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DOE OSTI2020

𝐹 𝐾 ⁡/𝐹 𝜋 from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles

We report the results of a lattice quantum chromodynamics calculation of 𝐹 𝐾 ⁡/𝐹 𝜋 using Möbius domain-wall fermions computed on gradient-flowed 𝑁 𝑓 =2 +1 +1 highly improved staggered quark (HISQ) ensembles. The calculation is performed with five values of the pion mass ranging from 130 ≲ 𝑚 𝜋 ≲ 400 MeV , four lattice spacings of 𝑎 ∼ 0.15, 0.12, 0.09 and 0.06 fm and multiple values of the lattice volume. The interpolation/extrapolation to the physical pion and kaon mass point, the continuum, and infinite volume limits are performed with a variety of different extrapolation functions utilizing both the relevant mixed-action effective field theory expressions as well as discretization-enhanced continuum chiral perturbation theory formulas. We find that the 𝑎 ∼ 0.06 fm ensemble is helpful, but not necessary to achieve a subpercent determination of 𝐹 𝐾 ⁡/𝐹 𝜋 . We also include an estimate of the strong isospin breaking corrections and arrive at a final result of 𝐹 $\hat{K}$ + ⁡ /𝐹 $\hat{𝜋}$ + = 1.1942⁢(45) with all sources of statistical and systematic uncertainty included. This is consistent with the Flavour Lattice Averaging Group average value, providing an important benchmark for our lattice action. Combining our result with experimental measurements of the pion and kaon leptonic decays leads to a determination of |𝑉 𝑢⁢𝑠 |/|𝑉 𝑢⁢𝑑 | = 0.2311⁢(10).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Kaon mixing beyond the standard model with physical masses

We present nonperturbative results for beyond the standard model kaon mixing matrix elements in the isospin symmetric limit ( m u = m d ) of QCD, including a complete estimate of all dominant sources of systematic error. Our results are obtained from numerical simulations of lattice QCD with N f = 2 + 1 flavors of dynamical domain wall fermions. For the first time, these quantities are simulated directly at the physical pion mass m π ∼ 139 MeV for two different lattice spacings. We include data at three lattice spacings in the range a = 0.11 – 0.07 fm and with pion masses ranging from the physical value up to 450 MeV. Compared to our earlier work, we have added both direct calculations at physical quark masses and a third lattice spacing making the removal of discretization effects significantly more precise and eliminating the need for any significant mass extrapolation beyond the range of simulated data. We renormalize the lattice operators nonperturbatively using RI-SMOM off-shell schemes. These schemes eliminate the need to model and subtract nonperturbative pion poles that arises in the RI-MOM scheme and, since the calculations are performed with domain wall fermions, the unphysical mixing between chirality sectors is suppressed. Our results for the bag parameters in the MS ¯ scheme at 3 GeV are B K ≡ B 1 = 0.5240 ( 17 ) ( 54 ) , B 2 = 0.4794 ( 25 ) ( 35 ) , B 3 = 0.746 ( 13 ) ( 17 ) , B 4 = 0.897 ( 02 ) ( 10 ) and B 5 = 0.6882 ( 78 ) ( 94 ) , where the first error is from lattice uncertainties and the second is the uncertainty due to the perturbative matching to MS ¯ . Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Particle production as a function of charged-particle flattenicity in 𝑝⁢𝑝 collisions at $\sqrt{s}$ = 13 TeV

