy technique applied to data from the heavy-ion collisions. We list the sources of systematic errors coming from the method itself and the usual assumptions. We describe robust analysis methods and discuss their limitations.