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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Measurements of Pion and Muon Nuclear Capture at Rest on Argon in the LArIAT Experiment

We report the measurement of the final-state products of negative pion and muon nuclear capture at rest on argon by the LArIAT experiment at the Fermilab Test Beam Facility. We measure a population of isolated MeV-scale energy depositions, or blips, in 296 LArIAT events containing tracks from stopping low-momentum pions and muons. The average numbers of visible blips are measured to be 0.74 ± 0.19 and 1.86 ± 0.17 near muon and pion track endpoints, respectively. The 3.6⁢𝜎 statistically significant difference in blip content between muons and pions provides the first demonstration of a new method of pion-muon discrimination in neutrino liquid argon time projection chamber experiments. LArIAT Monte Carlo simulations predict substantially higher average blip counts for negative muon (1.22 ± 0.08) and pion (2.34 ± 0.09) nuclear captures. We attribute this difference to geant4’s inaccurate simulation of the nuclear capture process.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Measurement of the Negative Pion and Positive Kaon Total Hadronic Cross Sections on Argon at the LArIAT Experiment

The Liquid Argon Time Projection Chamber (LArTPC) represents one of the most advanced experimental technologies for physics at the Intensity Frontier due to its full 3D-imaging, excellent particle identication and precise calorimetric energy reconstruction. By deploying a LArTPC in a dedicated calibration test beam line at Fermilab, LArIAT (Liquid Argon In A Testbeam) aims to experimentally calibrate this technology in a controlled environment and to provide physics results key to the neutrino oscillation physics and proton decay searches of the Short Baseline Neutrino (SBND, MicroBooNE, ICARUS) and Long Baseline Neutrino programs (DUNE). LArIAT's physics program entails a vast set of topics with a particular focus on the study of nuclear eects such as pion and kaon characteristic interaction modes. This thesis presents two measurements performed for the rst time: the measure- ment of the negative pion total hadronic cross section on argon in the 100-1050 MeV kinetic energy range and the measurement of the positive kaon total hadronic cross section on argon in the 100-650 MeV kinetic energy range. The analyses devised for these measurements use both the core elements of LArIAT: beamline and LArTPC. The rst step in each analysis is the development of an event selection based on beam- line and TPC information geared towards the identication of the hadron of interest. We then proceed to match the beamline candidate to a suitable TPC track. Finally, we apply the \thin slice method" technique and measure the cross section, correcting for background contamination and detector eects. The thin slice technique is a new method to measure hadron-argon cross sections possible only due to the combination of the tracking and calorimetry capability of the LArTPC technology. Albeit never on argon, the hadronic cross section of pions has been extensively measured before on lighter and heavier dierent elements in thin target experiments, leading to solid predictions for measurements on argon. Through the use of a dierent technique, our measurement of the negative pion total hadronic cross section on argon is in general agreement with the predictions by the Geant4 Bertini Cascade model which are based on data from thin target experiments. On the contrary, cross section measurements for kaons are extremely scarce, thus more dicult to model. Our measurement of the positive kaon total hadronic cross section on argon is mostly in tension with the Geant4 prediction over the explored range of energies and provides new experimental data to properly compare existing interaction models. This thesis also reports two ancillary detector physics measurements necessary for the cross section analyses: the measurements of the LArIAT electric eld and calorimetry constants. We developed a technique to measure the LArIAT electric eld using cathode-anode piercing tracks with cosmic data. We applied a new technique for the measurement of the calorimetry calibration constants based on the particles' momentum measurement. The negative pion and the positive kaon total hadronic cross measurements are the rst physics results of the LArIAT experiment and will be the basis for the future LArIAT measurements of pion and kaon cross sections in the exclusive channels. The outcome of these measurements will ultimately enable to quantify and reduce the systematic associated with the hadronic interaction models in neutrino-argon interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

A pion-argon cross section measurement in the ProtoDUNE-SP experiment with cosmogenic muon

Neutrinos are tiny mysterious fundamental particles with small cross sections. Through neutrino physics, scientists across the world are trying to answer many intriguing questions about nature such as the dominance of matter over antimatter, CP violation in the lepton sector, number of supernovas in the early universe, etc. Detection of neutrinos requires massive particle detectors and intense neutrino beam owing to their small cross section. Deep Underground Neutrino Experiment (DUNE) is a next-generation neutrino experiment that is planned to start taking data beginning in 2026. DUNE will consist of 4 massive detectors, the first of which will be using single-phase liquid argon time projection chamber (LArTPC) technology. The ProtoDUNE-SP experiment is a prototype of the DUNE built at the CERN neutrino platform and uses the same detector technology that will be used in DUNE first module. The ProtoDUNE-SP experiment collected months of test beam and cosmic ray data beginning in September 2018. It was built to provide a testbed for the installation of detector parts for DUNE, showing long-term stability of the detector, understanding detector response for different test beam particles (including protons, pions, electrons, kaons, muons), and measurement of hadron-argon cross sections. When a particle passes through LArTPC electron-ion pairs are produced. To reconstruct the position and energy of a particle passing through the medium knowledge of ionization electron drift velocity is essential. The electron drift velocity is distorted by an excess positive charge built up in the detector, known as space charge. This study discusses a novel technique for measuring the ionization electron drift velocity using cosmic-ray muons. The technique uses tracks that travel the entire drift distance of the TPC for drift velocity determination. Secondly, the study discusses a method for converting the charge deposited into energy. The method is carried out in two step s. In th e first step detector response for energetic cosmic ray muons crossing the entire the TPC is used to make the charge deposition uniform throughout the TPC, and in the second step stopping cosmic-ray muons are used for determining the energy scale. Finally, the study discusses a pion-argon cross section measurement based on reweighting of Monte Carlo simulations using J. Calcutt's Geant4Reweight framework. Neutrinos cannot be directly detected; they are identified based on the interaction products. Pions are a common interaction product in a neutrino interaction. For precise modeling of neutrino event generators, it is essential to understand the pion-argon interaction. Pion-argon cross section measurement serves as an important input for neutrino interaction models. The results of the pion-argon total reaction cross section using the Geant4 reweighting technique are found to be in good agreement with Geant4 predictions. The many studies carried out in the ProtoDUNE-SP experi ment wil l be useful for current and future neutrino experiments using LArTPC technology including ICARUS, MicroBooNE, DUNE

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1985

Theoretical spectral distributions and total cross sections for neutral subthreshold pion production in carbon-carbon collisions

A coherent isobar formalism is employed to model subthreshold production of neutral pions in carbon-carbon collisions at energies below 100 MeV/nucleon. No arbitrary scale factors or adjustable free parameters are used in calculation of the Lorentz-invariant cross sections for pion production in the projectile, which produces an excited state that goes to M1 resonance in the target by conservation of spin and isospin. Pion production is also modeled for the projectile, which also reaches M1 resonance. The overall pion spectral distribution in the center of mass system is then integrated over the energy range 35-84 MeV/nucleon. The results expose an energy loss in the incident ions, as observed experimentally, and indicate that an isobar mechanism is responsible for higher energy pion production. Lower energy pions are a result of thermal processes.

Norbury, J. W.↗
NASA NTRS2010

Pion Production Data Needed for Space Radiation

A recent discovery concerning the importance of hadron production in space radiation is that pions can contribute up to twenty percent of the dose from galactic cosmic ray interactions (S. Aghara, S. Blattnig, J. Norbury, R. Singleterry, Nuclear Instruments and Methods, Vol. 267, 2009, p. 1115). Although the contribution for dose equivalent will be smaller, the dose contribution could be important for fluence based radiation models. Pion production cross sections will be an essential ingredient to such models, and it is of interest to investigate the adequacy of the pion production experimental data base for energies relevant to space radiation. The pion production threshold in nucleon - nucleon reactions is at 280 MeV and, in an interesting accident of nature, this lies near the peak of the galactic cosmic ray proton spectrum. Therefore, pion production data are needed from threshold up to energies around 50 GeV/nucleon, where the galactic cosmic ray fluence is of decreasing importance. Total and differential cross section data for pion production in this energy range will be reviewed. The availability and accuracy of theoretical models will also be discussed. It will be shown that there are a significant lack of data in this important energy range and that theoretical models still need improvement.

