Hadronic Observables Research Articles

Multisystem Bayesian constraints on the transport coefficients of QCD matter

We study the properties of the strongly-coupled quark-gluon plasma with a multistage model of heavy ion collisions that combines the T$_\mathrm{R}$ENTo initial condition ansatz, free-streaming, viscous relativistic hydrodynamics, and a relativistic hadronic transport. A model-to-data comparison with Bayesian inference is performed, revisiting assumptions made in previous studies. The role of parameter priors is studied in light of their importance towards the interpretation of results. We emphasize the use of closure tests to perform extensive validation of the analysis workflow before comparison with observations. Our study combines measurements from the Large Hadron Collider and the Relativistic Heavy Ion Collider, achieving a good simultaneous description of a wide range of hadronic observables from both colliders. The selected experimental data provide reasonable constraints on the shear and the bulk viscosities of the quark-gluon plasma at $T\sim$ 150-250 MeV, but their constraining power degrades at higher temperatures $T \gtrsim 250$ MeV. Furthermore, these viscosity constraints are found to depend significantly on how viscous corrections are handled in the transition from hydrodynamics to the hadronic transport. Several other model parameters, including the free-streaming time, show similar model sensitivity while the initial condition parameters associated with the T$_\mathrm{R}$ENTo ansatz are quite robust against variations of the particlization prescription. We also report on the sensitivity of individual observables to the various model parameters. Finally, Bayesian model selection is used to quantitatively compare the agreement with measurements for different sets of model assumptions, including different particlization models and different choices for which parameters are allowed to vary between RHIC and LHC energies.

Analysis of the tetraquark and hexaquark molecular states with the QCD sum rules

In this article, we construct the color-singlet-color-singlet type currents and the color-singlet-color-singlet-color-singlet type currents to study the scalar , tetraquark molecular states and the vector , hexaquark molecular states with the QCD sum rules in details. In calculations, we choose the pertinent energy scales of the QCD spectral densities with the energy scale formula and for the tetraquark and hexaquark molecular states respectively in a consistent way. We obtain stable QCD sum rules for the scalar , tetraquark molecular states and the vector hexaquark molecular state, but cannot obtain stable QCD sum rules for the vector hexaquark molecular state. The connected (nonfactorizable) Feynman diagrams at the tree level (or the lowest order) and their induced diagrams via substituting the quark lines make positive contributions for the scalar tetraquark molecular state, but make negative or destructive contributions for the vector hexaquark molecular state. It is of no use or meaningless to distinguish the factorizable and nonfactorizable properties of the Feynman diagrams in the color space in the operator product expansion so as to interpret them in terms of the hadronic observables, we can only obtain information about the short-distance and long-distance contributions.

Distillation at high momentum

Extraction of hadronic observables at finite-momenta from Lattice QCD (LQCD) is constrained by the well-known signal-to-noise problems afflicting all such LQCD calculations. Traditional quark smearing algorithms are commonly used tools to improve the statistical quality of hadronic $n$-point functions, provided operator momenta are small. The momentum smearing algorithm of Bali et al. extends the range of momenta that are cleanly accessible, and has facilitated countless novel lattice calculations. Momentum smearing has, however, not been explicitly demonstrated within the framework of distillation. In this work we extend the momentum-smearing idea, by exploring a few modifications to the distillation framework. Together with enhanced time slice sampling and expanded operator bases engendered by distillation, we find ground-state nucleon energies can be extracted reliably for $\left|\vec{p}\right|\lesssim3\text{ GeV}$ and matrix elements featuring a large momentum dependence can be resolved.

Reflections upon the emergence of hadronic mass

With discovery of the Higgs boson, science has located the source for $\lesssim 2$% of the mass of visible matter. The focus of attention can now shift to the search for the origin of the remaining $\gtrsim 98$%. The instruments at work here must be capable of simultaneously generating the 1 GeV mass-scale associated with the nucleon and ensuring that this mass-scale is completely hidden in the chiral-limit pion. This hunt for an understanding of the emergence of hadronic mass (EHM) has actually been underway for many years. What is changing are the impacts of QCD-related theory, through the elucidation of clear signals for EHM in hadron observables, and the ability of modern and planned experimental facilities to access these observables. These developments are exemplified in a discussion of the evolving understanding of pion and kaon parton distributions.