This paper reports the first measurement of the transverse momentum (𝑝 T ) spectra of primary charged pions, kaons, (anti)protons, and unidentified particles as a function of the charged-particle flattenicity in pp collisions at $\sqrt{s}$ =13 TeV. Flattenicity is a novel event shape observable that is measured in the pseudorapidity intervals covered by the V0 detector, 2.8 < 𝜂 < 5.1 and −3.7 < 𝜂 < −1.7. According to QCD-inspired phenomenological models, it shows sensitivity to multiparton interactions and is less affected by biases toward larger 𝑝 T due to local multiplicity fluctuations in the V0 acceptance than multiplicity. The analysis is performed in minimum-bias (MB) as well as in high-multiplicity events up to 𝑝 T = 20 GeV/⁢𝑐. The event selection requires at least one charged particle produced in the pseudorapidity interval |𝜂| < 1. The measured 𝑝 T distributions, average 𝑝 T , kaon-to-pion and proton-to-pion particle ratios, presented in this paper, are compared to model calculations using pythia 8 based on color strings and EPOS LHC. The modification of the 𝑝 T -spectral shapes in low-flattenicity events that have large event activity with respect to those measured in MB events develops a pronounced peak at intermediate 𝑝 T (2 < 𝑝 T < 8 GeV/𝑐), and approaches the vicinity of unity at higher 𝑝 T . The results are qualitatively described by pythia, and they show different behavior than those measured as a function of charged-particle multiplicity based on the V0M estimator.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Nucleon tensor form factors at large N c

We investigate nucleon tensor form factors in the large- N c limit. In this picture, the nucleon emerges as a state of the N c valence quarks, which were bound by pion mean fields that were created by the presence of the valence quarks self-consistently. We find that the tensor charge ( g T u − d = 0.99 ) and the anomalous tensor magnetic moment ( κ T u + d = 7.61 ) are dominated by valence quarks, while the tensor quadrupole moment ( Q T u − d = − 7.02 ) shows significant sea quark effects. We examine how these quantities vary as the average size of the pion mean field is changed, showing interpolation between nonrelativistic quark and Skyrme limits. We also observe that g T u − d and κ T u + d depend weakly on the pion mass. In contrast, Q T u − d exhibits strong enhancement near the chiral limit. The numerical results are in good agreement with available lattice quantum chromodynamics (QCD) data and provide predictions for unmeasured quantities. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Light chiral dark sector

An interesting possibility for dark matter is a scalar particle of mass of order 10 MeV-1 GeV, interacting with a U(1) gauge boson (dark photon) which mixes with the photon. We present a simple and natural model realizing this possibility. The dark matter arises as a composite pseudo-Nambu-Goldstone boson (dark pion) in a non-Abelian gauge sector, which also gives a mass to the dark photon. For a fixed non-Abelian gauge group, SU(N), and a U(1) charge of the constituent dark quarks, the model has only three free parameters: the dynamical scale of the non-Abelian gauge theory, the gauge coupling of the dark photon, and the mixing parameter between the dark and standard model photons. In particular, the gauge symmetry of the model does not allow any mass term for the dark quarks, and the stability of the dark pion is understood as a result of an accidental global symmetry. The model has a significant parameter space in which thermal relic dark pions comprise all of the dark matter, consistently with all experimental and cosmological constraints. In a corner of the parameter space, the discrepancy of the muon g-2 between experiments and the standard model prediction can also be ameliorated due to a loop contribution of the dark photon. Smoking-gun signatures of the model include a monophoton signal from the e + e - collision into a photon and a "dark rho meson." Observation of two processes in e + e - collision - the mode into the dark photon and that into the dark rho meson - would provide strong evidence for the model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Chiral phase structure of three flavor QCD at vanishing baryon number density

In this paper, we investigate the phase structure of QCD with three degenerate quark flavors as a function of the degenerate quark masses at vanishing baryon number density. We use the highly improved staggered quarks on lattices with temporal extent N τ = 6 and perform calculations for six values of quark masses, which in the continuum limit correspond to pion masses in the range 80 MeV ≲ m π ≲ 230 MeV. By analyzing the volume and temperature dependence of the chiral condensate and chiral susceptibility, we find no direct evidence for a first-order phase transition in this range of pion mass values. Finally, relying on the universal scaling behaviors of the chiral observables near an anticipated chiral critical point, we estimate an upper bound for the critical pion mass m c π ≲ 50 MeV, below which a region of first-order chiral phase transition is favored.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Octet baryon magnetic moments from lattice QCD: Approaching experiment from a three-flavor symmetric point

