Momentum Dependence Research Articles

Experimental studies of in-medium modification of [formula omitted] meson mass through [formula omitted] decays

ϕ meson is an ideal probe to explore mass modification inside the nucleus due to partial restoration of chiral symmetry with its narrow width. The modification of ϕ mass is related to the strange-quark condensate 〈s̄s〉 in a finite density. J-PARC E88 has been proposed as an experiment to study the modification of ϕ mass inside nuclei in proton–nucleus collisions. Complementary to ϕ→e+e− decay measurements at J-PARC E16, E88 will measure high-statistics ϕ→K+K− decays of about 1 M in p+C, p+Cu, and p+Pb collisions by deploying kaon identification detectors at forward angles in the E16 spectrometer. Utilizing the high-statistics data, the momentum and polarization dependence of mass modification will be studied to evaluate the strange quark condensate in nucleons, and Lorentz-symmetry breaking effects. In this paper, we will discuss physics goals, the experimental design and feasibility, the performance of kaon identification detectors, and the timeline of the E88.

Collision energy dependence of elliptic flow of identified hadrons in heavy-ion collisions using the PHSD model

We report the first predictions of elliptic flow (v2) of identified hadrons at mid-rapidity (|y|< 1.0) in Au+Au collisions at Elab=6.7,8,11,and 25 A GeV using the Parton Hadron String Dynamics (PHSD) model. The transverse momentum (pT) dependence of identified hadron v2 in different centrality intervals (0-10%, 10-40%, and 40-80%) is shown. A clear centrality dependence of v2(pT) is observed for particles at Elab=6.7,8,11,and 25 A GeV. Within the PHSD model, the number of constituent quark (NCQ) scaling of v2 approximately follows in Au+Au collisions at all beam energies. A collision energy (sNN) dependence of π, K, and pv2 is studied in comparison with available published experimental data in the beam energy range of 6-25 A GeV. These predictions will help in interpreting the data from the forthcoming Compressed Baryonic Matter (CBM) experiment at the Facility for Antiproton and Ion Research (FAIR) and Multi-Purpose Detector (MPD) at the Nuclotron-based Ion Collider facility (NICA).

Phenomenology of TMD parton distributions in Drell-Yan and Z0 boson production in a hadron structure oriented approach

We present a first practical implementation of a recently proposed hadron structure oriented (HSO) approach to transverse momentum dependent (TMD) phenomenology applied to Drell-Yan-like processes, including lepton pair production at moderate Q2 and Z0 boson production. We compare and contrast general features of our methodology with other common practices and emphasize aspects that we view as improvements. Separately, we discuss the importance of treatments that preserve various theoretical properties of the nonperturbative parts of TMD parametrizations for future applications that have the extraction of hadron structure as a primary goal. These include the HSO’s preservation of a basic TMD parton-model-like framework even while accounting for full TMD factorization and evolution, explicit preservation of the integral relationship between TMD and collinear parton density functions, and the ability to meaningfully compare different theoretical models of nonperturbative TMD parton distributions. In our examples, we show that there is significant sensitivity at moderate Q2 to both the form of the nonperturbative transverse momentum dependence and the parametrization of collinear parton densities. However, we also find that evolving to Q2=MZ2, without fitting, results in a satisfactory postdiction of existing data for Z0 production, nearly independently of the modeling of nonperturbative transverse momentum behavior. We argue that this demonstrates that moderate Q measurements should be given greater weight than high Q measurements in extractions of nonperturbative transverse momentum dependence. We also obtain new extractions of the nonperturbative Collins-Soper kernel within the HSO approach. We discuss its features and compare with some earlier extractions. Published by the American Physical Society 2024

Far-from-equilibrium attractors with full relativistic Boltzmann approach in boost-invariant and non-boost-invariant systems