Effects of the QCD phase transition on hadronic observables in relativistic hydrodynamic simulations of heavy-ion reactions in the FAIR/NICA energy regime

We investigate hadronic particle spectra and flow characteristics of heavy-ion reactions in the FAIR/NICA energy range of 1 AGeV ≤ Elab ≤ 10 AGeV within a relativistic ideal hydrodynamic one-fluid approach. The particlization is realized by sampling the Cooper-Frye distribution for a grand canonical hadron gas on a hypersurface of constant energy density. Results of the hydrodynamic calculations for different underlying equations of state are presented and compared with experimental data and microscopic transport simulations. The sensitivity of the approach to physical model inputs concerning the initial state and the particlization is studied.

Thermal properties of pi and rho meson

We computed the pole masses and decay constants of pi and rho meson at finite temperature in the framework of Dyson–Schwinger equations and Bethe–Salpeter equations approach. Below transition temperature, pion pole mass increases monotonously, while rho meson seems to be temperature independent. Above transition temperature, pion mass approaches the free field limit of screening mass sim 2pi T, whereas rho meson is about twice as large as that limit. Pion and the longitudinal projection of rho meson decay constants have similar behaviour as the order parameter of chiral symmetry, whereas the transverse projection of rho meson decay constant rises monotonously as temperature increases. The inflection point of decay constant and the chiral susceptibility get the same phase transition temperature. Though there is no access to the thermal width of mesons within this scheme, it is discussed by analyzing the Gell-Mann-Oakes-Renner (GMOR) relation in medium. These thermal properties of hadron observables will help us understand the QCD phases at finite temperature and can be employed to improve the experimental data analysis and heavy ion collision simulations.

Description of bulk properties of charged pions, kaons, and (anti)protons in Au+Au collisions from the STAR experiment in the Beam Energy Scan program within the improved HIJING code: Role of initial-state interactions

We have investigated the production yields of charged pions, kaons, and (anti)protons (restricted to midrapidity of $|y|l0.1$) in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}=7.7,\phantom{\rule{0.16em}{0ex}}11.5,\phantom{\rule{0.16em}{0ex}}19.6,\phantom{\rule{0.16em}{0ex}}27$, and 39 GeV, from the STAR experiment in the Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC), within an improved heavy-ion jet interaction generator (ImHIJING) code plus a relativistic transport (ART) model. Improvements of the dynamical content of ImHIJING code include (i) sampling of initial momenta of nuclear ground state, (ii) a Regge cascade for initial-state interaction effects, and (iii) an advanced popcorn mechanism for baryon production. It is found that the implementation of initial-state interactions in the $\mathrm{ImHIJING}+\mathrm{ART}$ model is crucial for the description of collision centrality dependence of bulk hadron observables in peripheral and semicentral ($\ensuremath{\approx}10%$--$70%$) $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}g11.5$ GeV.

Bayesian inference of nuclear symmetry energy from measured and imagined neutron skin thickness in Sn116,118,120,122,124,130,132, Pb208 , and Ca48

The neutron skin thickness $\Delta r_{np}$ in heavy nuclei has been known as one of the most sensitive terrestrial probes of the nuclear symmetry energy around $\frac{2}{3}$ of the saturation density $\rho_0$ of nuclear matter. Existing neutron skin data mostly from hadronic observables suffer from large uncertainties and their extraction from experiments are often strongly model dependent. While waiting eagerly for the promised model-independent and high-precision neutron skin data for $^{208}$Pb and $^{48}$Ca from the parity-violating electron scattering experiments (PREX-II and CREX at JLab as well as MREX at MESA), within the Bayesian statistical framework using the Skyrme-Hartree-Fock model we infer the posterior probability distribution functions (PDFs) of the slope parameter $L$ of the nuclear symmetry energy at $\rho_0$ from imagined $\Delta r_{np}(^{208}$Pb$)=0.15$, 0.20, and 0.30 fm as well as $\Delta r_{np}(^{48}$Ca$)=0.12$, 0.15, and 0.25 fm, with different $1\sigma$ error bars. The results are compared with the PDFs of $L$ inferred using the same approach from the available $\Delta r_{np}$ data for Sn isotopes from hadronic probes. They are also compared with results from a recent Bayesian analysis of the radius and tidal deformability data of canonical neutron stars from GW170817 and NICER. The neutron skin data for Sn isotopes gives $L=45.5^{+26.5}_{-21.6}$ MeV surrounding its mean value or $L=53.4^{+18.6}_{-29.5}$ MeV surrounding its maximum {\it a posteriori} value, respectively, with the latter smaller than but consistent with the $L=66_{-20}^{+12}$ MeV from the neutron star data within their 68\% confidence intervals. In order to provide additionally useful information on $L$ extracted from the $\Delta r_{np}$ of Sn isotopes, the experimental error bar of $\Delta r_{np}(^{208}$Pb) should be at least smaller than 0.06 fm aimed by some current experiments.

