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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Gluon parton distribution of the pion from lattice QCD

We present the first determination of the x-dependent pion gluon distribution from lattice QCD using the pseudo-PDF approach. We use lattice ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration, at two lattice spacings a ≈ 0.12 and 0.15 fm and three pion masses M π ≈ 220, 310 and 690 MeV. We use clover fermions for the valence action and momentum smearing to achieve pion boost momentum up to 2.29 GeV. We find that the dependence of the pion gluon parton distribution on lattice spacing and pion mass is mild. We compare our results from the lightest pion mass ensemble with the determination by JAM and xFitter global fits.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

First simultaneous global QCD analysis of kaon and pion parton distributions with lattice QCD constraints

We perform the first simultaneous global QCD analysis of pion and kaon parton distribution functions (PDFs) constrained by pion- and kaon-induced Drell-Yan (DY) and leading neutron electroproduction data together with lattice QCD data on pion and kaon PDF moments. The analysis indicates a softer valence u ¯ distribution in the K − than in the π − and a significantly more peaked valence s -quark density in K − compared with the u ¯ . The effective exponent governing the high- x behavior of the PDF is found to be larger for u ¯ in the kaon, β u ¯ K − = 1.6 ( 2 ) , than in the pion, β u ¯ π − = 1.16 ( 4 ) , in the range 0.7 ≤ x ≤ 0.95 . From the gluon momentum fractions, we find the pion’s gluon content accounts for ≈ 1 / 3 of the mass budget of the pion at μ = 2 GeV , but only ≈ 1 / 4 for the kaon.

Barry, P. C. [Argonne National Laboratory] (ORCID:↗
DOE OSTI2019

Electroweak pion production on nuclei within the extended factorization scheme

We have applied the extended factorization scheme to investigate the electroweak pion production on nuclei. The ANL-Osaka model, which was obtained by analyzing the data of πN, γN, N(e,e'π), and N(ν,μπ) reactions up to invariant mass W=2GeV, is used to generate the matrix elements of current operators relevant to pion production off the nucleon. Medium effects on the Δ (1232) component of the meson-exchange current are included by using a Δ-nucleus potential determined from the previous Δ-hole model studies of pion-nucleus reactions. Nuclear correlations in the initial target state and in the spectator system(s) are modeled using realistic hole spectral functions. As a first step, we show that the data of 12 C(e,e') up to the Δ (1232) region can be described reasonably well. The interplay between the pion production and two-body meson-exchange mechanisms is shown to be essential in improving the agreement with the data in the “dip” region, between the quasielastic and the Δ (1232) peaks. Predictions for 12 C(ν,μπ) have also been made. They can be used to estimate pion-emission rates in neutrino-nucleus cross section, which constitutes an important systematic uncertainty to the reconstructed neutrino energy. With further improvements of the Metropolis Monte Carlo techniques to account for final states comprised of more than two particles, our approach can be employed up to W=2 GeV, where two-pion production and higher mass nucleon resonances must be included for analyzing the data from accelerator-based neutrino-oscillation experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Pions in hot dense matter and their astrophysical implications

Here we study the role of pions in hot dense matter encountered in astrophysics. We find that strong interactions enhance the number density of negatively charged pions and that this enhancement can be calculated reliably for a relevant range of density and temperature by using the virial expansion. We assess the influence of pions and muons on the equation of state (EOS) and weak-interaction rates in hot dense matter. We find that thermal pions increase the proton fraction and soften the EOS. We also find that charged current weak reactions involving pions and muons $\bar{ν}_ μ + μ^– → π$ and $ν_μ + π^– → μ^–$ make an important contribution to the opacity of muon neutrinos. This could influence the dynamics of core-collapse supernovae and neutron-star mergers. Finally, we note that pion-nucleon reactions can alter the evolution of the proton fraction when weak interactions are not in equilibrium.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Photoproduction of pion pairs at high energy and small angles