We study the universal behavior associated with a Relativistic Boltzmann Transport (RBT) approach with the full collision integral in 0+1D conformal systems. We show that all momentum moments of the distribution function exhibit universal behavior. Furthermore, the RBT approach allows to calculate the full distribution function, showing that an attractor behavior is present in both the longitudinal and transverse momentum dependence. We compare our results to the far-from-equilibrium attractors determined with other approaches, such as kinetic theory in Relaxation Time Approximation (RTA) and relativistic hydrodynamic theories, both in their viscous (DNMR) an anisotropic (aHydro) formulations, finding a very similar evolution, but an even faster thermalization in RBT for higher order moments. For the first time, we extended this analysis also to study the attractor behavior under a temperature-dependent viscosity η/s(T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta /s(T)$$\\end{document}, accounting also for the rapid increase toward the hadronic phase. We find that a partial breaking of the scaling behavior with respect to τ/τeq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au /\ au _{eq}$$\\end{document} emerges only at T≈Tc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T \\approx T_c$$\\end{document} generating a transient deviation from attractors; interestingly this in realistic finite systems may occur around the freeze-out dynamics. Finally, we investigate for the first time results beyond the boost-invariant picture, finding that also in such a case the system evolves toward the universal attractor. In particular, we present the forward and pull-back attractors at different space-time rapidities including rapidity regions where initially the distribution function is even vanishing.

Form factors, spectral and Källén-Lehmann representation in nonlocal quantum gravity

We discuss the conical region of convergence of exponential and asymptotically polynomial form factors and their integral representations. Then, we calculate the spectral representation of the propagator of nonlocal theories with entire form factors, in particular, of the above type. The spectral density is positive-definite and exhibits the same spectrum as the local theory. We also find that the piece of the propagator corresponding to the time-ordered two-point correlation function admits a generalization of the Källén-Lehmann representation with a standard momentum dependence and a spectral density differing from the local one only in the presence of interactions. These results are in agreement with what already known about the free theory after a field redefinition and about perturbative unitarity of the interacting theory. The spectral and Källén-Lehmann representations have the same standard local limit, which is recovered smoothly when sending the fundamental length scale ℓ* in the form factor to zero.

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 sNN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s_{\ extrm{NN}}} $$\\end{document} = 8.16 TeV and lead-lead (PbPb) collisions at sNN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s_{\ extrm{NN}}} $$\\end{document} = 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 (∆η) and relative azimuthal angle (∆ϕ), for various multiplicity and transverse momentum (pT) intervals. A multiplicity dependence of the balance function is observed in ∆η and ∆ϕ 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.

Isotropization of a longitudinally expanding system of scalar fields in the 2PI formalism

Motivated by isotropization of QCD matter in the initial stages of heavy-ion collisions, we consider a system of scalar fields that undergoes a boost invariant longitudinal expansion. We use the framework of the two-particle irreducible (2PI) effective action, which is close to the underlying quantum field theory, and resum self-energy corrections up to three loops. The resulting 2PI equations of motion are expressed in terms of the Milne coordinates to account for longitudinal expansion. By solving numerically these equations of motion, we can extract the occupation density and the effective mass generated by in-medium interactions. At the largest values of the coupling considered in this study, we observe the onset of isotropization both in the occupation number and in the momentum dependence of the effective mass.

Effect of Angular Momentum–Dependent Transparency on the Neutron-Nucleus Cross Section

We study the effect of the angular momentum dependence of the optical potential transparency on the neutron-nucleus cross section. In this work, we derive a functional form of the neutron-nucleus cross section with respect to spherical optical potential using the collision matrix and modify it. We also apply an analytical model (Ramsauer) to the square optical potential and the optical model using the TALYS 1.96 code to get the angular momentum–independent transparency and demonstrate the effect of the angular momentum dependence via comparison of two models. In this work, we calculate the neutron cross sections for 40 ≤ A ≤ 90 nuclei, with energies 100 MeV ≤ En ≤ 200MeV theoretically, the for ℓ ≠ 0 case. We find that the angular momentum dependence of the transparency treats good calculations of the neutron-nucleus cross section; a finite number of angular momentums will contribute appreciably to the nuclear reaction. The present study on smooth optical potential leads to useful insight into the mechanisms of neutron-induced reactions, particularly for medium nuclei at high energies.