We used lattice QCD calculations with background magnetic fields to determine the magnetic moments of the octet baryons. Computations are performed at the physical value of the strange quark mass, and two values of the light quark mass, one corresponding to the SU(3) flavor-symmetric point, where the pion mass is m π ~ 800 MeV, and the other corresponding to a pion mass m π ~ 450 MeV. The moments are found to exhibit only mild pion-mass dependence when expressed in terms of appropriately chosen magneton units---the natural baryon magneton. This suggests that simple extrapolations can be used to determine magnetic moments at the physical point, and extrapolated results are found to agree with experiment within uncertainties. A curious pattern is revealed among the anomalous baryon magnetic moments which is linked to the constituent quark model, however, careful scrutiny exposes additional features. Relations expected to hold in the large-N c limit of QCD are studied; and, in one case, the quark model prediction is significantly closer to the extracted values than the large-N c prediction. The magnetically coupled Λ-Σ 0 system is treated in detail at the SU(3) F point, with the lattice QCD results comparing favorably with predictions based on SU(3) F symmetry. Our analysis enables the first extraction of the isovector transition magnetic polarizability. The possibility that large magnetic fields stabilize strange matter is explored, but such a scenario is found to be unlikely.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Nucleon transverse momentum-dependent parton distributions in lattice QCD: Renormalization patterns and discretization effects

Lattice QCD calculations of transverse momentum-dependent parton distribution functions (TMDs) in nucleons are presented in this paper, based on the evaluation of nucleon matrix elements of quark bilocal operators with a staple-shaped gauge connection. Both time-reversal odd effects, namely, the generalized Sivers and Boer-Mulders transverse momentum shifts, as well as time-reversal even effects, namely, the generalized transversity and one of the generalized worm-gear shifts, are studied. Results are obtained on two different n f = 2 + 1 flavor ensembles with approximately matching pion masses but very different discretization schemes: domain-wall fermions (DWF) with lattice spacing a = 0.084 fm and pion mass 297 MeV, and Wilson-clover fermions with a = 0.114 fm and pion mass 317 MeV. Comparison of the results on the two ensembles yields insight into the length scales at which lattice discretization errors are small, and into the extent to which the renormalization pattern obeyed by the continuum QCD TMD operator continues to apply in the lattice formulation. For the studied TMD observables, the results are found to be consistent between the two ensembles at sufficiently large separation of the quark fields within the operator, whereas deviations are observed in the local limit and in the case of a straight link gauge connection, which is relevant to the studies of parton distribution functions. Finally and furthermore, the lattice estimates of the generalized Sivers shift obtained here are confronted with, and are seen to tend towards, a phenomenological estimate extracted from experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Mass dependence of pseudoscalar meson elastic form factors

A continuum approach to quark-antiquark bound-states is used to determine the electromagnetic form factors of pion-like mesons with masses m 0- /GeV = 0.14, 0.47, 0.69, 0.83 on a spacelike domain that extends to Q 2 ≲ 10 GeV 2 . The results enable direct comparisons with contemporary lattice-QCD calculations of heavy-pion form factors at large values of momentum transfer and aid in understanding them. Finally, they also reveal, inter alia, that the form factor of the physical pion provides the best opportunity for verification of the factorised hard-scattering formula relevant to this class of exclusive processes and that this capacity diminishes steadily as the meson mass becomes heavier.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Parton Distribution Functions from a Light Front Hamiltonian and QCD Evolution for Light Mesons

Here, we obtain the pion and the kaon parton distribution functions from the eigenstates of a light front effective Hamiltonian in the constituent quark-antiquark representation suitable for low-momentum scale applications. By taking these scales as the only free parameters, the valence quark distribution functions of the pion, after QCD evolution, are consistent with the data from the FNAL-E615 experiment. The ratio of the up quark distribution of the kaon to that of the pion also agrees with the CERN-NA3 experiment. Supplemented by known parton distribution functions for the nucleons, we also obtain the cross section consistent with experimental data for the π - nucleus → μ + μ - X Drell-Yan process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