Influence of the electromagnetic fields on hadronic observables in proton-induced collisions

We investigate proton-gold collisions at top RHIC energy GeV within the Parton-Hadron-String Dynamics (PHSD) approach, focusing on the influence of the electromagnetic fields on final hadronic observable. We discuss the space-time distribution of the magnetic and electric field components, showing that the electric field Ex along the impact parameter direction is comparable in magnitude to the magnetic field By perpendicular to the reaction plane. We discuss the effect of these fields on the directed flow υ1 of pions and kaons. While there is no visible effect of electromagnetic fields in 5% central collisions, the result for collisions at fixed impact parameter clearly indicates an electromagnetically-induced splitting in the v1 of positively and negatively charged mesons; the effect, driven by the huge Ex component, is larger for kaons than to pions and increases with the impact parameter of the collision.

Exploring the partonic phase at finite chemical potential within a covariant off-shell transport approach

We report on the extended Parton-Hadron-String Dynamics (PHSD) transport approach in the partonic sector by explicitly calculating the total and differential partonic scattering cross sections as a function of temperature T and baryon chemical potential μऔ on the basis of the effective propagators and couplings from the Dynamical QuasiParticle Model (DQPM). We calculated the ratio of shear viscosity η over entropy density s, i.e. η/s is evaluated using the collisional widths and compared to lQCD calculations for μB = 0 as well. We find that the ratio η/s does not differ very much from that calculated within the original DQPM on the basis of the Kubo formalism. Furthermore, there is only a very modest change of η/s with the baryon chemical μB as a function of the scaled temperature T/TC(μ B). This also holds for a variety of hadronic observables from central A+A collisions in the energy range 5 GeV GeV when implementing the differential cross sections into the PHSD approach. Accordingly, it will be difficult to extract finite μB-signals from the partonic dynamics based on bulk observables.

Hadron production in elementary nucleon–nucleon reactions from low to ultra-relativistic energies

We study the hadron production in $$p+p$$ , $$p+n$$ and $$n+n$$ reactions within the microscopic Parton–Hadron-Dynamics (PHSD) transport approach in comparison to PYTHIA 8.2. We discuss the details of the “PHSD tune” of the Lund string model (realized by event generators FRITIOF and PYTHIA) in the vacuum (as in $$N+N$$ collisions) as well as its in-medium modifications relevant for heavy-ion collisions where a hot and dense matter is produced. We compare the results of PHSD and PYTHIA 8.2 (default version) for the excitation function of hadron multiplicities as well as differential rapidity y, transverse momentum $$p_T$$ and $$x_F$$ distributions in $$p+p$$ , $$p+n$$ and $$n+n$$ reactions with the existing experimental data in the energy range $$\sqrt{s_{NN}} = 2.7 - 7000$$ GeV. We discuss the production mechanisms of hadrons and the role of final state interactions (FSI) due to the hadronic rescattering. We also show the influence of the possible quark–gluon plasma (QGP) formation on hadronic observables in $$p+p$$ collisions at LHC energies. We stress the importance of developing a reliable event generator for elementary reactions from low to ultra-relativistic energies in view of actual and upcoming heavy-ion experiments.

Frame-independent spatial coordinate z̃ : Implications for light-front wave functions, deep inelastic scattering, light-front holography, and lattice QCD calculations

A general procedure for obtaining frame-independent three-dimensional light-front coordinate-space wave functions is introduced. The third spatial coordinate $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{z}$ is the boost and Lorentz frame-independent coordinate conjugate to the light-front momentum coordinate $x=\frac{{k}^{+}}{{P}^{+}}$ which appears in the momentum-space light-front wave functions underlying generalized parton distributions, structure functions, distribution amplitudes, form factors, and other hadronic observables. These causal light-front coordinate-space wave functions are used to derive a general expression for the quark distribution function of hadrons as an integral over the frame-independent longitudinal distance (the Ioffe time) between virtual-photon absorption and emission appearing in the forward virtual photon-hadron Compton scattering amplitude. Specific examples using models derived from light-front holographic QCD show that the spatial extent of the proton eigenfunction in the longitudinal direction can have a very large extent in $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{z}$.

