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Parameterizations of Pion Energy Spectrum in Nucleon-Nucleon Collisions

The effects of pion (PI) production are expected to play an important role in radiation exposures in the upper atmosphere or on the Martian surface. Nuclear databases for describing pion production are developed for radiation transport codes to support these studies. We analyze the secondary energy spectrum of pions produced in nucleon-nucleon (NN) collisions in the relativistic one-pion exchange model. Parametric formulas of the isospin cross sections for one-pion production channels are discussed and are used to renormalize the model spectrum. Energy spectra for the deuteron related channels (NN yields dPi) are also described.

Cucinotta, Franics A.

Medium Modified Nucleon-Nucleon Cross Sections in a Nucleus

A simple reliable formalism is presented for obtaining nucleon-nucleon cross sections within a nucleus in nuclear collisions for a given projectile and target nucleus combination at a given energy for use in transport, Monte Carlo and other calculations. The method relies on extraction of these values from experiments and has been tested for absorption experiments to give excellent results.

Tripathi, R. K.

Nucleon-Nucleon Total Cross Section

The total proton-proton and neutron-proton cross sections currently used in the transport code HZETRN show significant disagreement with experiment in the GeV and EeV energy ranges. The GeV range is near the region of maximum cosmic ray intensity. It is therefore important to correct these cross sections, so that predictions of space radiation environments will be accurate. Parameterizations of nucleon-nucleon total cross sections are developed which are accurate over the entire energy range of the cosmic ray spectrum.

Norbury, John W.

Pion Total Cross Section in Nucleon - Nucleon Collisions

Total cross section parameterizations for neutral and charged pion production in nucleon - nucleon collisions are compared to experimental data over the projectile momentum range from threshold to 300 GeV. Both proton - proton and proton - neutron reactions are considered. Overall excellent agreement between parameterizations and experiment is found, except for notable disagreements near threshold. In addition, the hypothesis that the neutral pion production cross section can be obtained from the average charged pion cross section is checked. The theoretical formulas presented in the paper obey this hypothesis for projectile momenta below 500 GeV. The results presented provide a test of engineering tools used to calculate the pion component of space radiation.

Norbury, John W.

Bayesian analysis of nucleon-nucleon scattering data in pionless effective field theory

We perform Bayesian model calibration of two-nucleon (NN) low-energy constants (LECs) appearing in an NN interaction based on pionless effective field theory (πEFT). The calibration is carried out for potentials constructed using naive dimensional analysis in NN relative momenta (p) up to next-to-leading order [NLO, O(p 2 )] and next-to-next-to-next-to-leading order [N3LO, O(p 4 )]. We consider two classes of pionless πEFT potential: one that acts in all partial waves and another that is dominated by s-wave physics. The two classes produce broadly similar results for calibrations to NN data up to E lab = 5 MeV. Our analysis accounts for the correlated uncertainties that arise from the truncation of the pionless πEFT. We simultaneously estimate both the πEFT LECs and the parameters that quantify the truncation error. This permits the first quantitative estimates of the pionless πEFT breakdown scale, Λ b : the 95% intervals are Λ b ∈[50.11,63.03] MeV at NLO and Λ b ∈[72.27,88.54] MeV at N3LO. Furthermore, invoking naive dimensional analysis for the NN potential, therefore, does not lead to consistent results across orders in pionless πEFT. This exemplifies the possible use of Bayesian tools to identify inconsistencies in a proposed EFT power counting.

Bayesian methods

Total Cross Section Parameterizations for Pion Production in Nucleon-Nucleon Collisions

Total cross section parameterizations for neutral and charged pion production in nucleon-nuelcon collisions are compared to an extensive set of experimental data over the projectile momentum range from threshold to 300 GeV. Both proton-proton and proton-neutron reactions are considered. Good agreement between parameterizations and experiment is found, and therefore the parameterizations will be useful for applications, such as transport codes.

Norbury, John W.

String-based parametrization of nucleon GPDs at any skewness: A comparison to lattice QCD

We introduce a string-based parametrization for nucleon quark and gluon generalized parton distributions (GPDs) valid at all skewness values. The conformal moments of the GPDs are expressed as sums of the spin-j nucleon A-form factor and the skewness-dependent spin-j nucleon D-form factor. This representation, which fulfills the polynomiality condition (due to Lorentz invariance) and does not rely on model-specific assumptions, is derived from t-channel string exchanges in anti-de Sitter spaces. The spin-j nucleon D-form factor is closely related to the spin-j nucleon A-form factor. We use the Mellin moments from empirical parton distributions to model the spin-j nucleon A-form factors. Using only five Regge slope parameters, fixed from the electromagnetic and gravitational form factors, our string-based parametrization generates accurate singlet, nonsinglet, isovector, and flavor-separated nucleon quark GPDs, along with symmetric nucleon gluon GPDs from their Mellin-Barnes integral representations. Our isovector nucleon quark GPD is in agreement with existing lattice data. Our string-based parametrization should facilitate the empirical extraction and global analysis of nucleon GPDs in exclusive processes, bypassing the deconvolution challenge.