First-Principles Calculation of Electroweak Box Diagrams from Lattice QCD

We present the first realistic lattice QCD calculation of the $γ W$-box diagrams relevant for beta decays. The nonperturbative low-momentum integral of the $γ W$ loop is calculated using a lattice QCD simulation, complemented by the perturbative QCD result at high momenta. Using the pion semileptonic decay as an example, we demonstrate the feasibility of the method. By using domain wall fermions at the physical pion mass with multiple lattice spacings and volumes, we obtain the axial γ W -box correction to the semileptonic pion decay, $\square$$\frac{VA}{γW}|_π$ = 2.830 (11) stat (26 )syst × 10 –3 , with the total uncertainty controlled at the level of ~1% . This study sheds light on the first-principles computation of the $γ W$-box correction to the neutron decay, which plays a decisive role in the determination of $|V_ud|$ .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Gauge Theory Bootstrap

We propose the gauge theory bootstrap, a method to compute the pion S matrix that describes the low-energy physics of the strong interaction and other similar gauge theories. The phase shifts of the S 0 , P 1 , and S 2 waves obtained are in good agreement with experimental results. The only numerical inputs are the quark mass m q , the QCD scale Λ QCD , the pion mass m π , and the pion decay constant f π without any other experimental data. We make use of the form-factor bootstrap recently proposed by Karateev, Kuhn, and Penedones together with a finite energy version of the Shifman-Veinshtein-Zakharov sum rules. Published by the American Physical Society 2024

He, Yifei (ORCID:0000000213666157)↗

DOE OSTI2025

Precision beam diagnostics at the NuMI facility using muon monitor observations

The Neutrinos at the Main Injector (NuMI) facility at Fermilab delivers an intense neutrino beam for multiple experiments by producing pions that decay into neutrinos, muons, and other particles. Magnetic horns—the primary pion focusing elements in the NuMI beamline—exhibit predominantly linear optics, enabling a predictable relationship between the proton beam and the resulting pion and muon phase spaces. This study has two primary objectives: first, to evaluate and confirm the linearity of the horn focusing mechanism using analytical models and numerical simulations; and second, to demonstrate that key beam parameters—such as proton beam intensity, beam position on target, and horn current—can be extracted from muon monitor observations within this linear optics framework. Using a machine learning model trained on spill-by-spill muon monitor data, we infer the horn current with a precision of ±0.05%, the beam intensity with ±0.1%, and the beam position on target with ±0.018⁢ mm horizontally and ±0.013⁢ mm vertically. This approach provides a reliable cross-check of beam parameters, helping to reduce systematic uncertainties that are critical for future experiments such as the Deep Underground Neutrino Experiment, which will rely on the neutrino beam produced by the Long-Baseline Neutrino Facility.

Beam control↗

DOE OSTI2026

Measurement of 𝜋 0 production in $\bar{v}_μ$ charged-current interactions in the NOvA near detector

We present a high-statistics measurement of muon antineutrino-induced charged-current neutral pion production on a hydrocarbon target using the NOvA near detector. The differential cross sections as functions of the momenta and angles of the outgoing pion and muon, the squared four-momentum transfer, and the invariant mass of the hadronic system at an average neutrino energy of 2 GeV are measured and compared with predictions from various neutrino interaction models. The results agree with the GENIE prediction but suggest that other models underestimate the cross section in the Δ⁡(1232) resonance region. These results represent the most precise measurement of antineutrino-induced neutral pion production to date.

neutrino detection↗

DOE OSTI2016

Test of the CLAS12 RICH large-scale prototype in the direct proximity focusing configuration

