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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Investigating late-stage particle production in pp collisions with balance functions

Balance functions have been regarded in the past as a method of investigating the late-stage hadronization found in the presence of a strongly-coupled medium. They are also used to constrain mechanisms of particle production in large and small collision systems. Charge balance functions for inclusive and identified particle pairs are reported as a function of charged particle multiplicity in proton–proton collisions simulated with the PYTHIA8 and the EPOS4 models. The charge balance functions of inclusive, pion, kaon, and proton pairs exhibit amplitudes and shapes that depend on particle species and differ significantly in the two models due to the different particle production mechanisms implemented in PYTHIA and EPOS. The shapes and amplitudes also evolve with multiplicity in both models. In addition, the evolution of the longitudinal rms width and that of balance functions integrals with multiplicity (and average transverse momentum) feature significant differences in the two models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Mixed-species charge and baryon balance functions studies with PYTHIA

Mixed species charge and baryon balance functions are computed based on proton-proton ( p p ) collisions simulated with the PYTHIA8 model. Simulations are performed with selected values of the collision energy s and the Monash tune and the ropes and shoving modes of PYTHIA8 to explore whether such measurements provide useful new information and constraints on mechanisms of particle production in p p collisions. Charge balance functions are studied based on mixed pairs of pions, kaons, and protons, whereas baryon balance functions are computed for mixed low mass strange and nonstrange baryons. Both charge and baryon balance functions of mixed particle pairs feature shapes and amplitudes that sensitively depend on the particle considered owing largely to the particle production mechanisms implemented in PYTHIA. The evolution of balance functions integrals with the longitudinal width of the acceptance are presented and one finds that sums of such integrals for a given reference particle obey expected sum rules for both charge and baryon balance functions. Additionally, both types of balance functions are found to evolve in shape and amplitude with increasing collision energy s and the PYTHIA tunes considered. Published by the American Physical Society 2024

Physics↗
DOE OSTI2024

Multiplicity and transverse momentum dependence of charge-balance functions in pPb and PbPb collisions at LHC energies

Measurements of the charge-dependent two-particle angular correlation function in proton-lead (pPb) collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_{NN}}$ = 8.16 TeV and lead-lead (PbPb) collisions at $\sqrt{s_{NN}}$ = 5.02 TeV are reported. The pPb and PbPb data sets correspond to integrated luminosities of 186 nb -1 and 0.607 nb -1 , respectively, and were collected using the CMS detector at the CERN LHC. The charge-dependent correlations are characterized by balance functions of same- and opposite-sign particle pairs. The balance functions, which contain information about the creation time of charged particle pairs and the development of collectivity, are studied as functions of relative pseudorapidity (Δη) and relative azimuthal angle (Δφ), for various multiplicity and transverse momentum (p T ) intervals. A multiplicity dependence of the balance function is observed in Δη and Δφ for both systems. The width of the balance functions decreases towards high-multiplicity collisions in the momentum region < 2 GeV, for pPb and PbPb results. Integrals of the balance functions are presented in both systems, and a mild dependence of the charge-balancing fractions on multiplicity is observed. No multiplicity dependence is observed at higher transverse momentum. The data are compared with HYDJET, HIJING, and AMPT generator predictions, none of which capture completely the multiplicity dependence seen in the data. The comparison of results with different center-of-mass energies suggests that the balance functions become narrower at higher energies, which is consistent with the idea of delayed hadronization and the effect of radial flow.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Using baryonic charge balance functions to resolve questions about the baryo-chemistry of the quark gluon plasma

Baryon annihilations during the hadronic stage of heavy-ion collisions affects final-state baryon and antibaryon yields and final-state correlations of baryons and antibaryons. Understanding annihilation is important for addressing questions about the chemistry at the beginning of the hadronic stage and for interpreting charge-balance correlations involving baryons. Here, charge balance functions, using protons and antiprotons binned by relative momentum, rapidity, and azimuthal angle are shown to clarify the amount of annihilation in the hadronic stage. This enables a more accurate extraction of the baryo-chemistry at the beginning of the hadronic stage. Understanding annihilation is also crucial if charge balance correlations are to be used to infer the chemistry of the earliest stages of a heavy-ion collision. Furthermore, calculations are presented based on microscopic simulations of the hadronic stage coupled to a hydrodynamic description of the earlier stage, along with a detailed modeling of correlations of protons and antiprotons, known as charge-balance functions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Charge balance functions for heavy-ion collisions at energies available at the CERN Large Hadron Collider