Exclusive-final-state hadron observables from neutrino-nucleus multinucleon knockout

We present results of an updated calculation of the 2p2h (two particle two hole) contribution to the neutrino-induced charge-current cross section. We provide also some exclusive observables, interesting from the point of view of experimental studies, e.g. distributions of momenta of the outgoing nucleons and of available energy, which we compare with the results obtained within the NEUT generator. We also compute, and separate from the total, the contributions of 3p3h mechanisms. Finally, we discuss the differences between the present results and previous implementations of the model in MC event-generators, done at the level of inclusive cross sections, which might significantly influence the experimental analyses, particularly in the cases where the hadronic observables are considered.

Lifetime Estimations and a Non-Monotonic Initial Energy Density in Heavy Ion Collisions at RHIC and LHC

We highlight some connections between the final state hadronic observables and the initial conditions using a recently found new exact family of solutions of relativistic hydrodynamics. These relations provide explicit examples of the scaling behaviour in relativistic hydrodynamics and may provide an advanced estimate of the lifetime and the initial energy density in $\sqrt{s_{NN}} = 62.4$, $130$, and $200$ GeV Au+Au collisions at RHIC and $\sqrt{s_{NN}} = 5.0$ TeV Pb+Pb and $5.44$ TeV Xe+Xe as well as $\sqrt{s} = 7$, $8$ and $13$ TeV p+p collisions at LHC energies. A surprising result is that these advanced estimates yield a non-monotonic increase of the initial energy density with increasing collision energy at the RHIC energy range.

OpenQ*D code: a versatile tool for QCD+QED simulations

We present the open-source package openQ*D-1.0 (openQ*D. GitLab: https://gitlab.com/rcstar/openQxD. CSIC: https://dx.doi.org/10.20350/digitalCSIC/8591. https://hdl.handle.net/10261/173334, 2019), which has been primarily, but not uniquely, designed to perform lattice simulations of QCD+QED and QCD, with and without mathrm {C}^* boundary conditions, and O(a) improved Wilson fermions. The use of mathrm {C}^* boundary conditions in the spatial direction allows for a local and gauge-invariant formulation of QCD+QED in finite volume, and provides a theoretically clean setup to calculate isospin-breaking and radiative corrections to hadronic observables from first principles. The openQ*D code is based on openQCD-1.6 (Simulation program for lattice QCD (openQCD code). https://cern.ch/luscher/openQCD, 2016) and NSPT-1.4 (Numerical Stochastic Perturbation Theory (NSPT code). https://cern.ch/luscher/NSPT, 2017). In particular it inherits from openQCD-1.6 several core features, e.g. the highly optimized Dirac operator, the locally deflated solver, the frequency splitting for the RHMC, or the 4th order OMF integrator.

Spectroscopy of mathbf {B_c} mesons and the possibility of finding exotic mathbf {B_c}-like structures

The bottom-charmed (B_c) mesons are more stable than their charmonium (c{{bar{c}}}) and bottomium (b{{bar{b}}}) partners because they cannot annihilate into gluons. However, the low production cross-sections and signal-to-background ratios avoided until now their clear identification. The recent experimental results reported by CMS and LHCb at CERN open the possibility of having a B_c spectrum as complete as the ones of charmonium and bottomonium. Motivated by this expectation, we compute bottom-charmed meson masses in the region energies in which decay meson–meson thresholds are opened, looking for the analogs to the X(3872) in the B_c spectroscopy. We use a constituent quark model in which quark–antiquark degrees of freedom are complemented by four-body Fock states configurations. The model has been applied to a wide range of hadronic observables, in particular to the X(3872), and thus the model parameters are completely constrained. No extra states are found in the J^P=0^+ and J^P=1^+ sectors. However, in the J^P=2^+ sector we found an additional state very close to the D^*B^* threshold which could be experimentally detected.

Study of collective anisotropies v_2 and v_3 and their fluctuations in pA collisions at LHC within a relativistic transport approach

We have developed a relativistic transport approach at fixed eta /s(T) that incorporates initial space fluctuations generated by wounded quark model to study the hadron observables in 5.02 TeV p + Pb collisions. We find that our approach is able to correctly predict quite well several existing experimental measurements assuming a matter with eta /s=1/4pi , a result similar to previous studies within a viscous hydrodynamics approach. Besides, we further discuss the sensitivity of the results on both eta /s(T) and the smearing width. Our transport approach has the possibility to include in initial conditions the power law tail associated to minijet, and this improvement extends the agreement with the experimental data to higher p_T ranges. We also perform a comparison to Pb + Pb collisions pointing out that even if the collective flows have a similar magnitude the features of the matter created are different. By studying the correlation between collective flows and initial geometry, we find that the correlation decreases faster in small systems with the increase of n and centrality. In particular we show that the variance of sigma _{v_n}/langle v_nrangle has a quite different evolution with centrality for p + Pb, so their measurement could provide some further hint about the correctness of current modelling.

