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DOE OSTI2016

Pion Electromagnetic Form Factor in Virtuality Distribution Formalism

We discuss two applications of the {\it Virtuality Distribution Amplitudes} (VDA) formalism developed in our recent papers. We start with an overview of the main properties of the pion distribution amplitude emphasizing the quantitative measures of its width, and possibility to access them through the pion transition form factor studies. We formulate the basic concepts of the VDA approach and introduce the pion {\it transverse momentum distribution amplitude} (TMDA) which plays, in a covariant Lagrangian formulation, a role similar to that of the pion wave function in the 3-dimensional Hamiltonian light-front approach. We propose simple factorized models for soft TMDAs, and use them to describe existing data on the pion transition form factor, thus fixing the scale determining the size of the transverse-momentum effects. Finally, we apply the VDA approach to the one-gluon exchange contribution for the pion electromagnetic form factor. We observe a very late $Q^2 \gtrsim 20$ GeV$^2$ onset of transition to the asymptotic pQCD predictions and show that in the $Q^2 \lesssim 10$ GeV$^2$ region there is essentially no sensitivity to the shape of the pion distribution amplitude. Furthermore, the magnitude of the one-gluon exchange contribution in this region is estimated to be an order of magnitude below the Jefferson Lab data, thus leaving the Feynman mechanism as the only one relevant to the pion electromagnetic form factor behavior for accessible $Q^2$.

Radyushkin, Anatoly V.↗

DOE OSTI2016

Pion-photon reactions and chiral dynamics in Primakoff processes at COMPASS

With the COMPASS experiment at CERN, pion-photon reactions are investigated via the Primakoff effect, implying that high-energetic pions react with the quasi-real photon field surrounding the target nuclei. The production of a single hard photon in such a pion scattering at lowest momentum transfer to the nucleus is related to pion Compton scattering. From the measured cross-section shape, the pion polarisability is determined. The COMPASS measurement is in contradiction to the earlier dedicated measurements, and rather in agreement with the theoretical expectation from chiral perturbation theory. In the same data taking, reactions with neutral and charged pions in the final state are measured and analyzed. At low energy in the pion-photon centre-of-momentum system, these reactions are governed by chiral dynamics and contain information relevant for chiral perturbation theory. At higher energies, resonances are produced and their radiative coupling is investigated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Gravitational wave from dark sector with dark pion

In this work, we investigate the spectra of gravitational waves produced by chiral symmetry breaking in dark quantum chromodynamics (dQCD) sector. The dark pion (π) can be a dark matter candidate as weakly interacting massive particle (WIMP) or strongly interacting massive particle (SIMP). For a WIMP scenario, we introduce the dQCD sector coupled to the standard model (SM) sector with classical scale invariance and investigate the annihilation process of the dark pion via the 2π → 2 SM process. For a SIMP scenario, we investigate the 3π → 2π annihilation process of the dark pion as a SIMP using chiral perturbation theory. We find that in the WIMP scenario the gravitational wave background spectra can be observed by future space gravitational wave antennas. On the other hand, when the dark pion is the SIMP dark matter with the constraints for the chiral perturbative limit and pion-pion scattering cross section, the chiral phase transition becomes crossover and then the gravitational waves are not produced.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Off-shell pion properties: Electromagnetic form factors and light-front wave functions

The off-shell pion electromagnetic form factors are explored with corresponding off-shell light-front wave functions modeled by constituent quark and antiquark. We apply the Mandelstam approach for the microscopic computation of the form factors relating the model parameters with the pion decay constant and charge radius. Analyzing the existing data on the cross sections for the Sullivan process, 1 H(e,e',π + )⁢n, Charged pion form factor between Q 2 = 0.60, and 2.45 GeV 2 . I. Measurements of the cross section for the 1 H⁡(e,e'⁢π + )⁢n reaction, we extract the off-shell pion form factor using the relation derived from the generalized Ward-Takahashi identity for the pion electromagnetic current. They are compared with our previous results from exactly solvable manifestly covariant model of a (3+1)-dimensional fermion field theory. We find that the adopted constituent quark model reproduces the extracted off-shell form factor F 1 ⁡(Q 2 ,t) from the experimental data within a few percent difference and matches well with our previous theoretical simulation which exhibits a variation of about 10% for the extracted off-shell pion form factor g(Q 2 ,t). We also identify the pion valence parton distribution function (PDF) and transverse momentum distribution (TMD) in terms of the light-front wave function and discuss their off-shell properties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Study of the charge dependence of the pion–nucleon coupling constant on the basis of data on low-energy nucleon–nucleon interactions

The relation between quantities that characterize the pion–nucleon and nucleon–nucleon interactions is studied with allowance for the fact that, at low energies, nuclear forces in nucleon–nucleon systems are mediated predominantly by one-pion exchange. On the basis of the values currently recommended for the low-energy parameters of the proton–proton interaction, the charged pion–nucleon coupling constant is evaluated at g{sub π}{sup 2}±/4π = 14.55(13). This value is in perfect agreement with the experimental value of g{sub π}{sup 2}±/4π = 14.52(26) found by the Uppsala Neutron Research Group. At the same time, the value obtained for the charged pion–nucleon coupling constant differs sizably from the value of the pion–nucleon coupling constant for neutral pions, which is g{sub π}{sup 2} 0/4π = 13.55(13). This is indicative of a substantial charge dependence of the coupling constant.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

Comparison of GiBUU calculations with MiniBooNE pion production data

Background: Neutrino-induced pion production can give important informationon the axial coupling to nucleon resonances. Furthermore, pion production represents a major background to quasielastic-like events. one pion production data from the MiniBooNE in charged current neutrino scattering in mineral oil appeared higher than expected within conventional theoretical approaches. Purpose: We aim to investigate which model parameters affect the calculated cross section and how they do this. Method: The Giessen Boltzmann–Uehling–Uhlenbeck (GiBUU) model is used for an investigation of neutrino-nucleus reactions. Results: Presented are integrated and differential cross sections for 1π{sup +} and 1π{sup 0} production before and after final state interactions in comparison with the MiniBooNE data. Conclusions: For the MiniBooNE flux all processes (QE, 1π-background, Δ, higher resonance production, DIS) contribute to the observed final state with one pion of a given charge. The uncertainty in elementary pion production cross sections leads to a corresponding uncertainty in the nuclear cross sections. Final state interactions change the shape of the muon-related observables only slightly, but they significantly change the shape of pion distributions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Bulk viscosity of nuclear matter with pions in the neutrino-trapped regime

Recent work has shown that a population of thermal pions could modify the equation of state and transport properties of hot and dense neutron-rich matter and introduce new reaction pathways to change the proton fraction. In this article we study their impact on the bulk viscosity of dense matter, focusing on the neutrino-trapped regime that would be realized in neutron star mergers and supernovae. We find that the presence of a thermal population of pions alters the bulk viscosity by modifying the EoS (via the susceptibilities) and by providing new reaction pathways to achieve beta equilibrium. In neutron star merger conditions, the bulk viscosity in neutrino-trapped npeμ matter (without pions) has its peak at temperatures of at most a couple MeV and is quite small at temperatures of tens of MeV. We find that thermal pions enhance the low-temperature peak of the bulk viscosity by a factor of a few and shift it to slightly lower temperatures. At higher temperatures, where the pion abundance is large but the bulk viscosity is traditionally small, pions can increase the bulk viscosity by an order of magnitude or more, although it is still orders of magnitude smaller than its peak value.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Pion and kaon parton distribution functions from basis light front quantization and QCD evolution

We investigate the parton distribution functions (PDFs) of the pion and the kaon by combining quantum chromodynamics (QCD) evolution with the basis light front quantization. The initial PDFs result from the light front wave functions obtained by diagonalizing the effective Hamiltonian consisting of the holographic QCD confinement potential, a complementary longitudinal confinement potential, and the color-singlet Nambu–Jona-Lasinio interactions. The valence-quark PDF of the pion, after QCD evolution, is consistent with the result from the E-0615 experiment at Fermilab. Meanwhile, the pion structure function calculated from the PDFs agrees with the ZEUS and the H1 experiments at DESY-HERA for large x. Additionally, the ratio of the up quark PDF of the kaon to that of the pion is in agreement with the NA-003 experiment at CERN. Finally, we also present the cross section for the pion-nucleus induced Drell-Yan process with the obtained pion PDFs supplemented by the PDFs of the target nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Analysis of parton distributions in a pion with Bézier parametrizations

We explore the role of parametrizations for nonperturbative QCD functions in global analyses, with a specific application to extending a phenomenological analysis of the parton distribution functions (PDFs) in the charged pion realized in the xFitter fitting framework. The parametrization dependence of PDFs in our pion fits substantially enlarges the uncertainties from the experimental sources estimated in the previous analyses. We systematically explore the parametrization dependence by employing a novel technique to automate generation of polynomial parametrizations for PDFs that makes use of Bézier curves. This technique is implemented in a ++ module that is included in the xFitter program. Our analysis reveals that the sea and gluon distributions in the pion are not well disentangled, even when considering measurements in leading-neutron deep inelastic scattering. For example, the pion PDF solutions with a vanishing gluon and large quark sea are still experimentally allowed, which elevates the importance of ongoing lattice and nonperturbative QCD calculations, together with the planned pion scattering experiments, for conclusive studies of the pion structure. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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↗