Norbury, John W.↗
DOE OSTI2024

Comparing pion production in transport simulations of heavy-ion collisions at 270⁢𝐴 MeV under controlled conditions

Within the TMEP, we present a detailed study of the performance of different transport models in Sn+Sn collisions at 270A MeV, and put particular emphasis on the production of pions and Delta resonances, which have been used as probes of the nuclear symmetry energy. We prescribe a common and rather simple physics model, and follow in detail the results of 4 BUU models and 6 QMD models. The nucleonic evolution of the collision and the nucleonic observables in these codes do not completely converge, but the differences among the codes can be understood as being due to several reasons: the basic differences between BUU and QMD models in the representation of the phase-space distributions, computational differences in the mean-field evaluation, and differences in the adopted strategies for the Pauli blocking in the collision integrals. For pionic observables, we find that a higher maximum density leads to an enhanced pion yield and a reduced pi- pi+ yield ratio, while a more effective Pauli blocking generally leads to a slightly suppressed pion yield and an enhanced pi- pi+ yield ratio. We specifically investigate the effect of the Coulomb force, and find that it increases the total pi- pi+ yield ratio but reduces the ratio at high pion energies, although differences in its implementations do not have a dominating role in the differences among the codes. Taking into account only the results of codes that strictly follow the homework specifications, we find a convergence of the codes in the final charged pion yield ratio to a 1 sigma deviation of about 5%. Furthermore, the uncertainty is expected to be reduced to about 1.6% if the same or similar strategies and ingredients, i.e., an improved Pauli blocking and calculation of the non-linear term in the mean-field potential, are similarly used in all codes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Near-threshold incoherent pion photoproduction on the deuteron with final-state interaction effects

Highlights: • Incoherent pion photoproduction on the deuteron near threshold is investigated including rescattering effects. • For the first time, polarization observables are predicted near threshold. • The influence of NN-FSI effect is moderate in the π{sup 0}-production. • πN-rescattering has a noticeable contribution only in the π{sup 0}-production. • The unpolarized cross sections have a satisfactory agreement with experiment and other theories. - Abstract: Incoherent pion photoproduction on the deuteron γd→πNN is investigated in the energy region E{sub γ}{sup thr}≤E{sub γ}≤ 160 MeV. The model applied contains the amplitudes of the impulse approximation as well as the NN and πN rescattering in the final state. For the elementary γN→πN amplitude, the unitary isobar MAID-2007 model is used. This model is parameterized in terms of invariant amplitudes and allows one to give a more reliable description of the threshold region. The half-off-shell NN and πN scattering amplitudes are obtained from separable representations of realistic NN and πN interactions, respectively. For the first time, numerical results for the linear photon asymmetry Σ, vector T{sub 11} and tensor T{sub 2M} (M=0,1,2) deuteron spin asymmetries for the reactions γd→π{sup −}pp, γd→π{sup +}nn, and γd→π{sup 0}np are presented. In addition, results for the unpolarized differential and total cross sections are given. We found that the influence of NN rescattering is moderate in both charged-and neutral-pion production channels, whereas πN rescattering is almost negligible in the charged-pion production channels which is not the case in neutral-pion production since a noticeable contribution is obtained. The calculated results for unpolarized differential and total cross sections are compared with the available experimental data and other theoretical models, and a satisfactory agreement is obtained.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Gluon moment and parton distribution function of the pion from 𝑁 𝑓 = 2 +1 +1 lattice QCD

We present the first calculation of the pion gluon moment from lattice QCD in the continuum-physical limit. The calculation is done using clover fermions for the valence action with three pion masses, 220, 310 and 690 MeV, and three lattice spacings, 0.09, 0.12, and 0.15 fm, using ensembles generated by MILC Collaboration with 2+1+1 flavors of highly improved staggered quarks (HISQ). On the lattice, we nonperturbatively renormalize the gluon operator in RI/MOM scheme using the cluster-decomposition error reduction (CDER) technique to enhance the signal-to-noise ratio of the renormalization constant. We extrapolate the pion gluon moment to the continuum-physical limit and obtain ⟨𝑥⟩ 𝑔 = 0.394⁢(58) stat+NPR ⁢(39) mixing in the $\overline{MS}$ scheme at 2 GeV, with first error being the statistical error and uncertainties in nonperturbative renormalization, and the second being a systematic uncertainty estimating the effect of ignoring quark mixing. Our pion gluon momentum fraction has a central value lower than two recent single-ensemble lattice-QCD results near physical pion mass but is consistent with the recent global fits by JAM and xFitter and with most QCD-model estimates.