Here, we explore the photoproduction mechanisms for charged and neutral pion pairs off a heavy nucleus at threshold. We calculate the production of charged pairs in the Coulomb field of the nucleus in the Born approximation using explicit expressions for the differential cross sections and their connection with the total cross section σ(γγ→π + π - ). The production of σ mesons at threshold and their subsequent decay into pions is an important mechanism and is investigated quantitatively in a framework that can be used for both charged and neutral pions. σ mesons can be produced via electromagnetic (photon exchange) or strong (ω exchange) interactions. For neutral pions, another production mechanism consists of the two-step process where charged pions are produced first and then charge exchange into two neutral pions. Differential and total cross sections are computed for each production mechanism.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Spatial and momentum imaging of the pion and kaon

We determine the leading Fock state light front wave functions (LFWFs) of the pion and kaon via light front projections of the covariant Bethe-Salpeter wave function. Using these LFWFs we study the multidimensional images of the valence quarks in the pion and kaon that are provided by their generalized parton distribution functions (GPDs) and transverse momentum dependent parton distribution functions (TMDs). Moments of the GPDs are taken to obtain the electromagnetic and gravitational form factors of the pion and kaon, and comparisons to available experimental and lattice data are made. Highlights from this study include predictions that the mean-squared impact parameter for the quarks in the pion and kaon are: ( b T 2 ) u π = 0.11 fm 2 , ( b T 2 ) s K = 0.08 fm 2 , and ( b T 2 ) u K = 0.13 fm 2 , and therefore the s quark in the kaon is much closer to the center of transverse momentum than the u quark. From the electromagnetic and gravitational form factors we find that the light-cone energy radii are about 60% smaller than the light-cone charge radii for each quark sector in the pion and kaon. A quantitative measure of the importance of the leading Fock state is obtained via comparison with a full Dyson-Schwinger equations calculation (containing an infinite tower of Fock states) for the pion form factor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Lattice QCD calculation of 𝑥-dependent meson distribution amplitudes at physical pion mass with threshold logarithm resummation

We present a lattice quantum chromodynamics (QCD) calculation of the 𝑥-dependent pion and kaon distribution amplitudes (DA) in the framework of large momentum effective theory. This calculation is performed on a fine lattice of 𝑎 = 0.076 fm at physical pion mass, with the pion boosted to 1.8 GeV and kaon boosted to 2.3 GeV. We renormalize the matrix elements in the hybrid scheme and match to Math output error with a subtraction of the leading renormalon in the Wilson-line mass. The perturbative matching is improved by resumming the large logarithms related to the small quark and gluon momenta in the soft-gluon limit. After resummation, we demonstrate that we are able to calculate a range of 𝑥 ∈[𝑥 0 ,1 − 𝑥 0 ] with 𝑥 0 = 0.25 for pion and 𝑥 0 = 0.2 for kaon with theoretical systematic errors under control. The kaon DA is shown to be slighted skewed, and narrower than pion DA. Although the 𝑥-dependence cannot be direct calculated beyond these ranges, we estimate higher moments of the pion and kaon DAs by complementing our calculation with short-distance factorization.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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↗
DOE OSTI2016

Pion Structure Function from Leading Neutron Electroproduction and SU(2) Flavor Asymmetry

We examine the efficacy of pion exchange models to simultaneously describe leading neutron electroproduction at HERA and the dbar-ubar flavor asymmetry in the proton. A detailed chi^2 analysis of the ZEUS and H1 cross sections, when combined with constraints on the pion flux from Drell-Yan data, allows regions of applicability of one-pion exchange to be delineated. The analysis disfavors several models of the pion flux used in the literature, and yields an improved extraction of the pion structure function and its uncertainties at small parton momentum fractions in the pion. We also provide estimates for leading proton structure functions in upcoming tagged deep-inelastic scattering experiments at Jefferson Lab on the deuteron with forward protons.

Melnitchouk, Wolodymyr↗
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↗