Measuring differential particle correlations in relativistic nuclear collisions

This study explores the transverse momentum (pT) dependencies of symmetric and asymmetric correlations (SC and ASC) with one and two particles of interest in Au+Au collisions at 200 GeV. Leveraging a multiphase transport (AMPT) model, the investigation delves into the sensitivity of these correlations to the final state effects, providing valuable insights into their potential for constraining the final state effects' pT dependencies. The HIJING model is employed as a benchmark for nonflow correlations, shedding light on their impact on interpreting SC and ASC data. Moreover, the study points out that differential SC and ASC with one and two particles of interest (POIs) typically incorporate contributions from event-plane angle fluctuations. Consequently, this work highlights the significance of SC and ASC with one and two POIs as valuable tools for investigating the pT nature of the final state effects and advocates for comprehensive experimental measurements across various beam energies and system sizes to enhance understanding and provide additional constraints for theoretical models. Published by the American Physical Society 2024

Machine learning-based study of open-charm hadrons in proton-proton collisions at the Large Hadron Collider

In proton-proton and heavy-ion collisions, the study of charm hadrons plays a pivotal role in understanding the QCD medium and provides an undisputed testing ground for the theory of strong interaction, as they are mostly produced in the early stages of collisions via hard partonic interactions. The lightest open charm, D0 meson (cu¯), can originate from two separate sources. The prompt D0 originates from either direct charm production or the decay of excited open charm states, while the nonprompt stems from the decay of beauty hadrons. In this paper, using different machine learning (ML) algorithms such as XGBoost, CatBoost, and Random Forest, an attempt has been made to segregate the prompt and nonprompt production modes of the D0 meson signal from its background. The ML models are trained using the invariant mass through its hadronic decay channel, i.e., D0→π+K−, pseudoproper time, pseudoproper decay length, and distance of closest approach of D0 meson, using 8 simulated pp collisions at s=13 TeV. The ML models used in this analysis are found to retain the pseudorapidity, transverse momentum, and collision energy dependence. In addition, we report the ratio of nonprompt to prompt D0 yield, the self-normalized yield of prompt and nonprompt D0, and explore the charmonium, J/ψ to open charm, D0 yield ratio as a function of transverse momenta and normalized multiplicity. The observables studied in this paper are well predicted by all the ML models compared to the simulation. Published by the American Physical Society 2024

Revisiting shear stress tensor evolution: Nonresistive magnetohydrodynamics with momentum-dependent relaxation time

This study aims to develop second-order relativistic viscous magnetohydrodynamics (MHD) derived from kinetic theory within an extended relaxation time approximation (momentum/energy dependent) for the collision kernel. The investigation involves a detailed examination of shear stress tensor evolution equations and associated transport coefficients. The Boltzmann equation is solved using a Chapman-Enskog-like gradient expansion for a charge-conserved conformal system, incorporating a momentum-dependent relaxation time. The derived relativistic nonresistive, viscous second-order MHD equations for the shear stress tensor reveal significant modifications in the coupling with dissipative charge current and magnetic field due to the momentum dependence of the relaxation time. By utilizing a power law parametrization to quantify the momentum dependence of the relaxation time, the anisotropic magnetic field-dependent shear coefficients in the Navier-Stokes limit have been investigated. The resulting viscous coefficients are seen to be sensitive to the momentum dependence of the relaxation time. Published by the American Physical Society 2024

Measurements of Normalized Differential Cross Sections of Inclusive η Production in e^{+}e^{-} Annihilation at Energy from 2.0000 to 3.6710GeV.

Using data samples collected with the BESIII detector operating at the BEPCII storage ring, the cross section of the inclusive process e^{+}e^{-}→η+X, normalized by the total cross section of e^{+}e^{-}→hadrons, is measured at eight center-of-mass energy points from 2.0000 to 3.6710GeV. These are the first measurements with momentum dependence in this energy region. Our measurement shows a significant discrepancy compared to the existing fragmentation functions. To address this discrepancy, a new QCD analysis is performed at the next-to-next-to-leading order with hadron mass corrections and higher twist effects, which can explain both the established high-energy data and our measurements reasonably well.

Heavy quark dynamics via the Gribov-Zwanziger approach

In this work, we investigate the momentum-dependent drag and diffusion coefficient of heavy quarks (HQs) moving in the quark-gluon plasma background. The leading order scattering amplitudes required for this purpose have been obtained using the Gribov-Zwanziger propagator for the mediator gluons to incorporate the nonperturbative effects relevant to the phenomenologically accessible temperature regime. The drag and diffusion coefficients so obtained have been implemented to estimate the temperature and momentum dependence of the energy loss of the HQ as well as the temperature dependence of the specific shear viscosity (η/s) of the background medium. Our results suggest a higher energy loss of the propagating HQ compared to the perturbative estimates, whereas the η/s is observed to comply with the AdS/CFT estimation over a significantly wider temperature range compared to the perturbative expectation. Published by the American Physical Society 2024

Identifying the transverse and longitudinal modes of the K* and K1 mesons through their angular-dependent decay modes

Observing the mass shifts of chiral partners will provide invaluable insight into the role of chiral symmetry breaking in the generation of hadron masses. Because both the K* and K1 mesons have vacuum widths smaller than 100 MeV, they are ideal candidates for realizing mass shift measurements. On the other hand, the different momentum dependence of the longitudinal and transverse modes smear the peak positions. In this work, we analyze the angular dependence of the two-body decays of both the K* and K1. It is found that the longitudinal and transverse modes of the K* can be isolated by observing the pseudoscalar decay in either the forward or perpendicular directions, respectively. For the K1 decaying into a vector meson and a pseudoscalar meson, one can accomplish the same goal by further observing the polarization of the vector meson through its angular dependence on the two pseudoscalar meson decay. Published by the American Physical Society 2024

Onset of scaling violation in pion and kaon elastic electromagnetic form factors

Using a symmetry-preserving truncation of the quantum field equations describing hadron properties, parameter-free predictions are delivered for pion and kaon elastic electromagnetic form factors, FP=π,K, thereby unifying them with kindred results for nucleon elastic electromagnetic form factors. Regarding positive-charge states, the analysis stresses that the presence of scaling violations in QCD entails that Q2FP(Q2) should exhibit a single maximum on Q2>0. Locating such a maximum is both necessary and sufficient to establish the existence of scaling violations. The study predicts that, for charged π, K mesons, the Q2FP(Q2) maximum lies in the neighbourhood Q2≃5 GeV2. Foreseeable experiments will test these predictions and, providing their Q2 reach meets expectations, potentially also provide details on the momentum dependence of meson form factor scaling violation.

Single spin asymmetry AULsin(2ϕh) in dihadron production in SIDIS

The paper calculates the helicity-dependent dihadron fragmentation function by extending the dihadron spectator model and examine the single longitudinal spin asymmetry AULsin(2ϕh) from dihadron in semi-inclusive inelastic scattering. This function elucidates the relationship between the longitudinal polarization of the fragmented quark and the transverse momentum of the resulting hadron pairs. A study by the COMPASS collaboration detected a minimal signal in their experimental search for this azimuthal asymmetry in semi-inclusive inelastic scattering. Here, we use the spectator model to calculate the unknown T-odd dihadron fragmentation function H1⊥. Adopting collinear factorization to describe the data, avoiding the transverse momentum dependent factorization and the associated resummation effects, helping us understand the asymmetry and explaining why the signal is so weak. We involve the approach of transverse momentum dependence in the model calculations, in order to formulate the differential cross sections and the spin asymmetries in terms of the collinear parton distributions and the collinear dihadron fragmentation functions. A transverse momentum factor analysis method was used, in which the transverse momentum of the final hadron pairs was not integrated. The asymmetry of sin(2ϕh) in COMPASS kinematics was calculated and compared with experimental data. In addition, predictions for the same asymmetry are also presented for HERMES and the Electron Ion Collider. Published by the American Physical Society 2024

Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC

Ultrarelativistic nuclear collisions create a strongly interacting state of hot and dense quark–gluon matter that exhibits a remarkable collective flow behavior with minimal viscous dissipation. To gain deeper insights into its intrinsic nature and fundamental degrees of freedom, we determine the speed of sound in an extended volume of quark–gluon plasma using lead–lead (PbPb) collisions at a center-of-mass energy per nucleon pair of 5.02 TeV. The data were recorded by the CMS experiment at the CERN LHC and correspond to an integrated luminosity of 0.607 nb−1. The measurement is performed by studying the multiplicity dependence of the average transverse momentum of charged particles emitted in head-on PbPb collisions. Our findings reveal that the speed of sound in this matter is nearly half the speed of light, with a squared value of 0.241±0.002(stat)±0.016(syst) in natural units. The effective medium temperature, estimated using the mean transverse momentum, is 219±8(syst)MeV . The measured squared speed of sound at this temperature aligns precisely with predictions from lattice quantum chromodynamic (QCD) calculations. This result provides a stringent constraint on the equation of state of the created medium and direct evidence for a deconfined QCD phase being attained in relativistic nuclear collisions.

Marginal Fermi liquid behavior at the onset of 2kF density wave order in two-dimensional metals with flat hot spots

We analyze quantum fluctuation effects at the onset of incommensurate 2kF charge- or spin-density-wave order in two-dimensional metals for a model in which the ordering wave vector Q connects a single pair of hot spots on the Fermi surface with a vanishing Fermi surface curvature. The tangential momentum dependence of the bare dispersion near the hot spots is proportional to |kt|α with α&gt;2. We first compute the order parameter susceptibility and the fermion self-energy in a random phase approximation (RPA). Logarithmic divergences are subsequently treated by a renormalization-group analysis. The coupling between the order parameter fluctuations and the fermions vanishes logarithmically in the low-energy limit. As a consequence, the logarithmic divergences found in the RPA do not sum up to anomalous power laws. Instead, only logarithmic corrections to Fermi liquid behavior are obtained. In particular, the quasiparticle weight and the Fermi velocity vanish logarithmically at the hot spots. Published by the American Physical Society 2024

Momentum dependent flavor radiative corrections to the coherent elastic neutrino-nucleus scattering for the neutrino charge-radius determination

Despite being neutral particles, neutrinos can have a non-zero charge radius, which represents the only non-null neutrino electromagnetic property in the standard model theory. Its value can be predicted with high accuracy and its effect is usually accounted for through the definition of a radiative correction affecting the neutrino couplings to electrons and nucleons at low energy, which results effectively in a shift of the weak mixing angle. Interestingly, it introduces a flavour-dependence in the cross-section. Exploiting available neutrino-electron and coherent elastic neutrino-nucleus scattering (CEνNS) data, there have been many attempts to measure experimentally the neutrino charge radius. Unfortunately, the current precision allows one to only determine constraints on its value. In this work, we discuss how to properly account for the neutrino charge radius in the CEνNS cross-section including the effects of the non-null momentum-transfer in the neutrino electromagnetic form factor, which have been usually neglected when deriving the aforementioned limits. We apply the formalism discussed to a re-analysis of the COHERENT cesium iodide and argon samples and the NCC-1701 germanium data from the Dresden-II nuclear power plant. We quantify the impact of this correction on the CEνNS cross-section and we show that, despite being small, it can not be neglected in the analysis of data from future high-precision experiments. Furthermore, this momentum dependence can be exploited to significantly reduce the allowed values for the neutrino charge radius determination.

A direct probe of Λ potential in nuclear medium

Using the Liège intranuclear-cascade model together with the ablation model ABLA, an investigation is conducted into the effects of Λ potential in Λ-nucleus and Λ-hypernucleus-nucleus collisions across various beam energies. The findings show that the angle and transverse-momentum distributions of scattered Λ hyperon, the scattering cross section of the Λ hyperon in Λ-nucleus collisions as well as the rapidity distribution of Λ hyperon in Λ-hypernucleus-nucleus collisions are significantly influenced by the strength of the Λ potential in these scattering reactions across various beam energies. These demonstrations, unhindered by the uncertainties of Λ and hypernuclei productions in nuclear medium, allow for a direct investigation of the Λ potential, especially its momentum dependence. The criticality of probing the Λ potential is closely associated with the resolution of the “hyperon puzzle” in neutron stars.