Heavy-ion collisions at the Large Hadron Collider provide the conditions to investigate regions of quark-gluon plasma that reach higher temperatures and that persist for longer periods of time compared with collisions at the Relativistic Heavy Ion Collider. This extended duration allows correlations from charge conservation to better separate during the quark-gluon plasma phase, and thus be better distinguished from correlations that develop during the hadron phase or during hadronization. Here, charge balance functions binned by relative rapidity and azimuthal angle and indexed by species are considered. A detailed theoretical model that evolves charge correlations throughout the entirety of an event is compared with preliminary results from the ALICE Collaboration. The comparison with experiment provides insight into the evolution of the chemistry and diffusivity during the collision. A ratio of balance functions is proposed to better isolate the effects of diffusion and thus better constrain the diffusivity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Probe Chiral Magnetic Effect with Signed Balance Function

In this paper a pair of observables are proposed as alternative ways, by examining the fluctuation of net momentum-ordering of charged pairs, to study the charge separation induced by the Chiral Magnetic Effect (CME) in relativistic heavy ion collisions. They are, the out-of-plane to in-plane ratio of fluctuation of the difference between signed balance functions measured in pair’s rest frame, and the ratio of it to similar measurement made in the laboratory frame. In this work, both observables have been studied with simulations including flow-related backgrounds, and for the first time, backgrounds that are related to resonance's global spin alignment. The two observables have similar positive responses to signal, and opposite, limited responses to identifiable backgrounds arising from resonance flow and spin alignment. Both observables have also been tested with two realistic models, namely, a multi-phase transport (AMPT) model and the anomalous-viscous fluid dynamics (AVFD) model. These two observables, when cross examined, will provide useful insights in the study of CME-induced charge separation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

General balance functions of identified charged hadron pairs of (π, Κ, ρ) in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

First measurements of balance functions (BFs) of all combinations of identified charged hadron (π, Κ, ρ) pairs in Pb–Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV recorded by the ALICE detector are presented. The BF measurements are carried out as two-dimensional differential correlators versus the relative rapidity (Δy) and azimuthal angle (Δφ) of hadron pairs, and studied as a function of collision centrality. The Δφ dependence of BFs is expected to be sensitive to the light quark diffusivity in the quark–gluon plasma. While the BF azimuthal widths of all pairs substantially decrease from peripheral to central collisions, the longitudinal widths exhibit mixed behaviors: BFs of ππ and cross-species pairs narrow significantly in more central collisions, whereas those of KK and pp are found to be independent of collision centrality. This dichotomy is qualitatively consistent with the presence of strong radial flow effects and the existence of two stages of quark production in relativistic heavy-ion collisions. Finally, the first measurements of the collision centrality evolution of BF integrals are presented, with the observation that charge balancing fractions are nearly independent of collision centrality in Pb–Pb collisions. Overall, the results presented provide new and challenging constraints for theoretical models of hadron production and transport in relativistic heavy-ion collisions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

A Test of Functional Balance Theory for Wetland Biomass Allocation in a Global Change Experiment

Abstract Forecasts of root growth and carbon sequestration under global change are compromised by uncertainty in how plants will allocate biomass between above and belowground pools. Here, we develop a simple model to assess whether functional balance theory can explain a complex biomass allocation response observed in a brackish marsh under experimental warming and elevated CO 2 . Our model shows how treatment‐driven changes in nitrogen supply and demand can explain divergent observations of root growth (i.e., maximum responses under intermediate warming and elevated CO 2 ). The model also reveals a surprising interaction between warming and eutrophication, where enhanced N loading to coastal marshes may reduce adverse impacts of warming on root growth. Our findings provide a mechanistic basis for incorporating biomass allocation into forecast models of marsh evolution. They also provide a general example of using ecological theory to decompose complex net responses observed in multi‐factor global change experiments into constituent processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Balancing Functionality and Printability: High-Loading Polymer Resins for Direct Ink Writing

Although direct ink writing (DIW) allows the rapid fabrication of unique 3D printed objects, the resins—or “inks”—available for this technique are in short supply and often offer little functionality, leading to the development of new, custom inks. However, when creating new inks, the ability of the ink to lead to a successful print, or the “printability,” must be considered. Thus, this work examined the effect of filler composition/concentration, printing parameters, and lattice structure on the printability of new polysiloxane inks incorporating high concentrations (50–70 wt%) of metallic and ceramic fillers as well as emulsions. Results suggest that strut diameter and spacing ratio have the most influence on the printability of DIW materials and that the printability of silica- and metal-filled inks is more predictable than ceramic-filled inks. Additionally, higher filler loadings and SC geometries led to stiffer printed parts than lower loadings and FCT geometries, and metal-filled inks were more thermally stable than ceramic-filled inks. The findings in this work provide important insights into the tradeoffs associated with the development of unique and/or multifunctional DIW inks, printability, and the final material’s performance.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Multiparticle integral and differential correlation functions

This paper formalizes the use of integral and differential cumulants for measurements of multiparticle event-by-event transverse momentum fluctuations, rapidity fluctuations, as well as net-charge fluctuations. This enables the introduction of multiparticle balance functions, defined based on differential correlation functions (factorial cumulants), that suppress two- and three-prong resonance decays effects and enable measurements of underlying long-range correlations obeying quantum number conservation constraints. These multiparticle balance functions satisfy simple sum rules determined by quantum number conservation. It is additionally shown that these multiparticle balance functions arise as an intrinsic component of high-order net-charge cumulants. This implies that the magnitude of these cumulants, measured in a specific experimental acceptance, is strictly constrained by charge conservation and primarily determined by the rapidity and momentum width of these balance functions. The paper also presents techniques to reduce the computation time of differential correlation functions up to order n = 10 based on the methods of moments. Published by the American Physical Society 2024

Physics↗
DOE OSTI2020

Calculating fluctuations and self-correlations numerically for causal charge diffusion in relativistic heavy-ion collisions

Here, we study the propagation and diffusion of electric charge fluctuations in the Bjorken hydrodynamic model with both white and Catteneo noise using purely numerical methods. We show that a lattice of noise fluctuations is required to fully calculate the two-point correlators of charge. We introduce a numerical procedure to solve the stochastic differential equations that arise from the charge conservation equation on the lattice event by event. We explicitly identify the self-correlation term in the case of Catteneo noise and provide a physical interpretation. We provide a numerical recipe to remove this contribution from the full two-point correlators. Finally, we calculate the balance functions for charged hadrons. By limiting the speed of signal propagation, we observe the expected narrowing of the balance functions after removing the self-correlations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Measurements of differential two-particle number and transverse momentum correlation functions in pp collisions at $\sqrt{\textit{s}}$ = 13 TeV

Differential two-particle normalized cumulants (R 2 ) and transverse momentum correlations (P 2 ) are measured as a function of the relative pseudorapidity and azimuthal angle difference (Δη, Δφ) of charged particle pairs in minimum bias pp collisions at $\sqrt{s}$ = 13 TeV. The measurements use charged hadrons in the pseudorapidity region of |η| < 0.8 and the transverse momentum range 0.2 < p T < 2.0 in order to focus on soft multiparticle interactions and to complement prior measurements of these correlation functions in p–Pb and Pb–Pb collisions. The correlation functions are reported for both unlike-sign and like-sign pairs and their charge-independent and charge-dependent combinations. Both the R 2 and P 2 measured in pp collisions exhibit features qualitatively similar to those observed in p–Pb and Pb–Pb collisions. The Δη and Δφ root mean square widths of the near-side peak of the correlation functions are evaluated and compared with those observed in p–Pb and Pb–Pb collisions and show smooth evolution with the multiplicity of charged particles produced in the collision. The comparison of the measured correlation functions with predictions from PYTHIA8 shows that this model qualitatively captures their basic structure and characteristics but feature important differences. In addition, the R$^{CD}_{2}$ is used to determine the charge balance function of hadrons produced within the detector acceptance of the measurements. The integral of the balance function is found to be compatible with those reported by a previous measurement in Pb–Pb collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Determining the diffusivity for light quarks from experiment

Charge balance functions reflect the evolution of charged pair correlations throughout the stages of pair production, dynamical diffusion, and hadronization in heavy-ion collisions. In this work, microscopic modeling of these correlations in the full collision volume shows that the balance functions are sensitive to the diffusivity of light quarks when studied as functions of relative azimuthal angle. By restricting our analysis to K + K – and $p\bar{p}$ pairs, we find that the diffusivity of light quarks, a fundamental property not currently well understood, can be constrained by experimental measurement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Quark flavor balancing in nuclear collisions

The notion of charge balance function, originally designed to study the evolution of charge production in heavy-ion collisions, is extended to consider quark flavor balancing. This extension is considered based on simulations performed with the PYTHIA 8 event generator in the context of pp collisions at √𝑠 = 13.6, 7, and 2.76 TeV but can be trivially applied to any other scenario and implemented in measurements of correlated particle production in pp, pA, and AA collisions at colliders. Correlation of selected flavor balancing pairs is examined as a function of the produced charged particle multiplicity. One finds that the amplitude of the correlations increases monotonically with the number of balanced flavors and the actual flavor content of correlated particles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

The comparison between effects of Taichi and conventional exercise on functional mobility and balance in healthy older adults: a systematic literature review and meta-analysis

Background Taichi is beneficial for functional mobility and balance in older adults. However, such benefits of Taichi when comparing to conventional exercise (CE) are not well understood due to large variance in study protocols and observations. Methods We reviewed publications in five databases. Eligible studies that examined the effects of Taichi on the outcomes of functional mobility and balance in healthy older adults as compared to CE were included. Subgroup analyses compared the effects of different types of CE (e.g., single and multiple-type exercise) and different intervention designs (e.g., Taichi types) on those outcomes (Registration number: CRD42022331956). Results Twelve studies consisting of 2,901 participants were included. Generally, compared to CE, Taichi induced greater improvements in the performance of Timed-Up-and-Go (SMD = −0.18, [−0.33 to −0.03], p = 0.040, I 2 = 59.57%), 50-foot walking (MD = −1.84 s, [−2.62 to −1.07], p < 0.001, I 2 = 0%), one-leg stance with eyes open (MD = 6.00s, [2.97 to 9.02], p < 0.001, I 2 = 83.19%), one-leg stance with eyes closed (MD = 1.65 s, [1.35 to 1.96], p < 0.001, I 2 = 36.2%), and functional reach (SMD = 0.7, [0.32 to 1.08], p < 0.001, I 2 = 86.79%) tests. Subgroup analyses revealed that Taichi with relatively short duration (<20 weeks), low total time (≤24 h), and/or using Yang-style, can induce significantly greater benefits for functional mobility and balance as compared to CE. Uniquely, Taichi only induced significantly greater improvements in Timed-Up-and-Go compared to single- (SMD = −0.40, [−0.55 to −0.24], p < 0.001, I 2 = 6.14%), but not multiple-type exercise. A significant difference between the effects of Taichi was observed on the performance of one-leg stance with eyes open when compared to CE without balance (MD = 3.63 s, [1.02 to 6.24], p = 0.006, I 2 = 74.93%) and CE with balance (MD = 13.90s, [10.32 to 17.48], p < 0.001, I 2 = 6.1%). No other significant difference was shown between the influences of different CE types on the observations. Conclusion Taichi can induce greater improvement in functional mobility and balance in older adults compared to CE in a more efficient fashion, especially compared to single-type CE. Future studies with more rigorous design are needed to confirm the observations here.

Li, Yiting↗