A large-area ring-imaging Cherenkov detector has been designed to provide clean hadron identi- fication capability in the momentum range from 3 GeV/c up to 8 GeV/c for the CLAS12 experiment at the upgraded 12 GeV continuous electron beam accelerator facility of Jefferson Laboratory. The adopted solution foresees a novel hybrid optics design based on aerogel radiator, composite mirrors and highly packed and highly segmented photon detectors. Cherenkov light will either be imaged directly (forward tracks) or after two mirror reflections (large-angle tracks). We report here the results of the tests of a large-scale prototype of the RICH detector performed with the hadron beam of the CERN T9 experimental hall for the direct detection configuration. The tests demonstrated that the proposed design provides the required pion-to-kaon rejection factor of 1 : 500 in the whole momentum range.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2017

The electromagnetic Sigma-to-Lambda hyperon transition form factors at low energies

Using dispersion theory the low-energy electromagnetic form factors for the transition of a Sigma to a Lambda hyperon are related to the pion vector form factor. The additionally required input, i.e. the two-pion-Sigma-Lambda amplitudes are determined from relativistic next-to-leading-order (NLO) baryon chiral perturbation theory including the baryons from the octet and optionally from the decuplet. Pion rescattering is again taken into account by dispersion theory. It turns out that the inclusion of decuplet baryons is not an option but a necessity to obtain reasonable results. The electric transition form factor remains very small in the whole low-energy region. The magnetic transition form factor depends strongly on one not very well determined low-energy constant of the NLO Lagrangian. Furthermore, one obtains reasonable predictive power if this low-energy constant is determined from a measurement of the magnetic transition radius. Such a measurement can be performed at the future Facility for Antiproton and Ion Research (FAIR).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Identifying the nature of the QCD transition in relativistic collision of heavy nuclei with deep learning

Using deep convolutional neural network (CNN), the nature of the QCD transition can be identified from the final-state pion spectra from hybrid model simulations of heavy-ion collisions that combines a viscous hydrodynamic model with a hadronic cascade “after-burner”. Two different types of equations of state (EoS) of the medium are used in the hydrodynamic evolution. The resulting spectra in transverse momentum and azimuthal angle are used as the input data to train the neural network to distinguish different EoS. Different scenarios for the input data are studied and compared in a systematic way. A clear hierarchy is observed in the prediction accuracy when using the event-by-event, cascade-coarse-grained and event-fine-averaged spectra as input for the network, which are about 80%, 90% and 99%, respectively. A comparison with the prediction performance by deep neural network (DNN) with only the normalized pion transverse momentum spectra is also made. High-level features of pion spectra captured by a carefully-trained neural network were found to be able to distinguish the nature of the QCD transition even in a simulation scenario which is close to the experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Neutrino interaction measurements with the MicroBooNE and ArgoNeuT liquid argon time projection chambers

Abstract Precise modeling of neutrino interactions on argon is crucial for the success of future experiments such as the Deep Underground Neutrino Experiment (DUNE) and the Short-Baseline Neutrino (SBN) program, which will use liquid argon time projection chamber (LArTPC) technology. Argon is a large nucleus, and nuclear effects—both on the initial and final-state particles in the interaction—are expected to be large in neutrino–argon interactions. Therefore, measurements of neutrino scattering cross sections on argon will be of particular importance to future DUNE and SBN oscillation measurements. This article presents a review of neutrino–argon interaction measurements from the MicroBooNE and ArgoNeuT collaborations, using two LArTPC detectors that have collected data in the NuMI and Booster Neutrino Beams at Fermilab. Measurements are presented of charged-current muon neutrino scattering in the inclusive channel, the ‘0 $$\pi $$ π ’ channel (in which no pions but some number of protons may be produced), and single pion production (including production of both charged and neutral pions). Measurements of electron neutrino scattering are presented in the form of $$\nu _e+\bar{\nu }_e$$ ν e + ν ¯ e inclusive scattering cross sections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