Astronomy & Astrophysics↗
DOE OSTI2024

Pion gravitational form factors in the QCD instanton vacuum. II

We revisit the hard QCD contributions to the pion gravitational form factors, in terms of the twist-2,3 pion distribution amplitudes (DAs), including novel semihard contributions from the instantons. The pion DAs are evaluated in the QCD instanton vacuum and then properly evolved to higher resolution. The results are compared to our recent results from the QCD instanton vacuum, as well as Bethe-Salpeter calculations and recent lattice data. The interpolated hard and soft contributions to the pion D form factor are used to derive the (gravitational) pressure and shear within the pion, with a clear delineation of their range.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

A theory of dark pions

We present a complete model of a dark QCD sector with light dark pions, broadly motivated by hidden naturalness arguments. The dark quarks couple to the Standard Model via irrelevant Z- and Higgs-portal operators, which encode the low-energy effects of TeV-scale fermions interacting through Yukawa couplings with the Higgs field. The dark pions, depending on their CP properties, behave as either composite axion-like particles (ALPs) mixing with the Z or scalars mixing with the Higgs. The dark pion lifetimes fall naturally in the most interesting region for present and proposed searches for long-lived particles, at the LHC and beyond. This is demonstrated by studying in detail three benchmark scenarios for the symmetries and structure of the theory. Within a coherent framework, we analyze and compare the GeV-scale signatures of flavor-changing meson decays to dark pions, the weak-scale decays of Z and Higgs bosons to hidden hadrons, and the TeV-scale signals of the ultraviolet theory. New constraints are derived from B decays at CMS and from Z-initiated dark showers at LHCb, focusing on the displaced dimuon signature. We also emphasize the strong potential sensitivity of ATLAS and CMS to dark shower signals with large multiplicities and long lifetimes of the dark pions. As a key part of our phenomenological study, we perform a new data-driven calculation of the decays of a light ALP to exclusive hadronic Standard Model final states. The results are provided in a general form, applicable to any model with arbitrary flavor-diagonal couplings of the ALP to fermions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Generalizing the relativistic quantization condition to include all three-pion isospin channels

We present a generalization of the relativistic, finite-volume, three-particle quantization condition for non-identical pions in isosymmetric QCD. The resulting formalism allows one to use discrete finite-volume energies, determined using lattice QCD, to constrain scattering amplitudes for all possible values of two- and three-pion isospin. As for the case of identical pions considered previously, the result splits into two steps: the first defines a non-perturbative function with roots equal to the allowed energies, E n (L), in a given cubic volume with side-length L. This function depends on an intermediate three-body quantity, denoted K d f , 3 , which can thus be constrained from lattice QCD in- put. The second step is a set of integral equations relating K d f , 3 to the physical scattering amplitude, M 3 . Both of the key relations, En(L) ↔ K d f , 3 and K d f , 3 &#x2194;<!-- ↔ --> M 3 , are shown to be block-diagonal in the basis of definite three-pion isospin, Iπππ , so that one in fact recovers four independent relations, corresponding to Iπππ = 0, 1, 2, 3. We also provide the generalized threshold expansion of K d f , 3 for all channels, as well as parameterizations for all three-pion resonances present for Iπππ = 0 and Iπππ = 1. As an example of the utility of the generalized formalism, we present a toy implementation of the quantization condition for Iπππ = 0, focusing on the quantum numbers of the ω and h 1 resonances.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

The Ghent Hybrid model in NuWro: a new neutrino single-pion production model in the GeV regime

Neutrino-induced single-pion production constitutes an essential interaction channel in modern neutrino oscillation experiments, with its products building up a significant fraction of the observable hadronic final states. Frameworks of oscillation analyses strongly rely on Monte Carlo neutrino event generators, which provide theoretical predictions of neutrino interactions on nuclear targets. Thus, it is crucial to integrate state-of-the-art single-pion production models with Monte Carlo simulations to prepare for the upcoming systematics-dominated landscape of neutrino measurements. In this work, we present the implementation of the Ghent Hybrid model for neutrino-induced single-pion production in the NuWro Monte Carlo event generator. The interaction dynamics includes coherently-added contributions from nucleon resonances and a non-resonant background, merged into the pythia branching predictions in the deep-inelastic regime, as instrumented by NuWro. This neutrino-nucleon interaction model is fully incorporated into the nuclear framework of the generator, allowing it to account for the influence of both initial- and final-state nuclear medium effects. We compare the predictions of this integrated implementation with recent pion production data from accelerator-based neutrino experiments. The results of the novel model show improved agreement of the generator predictions with the data and point to the significance of the refined treatment of the description of pion-production processes beyond the ∆ region.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Pion and kaon structure functions at an electron-ion collider

Pions and kaons are, along with protons and neutrons, the main building blocks of nuclear matter. They are connected to the Goldstone modes of dynamical chiral symmetry breaking, the mechanism thought to generate all hadron mass in the visible universe. The distribution of the fundamental constituents, the quarks and gluons, is expected to be different in pions, kaons, and nucleons. However, experimental data are sparse. As a result, there has been persistent doubt about the behaviour of the pion's valence quark structure function at large Bjorken-$x$ and virtually nothing is known about the contribution of gluons. The Electron-Ion Collider (EIC) with an acceptance optimized for forward physics could provide access to structure functions over a larger kinematic region. This would allow for measurements testing if the origin of mass is encoded in the differences of gluons in pions, kaons, and nucleons, and measurements that could serve as a test of assumptions used in the extraction of structure functions and the pion and kaon form factors. Furthermore, measurements at an EIC would also allow to explore the effect of gluons at high x.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Femtoscopic correlations of identical charged pions and kaons in $pp$ collisions at $\sqrt{s}$ = 13 TeV with event-shape selection

Collective behavior has been observed in high-energy heavy-ion collisions for several decades. Collectivity is driven by the high particle multiplicities that are produced in these collisions. At the CERN Large Hadron Collider (LHC), features of collectivity have also been seen in high-multiplicity proton-proton collisions that can attain particle multiplicities comparable to peripheral Pb-Pb collisions. One of the possible signatures of collective behavior is the decrease of femtoscopic radii extracted from pion and kaon pairs emitted from high-multiplicity collisions with increasing pair transverse momentum. This decrease can be described in terms of an approximate transverse mass scaling. In the present work, femtoscopic analyses are carried out by the ALICE Collaboration on charged pion and kaon pairs produced in pp collisions at $\sqrt{s}$=13TeV from the LHC to study possible collectivity in pp collisions. The event-shape analysis method based on transverse sphericity is used to select for spherical versus jetlike events, and the effects of this selection on the femtoscopic radii for both charged pion and kaon pairs are studied. This is the first time this selection method has been applied to charged kaon pairs. An approximate transverse-mass scaling of the radii is found in all multiplicity ranges studied when the difference in the Lorentz boost for pions and kaons is taken into account. This observation does not support the hypothesis of collective expansion of hot and dense matter that should only occur in high-multiplicity events. A possible alternate explanation of the present results is based on a scenario of common emission conditions for pions and kaons in pp collisions for the multiplicity ranges studied.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Pion production in a transport model based on mean fields from chiral effective field theory

We develop a Boltzmann-Uehling-Uhlenbeck (BUU) transport model based on the Sk χm* energy density functional, which is constructed from fitting the nuclear equation of state and nucleon effective masses in asymmetric nuclear matter predicted by the two- and three-body chiral interactions as well as the binding energies of finite nuclei. This new χBUU transport model is then used to study how baryon mean-field potentials affect the kinematics of a scattering or decay process and the equilibrium properties of a hot N–Δ–π system in a box with periodic boundary conditions. We find that the inclusion of mean-field potentials in the energy conservation condition for scattering and decay processes is necessary to maintain the equilibrium numbers of N,Δ, and π. Although the baryon mean-field potentials have significant effects on the total Δ and π numbers, they only slightly affect the ratio of effective negatively to positively charged pions. We also study pion production in central 197 Au + 197 Au collisions at the incident energy of E/A = 400 MeV and compare the results with the experimental data from the Four Pi (FOPI) Collaboration at the Gesellschaft für Schwerionenforschung mbH (GSI) in Germany. We find that our model can well describe the experimental results and the threshold effect due to baryon mean-field potentials does not affect much the charged pion ratio in this model. Here, we further make predictions on pion production for the ongoing experiments of 132 Sn + 124 Sn and 108 Sn + 112 Sn at the incident energy of E/A = 270 MeV by the SAMURAI Pion-Reconstruction and Ion-Tracker (SπRIT) Collaboration at the Institute of Physical and Chemical Research (RIKEN) in Japan.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Soft pions and transport near the chiral critical point

During the expansion of a heavy ion collision, the system passes close to the $\textit{O}$(4) critical point of QCD, and thus the fluctuations of the order parameter $(σ, \overrightarrow{π}$) are expected to be enhanced. In this work, our goal is to compute how these enhanced fluctuations modify the transport coefficients of QCD near the pseudocritical point. We also make a phenomenological estimate for how chiral fluctuations could effect the momentum spectrum of soft pions. We first formulate the appropriate stochastic hydrodynamic equations close to the $\textit{O}$(4) critical point. Then, working in mean field, we determine the correlation functions of the stress tensor and the currents which result from this stochastic real-time theory, and use these correlation functions to determine the scaling behavior of the transport coefficients. The hydrodynamic theory also describes the propagation of pion waves, fixing the scaling behavior of the dispersion curve of soft pions. We present scaling functions for the shear viscosity and the charge conductivities near the pseudocritical point and estimate the absolute magnitude of the critical fluctuations to these parameters and the bulk viscosity. Using the calculated pion dispersion curve, we estimate the expected critical enhancement of soft pion yields, and this estimate provides a plausible explanation for the excess seen in experiment relative to ordinary hydrodynamic computations. Our results motivate further phenomenological and numerical work on the implications of chiral symmetry on real-time properties of thermal QCD near the pseudocritical point.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Pion distribution amplitude and quasidistributions

We extend our analysis of quasidistributions onto the pion distribution amplitude. Using the formalism of parton virtuality distribution amplitudes, we establish a connection between the pion transverse momentum dependent distribution amplitude Ψ(x,k 2 ⊥ ) and the pion quasidistribution amplitude (QDA) Q π (y,p 3 ). We build models for the QDAs from the virtuality-distribution-amplitude-based models for soft transverse momentum dependent distribution amplitudes, and analyze the p3 dependence of the resulting QDAs. As there are many models claimed to describe the primordial shape of the pion distribution amplitude, we present the p 3 -evolution patterns for models producing some popular proposals: Chernyak-Zhitnitsky, flat, and asymptotic distribution amplitude. Finally, our results may be used as a guide for future studies of the pion distribution amplitude on the lattice using the quasidistribution approach.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

In-medium $\Delta (1232)$ potential, pion production in heavy-ion collisions and the symmetry energy

Using the dcQMD transport model, the isoscalar and isovector in-medium potentials of the Δ (1232) baryon are studied and information regarding their effective strength is obtained from a comparison to experimental pion production data in heavy-ion collisions below 800 MeV/nucleon impact energy. The best description is achieved for an isoscalar potential moderately more attractive than the nucleon optical potential and a rather small isoscalar relative effective mass $m$$^{*}_{Δ}$ ≈ 0.45. For the isovector component only a constraint between the potential’s strength at saturation and the isovector effective mass difference can be extracted, which depends on quantities such as the slope of the symmetry energy and the neutron-proton effective mass difference. These results are incompatible with the usual assumption, in transport models, that the Δ (1232) and nucleon potentials are equal. The density dependence of symmetry energy can be studied using the high transverse momentum tail of pion multiplicity ratio spectra. Results are however correlated with the value of neutron-proton effective mass difference. Furthermore, this region of spectra is shown to be affected by uncertain model ingredients such as the pion potential or in-medium correction to inelastic scattering cross-sections at levels smaller than 10%. Extraction of precise constraints for the density dependence of symmetry energy above saturation will require experimental data for pion production in heavy-ion collisions below 800 MeV/nucleon impact energy and experimental values for the high transverse momentum tail of pion multiplicity ratio spectra accurate to better than 5%.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