Electron-ion collisions

Inclusive studies of two- and three-nucleon short-range correlations in 3 H and 3 He

Inclusive electron scattering at carefully chosen kinematics can isolate scattering from the high-momentum nucleons in short-range correlations (SRCs). SRCs are produced by the hard, short-distance interactions of nucleons in the nucleus, and because the two-nucleon (2N) SRCs arise from the same N-N interaction in all nuclei, the cross section in the SRC-dominated regime is identical up to an overall scaling factor. This scaling behavior has been used to identify SRC dominance and to measure the contribution of SRCs in a wide range of nuclei. We examine this scaling behavior over a range of momentum transfers using new data on 2 H, 3 H, and 3 He, and find an expanded scaling region compared to heavy nuclei. Motivated by this improved scaling, we examine the 3 H and 3 He data in kinematics where three-nucleon SRCs may play an important role. The data for the largest struck nucleon momenta are consistent with isolation of scattering from three-nucleon SRCs, and suggest that the very highest momentum nucleons in 3 He have a nearly isospin-independent momentum configuration.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Nucleon Structure Studies at Jefferson Lab and the Electron Ion Collider

The research programs of Thomas Jefferson Laboratory (JLab) and the future Electron- Ion Collider (EIC) focus on one of the main goals of strong interaction studies : understanding the structure of nucleons in terms of the quarks and gluons composing them. Their structure is encoded in functions such as Generalized Parton Distributions (GPDs), which describe how quarks and gluons’ transverse position and longitudinal momentum are distributed inside nucleons. GPDs allow to obtain three-dimensional pictures of nucleons and to understand some of their fundamental properties, such as their internal pressure or the emergence of their spin from the dynamics of the partons composing them. At JLab and the EIC, electron beams are used to probe nucleons. Measurement of reactions such as Deeply Virtual Compton Scattering (DVCS) allows access to GPDs. The first longitudinally polarized-target experiment of the CLAS12 program at Jlab took place in 2022-2023. Combining polarized electron beams and nucleon targets, this experiment offers unique access to observables that allow the measurement of different types of GPDs. In particular, the DVCS beam- and target-spin asymmetries for protons and neutrons in deuterium will be measured for the first time. They give access to kinds of GPDs that are still poorly known, and the comparison between proton and neutron data will allow the extraction of the flavor dependence of the structure of nucleons. Specific analysis methods have been implemented to work with a polarized nuclear target and are presented in this thesis. These methods allow to obtain preliminary results for the asymmetries, waiting for the complete statistics to be available. In the long term, the experimental program for the EIC has been established with a strong emphasis on the measurement of the structure of nucleons at high energy. Measurements of reactions such as DVCS impose strict requirements on the electromagnetic calorimeter that will allow to measure the energy of the scattered electrons and photons. This calorimeter, which is under development, will be based on scintillating crystals read by Silicon Photomultipliers (SiPMs). A new type of glass-based scintillating material was tested, evaluating the possibilities to meet the technical requirements concerning their light yield and resistance to radiation damage in particular. Several models of SiPMs have been characterized, demonstrating they can operate over the vast energy range necessary to address the physics case at the EIC and providing guidelines for developing their readout electronics.

Pilleux, Noemie

Constraints on the finite volume two-nucleon spectrum at 𝑚𝜋 ≈806 MeV

The low-energy, finite-volume spectrum of the two-nucleon system at a quark mass corresponding to a pion mass of 𝑚𝜋≈806 MeV is studied with lattice quantum chromodynamics (LQCD) using variational methods. The interpolating-operator sets used in [Variational study of two-nucleon systems with lattice QCD, Phys. Rev. D 107, 094508 (2023).] are extended by including a complete basis of local hexaquark operators, as well as plane-wave dibaryon operators built from products of both positive- and negative-parity nucleon operators. Results are presented for the isosinglet and isotriplet two-nucleon channels. In both channels, noticeably weaker variational bounds on the lowest few energy eigenvalues are obtained from operator sets which contain only hexaquark operators or operators constructed from the product of two negative-parity nucleons, while other operator sets produce low-energy variational bounds which are consistent within statistical uncertainties. The consequences of these studies for the LQCD understanding of the two-nucleon spectrum are investigated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Di-nucleons do not form bound states at heavy pion mass

We perform a high-statistics lattice QCD calculation of the low-energy two-nucleon scattering amplitudes. To address discrepancies in the literature, the calculation is performed at a heavy pion mass in the limit that the light quark masses are equal to the physical strange quark mass, 𝑚 𝜋 = 𝑚 𝐾 ≃ 714 MeV. Using a state-of-the-art momentum space method, we rule out the presence of a bound di-nucleon in both the isospin 0 (deuteron) and 1 (di-neutron) channels, in contrast with many previous results that made use of compact hexaquark creation operators. To diagnose the discrepancy, we add such hexaquark interpolating operators to our basis and find that they do not affect the determination of the two-nucleon finite-volume spectrum, and thus they do not couple to deeply bound di-nucleons that are missed by the momentum-space operators. Furthermore, we perform a high-statistics calculation of the HAL QCD potential on the same gauge ensembles and find qualitative agreement with our main results. We conclude that di-nucleons do not form bound states at heavy pion masses and that previous identification of deeply bound di-nucleons must have arisen from a misidentification of the spectrum from off-diagonal elements of a correlation function.