Exploring the partonic phase at finite chemical potential within an extended off‐shell transport approach

AbstractWe extend the parton‐hadron‐string dynamics (PHSD) transport approach in the partonic sector by explicitly calculating the total and differential partonic scattering cross sections as a function of temperature T and baryon chemical potential μB on the basis of the effective propagators and couplings from the dynamical quasiparticle model (DQPM) that is matched to reproduce the equation of state of the partonic system above the deconfinement temperature Tc from lattice quantum chromodynamics (QCD). We calculate the collisional widths for the partonic degrees of freedom at finite T and μB in the time‐like sector and conclude that the quasiparticle limit holds sufficiently well. Furthermore, the ratio of shear viscosity η over entropy density s, that is, η/s, is evaluated using the collisional widths and compared to lattice QCD(lQCD) calculations for μB = 0 as well. We find that the ratio η/s does not differ very much from that calculated within the original DQPM on the basis of the Kubo formalism. Furthermore, there is only a very modest change of η/s with the baryon chemical μB as a function of the scaled temperature T/Tc(μB). This also holds for a variety of hadronic observables from central A + A collisions in the energy range 5 GeV 200 GeV when implementing the differential cross sections into the PHSD approach. Accordingly, it will be difficult to extract finite μB signals from the partonic dynamics based on “bulk” observables.

Lorentz- and CPT -violating standard model extension in chiral perturbation theory

Lorentz and CPT violation in hadronic physics must be tied to symmetry violations at the underlying quark and gluon level. Chiral perturbation theory provides a method for translating novel operators that may appear in the Lagrange density for color-charged parton fields into equivalent forms for effective theories at the meson and baryon levels. We extend the application of this technique to the study of Lorentz-violating and potentially CPT-violating operators from the minimal standard model extension. For dimension-4 operators, there are nontrivial relations between the coefficients of baryon-level operators related to underlying quark and gluon operators with the same Lorentz structures. Moreover, in the mapping of the dimension-3 operators from the quark and gluon level to the hadron level (considered here for the first time), many of the hadronic observables contain no new low-energy coupling constants at all, which makes it possible to make direct translations of bounds derived using experiments on one kind of hadron into bounds in a completely different corner of the hadronic sector. A notable consequence of this is bounds (at $10^{-15}$-$10^{-20}$ GeV levels) on differences $a^{\mu}_{B}-a^{\mu}_{B'}$ of Lorentz and CPT violation coefficients for $SU(3)_{f}$ octet baryons that differ in their structure by the replacement of a single valance $d$ quark by a $s$ quark. Never before has there been any proposal for how these kinds of differences could be constrained.

Exploring the partonic phase at finite chemical potential within an extended off-shell transport approach

We extend the Parton-Hadron-String Dynamics (PHSD) transport approach in the partonic sector by explicitly calculating the total and differential partonic scattering cross sections as a function of temperature $T$ and baryon chemical potential $\mu_B$ on the basis of the effective propagators and couplings from the Dynamical QuasiParticle Model (DQPM) that is matched to reproduce the equation of state of the partonic system above the deconfinement temperature $T_c$ from lattice QCD. The ratio of shear viscosity $\eta$ over entropy density $s$, i.e. $\eta/s$, is evaluated using the collisional widths and compared to lQCD calculations for $\mu_B$ = 0 as well. We find only a very modest change of $\eta/s$ with the baryon chemical $\mu_B$. This also holds for a variety of hadronic observables from central A+A and C+Au collisions in the energy range 5 GeV $\leq \sqrt{s_{NN}} \leq$ 200 GeV when implementing the differential cross sections into the PHSD approach. We only observe small differences in the strangeness and antibaryon sector with practically no sensitivity of rapidity and $p_T$ distributions to the $\mu_B$ dependence of the partonic cross sections. Since we find only small traces of a $\mu_B$-dependence in heavy-ion observables - although the effective partonic masses and widths as well as their partonic cross sections clearly depend on $\mu_B$ - this implies that one needs a sizable partonic density and large space-time QGP volume to explore the dynamics in the partonic phase. These conditions are only fulfilled at high bombarding energies where $\mu_B$ is, however, rather low. On the other hand, when decreasing the bombarding energy and thus increasing $\mu_B$, the hadronic phase becomes dominant and accordingly, it will be difficult to extract signals from the partonic dynamics based on "bulk" observables.