Physics - Physics of elementary particles and fiel

Toward the determination of 𝐶⁢𝑃-odd pion-nucleon couplings

The nucleon matrix elements (NMEs) associated with quark chromomagnetic dipole moments (cMDMs) play a crucial role in determining the 𝐶𝑃-odd pion-nucleon couplings induced by quark chromoelectric dipole moments. In recent years, it has been argued that the NMEs of cMDMs can be related to the third moment of the nucleon's higher-twist (specifically, twist-3) parton distribution function (PDF) 𝑒⁡(𝑥), which can, in principle, be measured through dihadron production in semi-inclusive deep inelastic scattering processes. By applying the spin-flavor expansion to the cMDM operators in the large-𝑁 𝑐 limit, where 𝑁 𝑐 is the number of quark colors, we show that the NMEs receive contributions not only from the twist-3 PDF 𝑒⁡(𝑥) but also from an additional, previously neglected nucleon form factor. Incorporating constraints from the spin-flavor expansion, recent experimental data on 𝑒⁡(𝑥), as well as model calculations of 𝑒⁡(𝑥), we estimate the NMEs of the cMDM operators. Our analysis indicates that the NMEs are dominated by the nucleon form factors, and the cMDM contributions to pion-nucleon couplings can be comparable to those from the quark sigma terms.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Di-nucleons do not form bound states at heavy pion mass

We perform a high-statistics lattice QCD calculation of the low-energy two-nucleon scattering amplitudes. In order to address discrepancies in the literature, the calculation is performed at a heavy pion mass in the limit that the light quark masses are equal to the physical strange quark mass, $m_π= m_K \simeq 714 $ MeV. Using a state-of-the-art momentum space method, we rule out the presence of a bound di-nucleon in both the isospin 0 (deuteron) and 1 (di-neutron) channels, in contrast with many previous results that made use of compact hexaquark creation operators. In order to diagnose the discrepancy, we add such hexaquark interpolating operators to our basis and find that they do not affect the determination of the two-nucleon finite volume spectrum, and thus they do not couple to deeply bound di-nucleons that are missed by the momentum-space operators. Further, we perform a high-statistics calculation of the HAL QCD potential on the same gauge ensembles and find qualitative agreement with our main results. We conclude that two-nucleons do not form bound states at heavy pion masses and that previous identification of deeply bound di-nucleons must have arisen from a misidentification of the spectrum from off-diagonal elements of a correlation function.

FOS: Physical sciences

Interstellar propagation of galactic cosmic-ray nuclei 2 less than or equal to Z less than or equal to 8 in the energy range 10 to 1000 MeV per nucleon.

Analysis of the differential kinetic energy per nucleon spectra of galactic cosmic-ray He, Li, Be, B, C, N, and O with the University of Chicago cosmic-ray telescope on board the IMP-5 satellite in 1969-1970. The ratios He/(C + N + O) and (Li + Be + B)/(C + N + O) obtained from these spectra are found, within errors of about 20%, to be energy-independent over the energy range 10-1000 MeV per nucleon, and equal to about 15 and about 0.25, respectively. These results are compared with discrepancies existing among other measurements of these ratios, and with predictions of a class of steady-state models of cosmic-ray propagation which assume that Li, Be, and B are absent in cosmic-ray sources. The best fits for the present measurements are obtained for models with a source spectrum in the form of a power law in total energy per nucleon, but even these fits are outside the error limits at energies below 100 MeV per nucleon. In the context of the propagation models examined, it is concluded that the observed behavior of these ratios requires an additional mechanism operative at low energies. This mechanism may be adiabatic deceleration of cosmic rays in the solar wind. In order for this mechanism to be adiabatic deceleration, the deceleration in 1969 must have been such that particles observed at 10 to 20 MeV per nucleon had energies greater than 100 to 150 MeV per nucleon in the local interstellar space.

Mason, G. M.

Chiral properties of the nucleon interpolating current and θ-dependent observables

We revisit the chiral properties of nucleon interpolating currents, and show that of the two leading order currents j 1 and j 2 , only two linear combinations j 1 ± j 2 transform covariantly under the anomalous U⁢(1) A symmetry. As a result, calculations of quantities which vanish by symmetry in the chiral limit may produce unphysical results if carried out with different linear combinations of the currents. This includes observables such as electric dipole moments, induced by the quantum chromodynamics (QCD) parameter θ, and the θ-dependence of the nucleon mass. For completeness, we also exhibit the leading order results for nucleon electric dipole moments (d n,p ) induced by θ, and the nucleon magnetic moments (μ n,p ), when calculated using QCD sum rules for both the covariant choices of the nucleon interpolating current. The results in each channel, conveniently expressed as the ratios, d n,p /μ n,p , are numerically consistent, and reflect the required physical dependence on θ.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS