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NASA NTRS2019

MUSTANG Applications

Reducing nonrecurring cost and shortening the build schedule for space qualified avionics has been a recurring theme in Space Industry. The NASA Goddard Space Flight Center has leverage its heritage flight qualified design and developed a portfolio of modular avionics comprised of 22 different board designs in a form factor named MUSTANG (Modular Unified Space Technology Avionics for Next Generation) that can be utilized in a variety flight applications. Since the design has no backplane, the modules can be mixed and match to meet the needed requirements. The MUSTANG form factor is sized to fill the void between 3U and 6U form factor and with flexibility to adapting the design without relaying out the boards.

Space↗

DOE OSTI2023

$B$-meson semileptonic decays with highly improved staggered quarks

We present an update of the Fermilab Lattice and MILC Collaborations project to compute the form factors for semileptonic $B_{(s)}$-meson decays. Our calculation uses the highly improved staggered quark (HISQ) action for sea and valence quarks, and ensembles with up, down, strange, and charm quarks in the sea. Using a highly improved action with the MILC Collaboration's gauge ensembles with lattice spacings down to $a\approx0.03$ fm, allows the heavy valence quarks to be treated with the same discretization as the light and strange quarks. This unified treatment of the valence quarks allows for absolutely normalized vector currents, bypassing the need for perturbative matching, which has been a source of uncertainty in previous calculations of $B$-meson decay form factors by our collaboration. All preliminary form-factor results are blinded.

Lytle, Andrew↗

DOE OSTI2025

Recurrent features of amplitudes in planar $\mathcal{N}$ = 4 super Yang-Mills theory

The planar three-gluon form factor for the chiral stress tensor operator in planar maximally supersymmetric Yang-Mills theory is an analog of the Higgs-to-three-gluon scattering amplitude in QCD. The amplitude (symbol) bootstrap program has provided a wealth of high-loop perturbative data about this form factor, with results up to eight loops available. The symbol of the form factor at L loops is given by words of length 2L in six letters with associated integer coefficients. In this paper, we analyze this data, describing patterns of zero coefficients and relations between coefficients. We find many sequences of words whose coefficients are given by closed-form expressions which we expect to be valid at any loop order. Moreover, motivated by our previous machine-learning analysis, we identify simple recursion relations that relate the coefficient of a word to the coefficients of particular lower-loop words. These results open an exciting door for understanding scattering amplitudes at all loop orders.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1988

The ijk forms of factorization methods. I - Vector computers

This paper gives a detailed exposition of the 'ijk forms' of LU and Choleski factorization. Several aspects of these different organizations are discussed and their properties on vector computers are compared. Extensions of the ijk formalism to other algorithms is also given.

Ortega, J. M.↗

DOE OSTI2024

Improved measurement of the semileptonic decay D s + → K 0 e + ν e

Analyzing e + e − collision data corresponding to an integrated luminosity of 7.33 fb − 1 collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector, we measure the branching fraction of the semileptonic decay D s + → K 0 e + ν e to be ( 2.98 ± 0.2 3 stat ± 0.1 2 syst ) × 10 − 3 . Based on fit to the partial decay rates in various q 2 intervals, the product value of D s + → K 0 hadronic form factor and Cabibbo-Kobayashi-Maskawa element is measured to be f + K 0 ( 0 ) | V c d | = 0.143 ± 0.01 1 stat ± 0.00 3 syst . With | V c d | = 0.22486 ± 0.00067 as an input, the hadronic form factor is evaluated to be f + K 0 ( 0 ) = 0.636 ± 0.04 9 stat ± 0.01 3 syst . The branching fraction and form factor measurements are factors of 1.6 and 1.7 more precise than the previous world averages, respectively. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2020

Spectral fluctuations in the Sachdev-Ye-Kitaev model

We present a detailed quantitative analysis of spectral correlations in the Sachdev-Ye-Kitaev (SYK) model. We find that the deviations from universal Random Matrix Theory (RMT) behavior are due to a small number of long-wavelength fluctuations (of the order of the number of Majorana fermions N ) from one realization of the ensemble to the next one. These modes can be parameterized effectively in terms of Q-Hermite orthogonal polynomials, the main contribution being due to scale fluctuations for which we give a simple analytical estimate. Our numerical results for N = 32 show that only the lowest eight polynomials are needed to eliminate the nonuniversal part of the spectral fluctuations. The covariance matrix of the coefficients of this expansion can be obtained analytically from low-order double-trace moments. We evaluate the covariance matrix of the first six moments and find that it agrees with the numerics. We also analyze the spectral correlations in terms of a nonlinear σ-model, which is derived through a Fierz transformation, and evaluate the one and two-point spectral correlation functions to two-loop order. The wide correlator is given by the sum of the universal RMT result and corrections whose lowest-order term corresponds to scale fluctuations. However, the loop expansion of the σ-model results in an ill-behaved expansion of the resolvent, and it gives universal RMT fluctuations not only for q= 4 or higher even q-body interactions, but also for the q= 2 SYK model albeit with a much smaller Thouless energy while the correct result in this case should have been Poisson statistics. In our numerical studies we analyze the number variance and spectral form factor for N = 32 and q = 4. We show that the quadratic deviation of the number variance for large energies appears as a peak for small times in the spectral form factor. After eliminating the long-wavelength fluctuations, we find quantitative agreement with RMT up to an exponentially large number of level spacings for the number variance or exponentially short times in the case of the spectral form factor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Strange and charm quark spins from the anomalous Ward identity

In this article, we present a calculation of the strange and charm quark contributions to the nucleon spin from the anomalous Ward identity (AWI). This is performed with overlap valence quarks on 2 + 1 -flavor domain-wall fermion gauge configurations on a 2 4 3 × 64 lattice with lattice spacing a - 1 = 1.73 GeV and the light sea mass at m π = 330 MeV . To satisfy the AWI, the overlap fermion for the pseudoscalar density and the overlap Dirac operator for the topological density, which do not have multiplicative renormalization, are used to normalize the form factor of the local axial-vector current at finite q 2 . For the charm quark, we find that the negative pseudoscalar term almost cancels the positive topological term. For the strange quark, the pseudoscalar term is less negative than that of the charm. By imposing the AWI, the strange g A ( q 2 ) at q 2 = 0 is obtained by a global fit of the pseudoscalar and the topological form factors, together with g A ( q 2 ) and the induced pseudoscalar form factor h A ( q 2 ) at finite q 2 . The chiral extrapolation to the physical pion mass gives Δ s + Δ s ¯ = - 0.0403 ( 44 ) ( 78 ) .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Model-independent description of B → D π ℓ ν decays

We introduce a new parametrization of B → D π ℓ ν form factors using a partial-wave expansion and derive bounds on the series coefficients using analyticity and unitarity. This is the first generalization of the model-independent formalism developed by Boyd, Grinstein, and Lebed for B → D ℓ ν to semileptonic decays with multihadron final states, and enables data-driven form-factor determinations with robust, systematically improvable uncertainties. Using this formalism, we extract the form-factor parameters for B → D 2 * ( → D π ) ℓ ν decays in a model-independent way from fits of data from the Belle Experiment. We find that the semileptonic data are compatible with the presence of two poles in the D π S-wave channel, which is the scenario preferred by nonleptonic decays and unitarized chiral perturbation theory. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Energy momentum tensor on and off the light cone: exposition with scalar Yukawa theory

Abstract We compute the gravitational form factorsA i ,D i and$$ {\overline{c}}_i $$ c ¯ i of the scalar Yukawa theory using both the light-cone and covariant perturbation theory at the one-loop level. The light-cone formalism provides a potential approach to access these form factors beyond the perturbative regime. However, unlike the covariant formulation, the Poincaré symmetry on the light cone is not manifest. In this work, we use perturbation theory as a benchmark to extract the gravitational form factors from the light-front energy-momentum tensor. By comparing results on and off the light cone, we identifyT ++ ,T +a ,T +− ,T 12 as the “good currents” that are properly renormalized and can be used to extract the gravitational form factors.

Physics↗

DOE OSTI2024

Dissecting a strongly coupled scalar nucleon

We continue our investigation of the stress within a strongly coupled scalar nucleon, and now dissect the gravitational form factors into contributions from its constituents, the (mock) nucleon and the (mock) pion. The computation is based on a nonperturbative solution of the scalar Yukawa model in the light-front Hamiltonian formalism with a Fock sector expansion, including up to one nucleon and two pions. By employing the “good currents” T i + + , T i + − and T i 12 , we extract the full set of gravitational form factors A i , D i , c ¯ i without the contamination of the spurious form factors and free of uncanceled UV divergences. With these results, we decompose the mass of the system into its constituents and compute the matter and mechanical radii, gaining insights into the strongly coupled system. Published by the American Physical Society 2024

Cao, Xianghui (ORCID:0009000359096713)↗

DOE OSTI2016

The 3H-3He Charge Radii Difference

The upcoming E12-14-009 [1] experiment at Jefferson Lab will determine the ratio of the electric form factors for the A=3 mirror nuclei 3He and 3H. The measurement will use a 1.1 GeV electron beam, a special collimator plate to allow for simultaneous optics measurements, and the low-activity tritium target being prepared for Jefferson Lab. By observing the dependence of the form factor ratio as a function of Q2 over 0.05–0.09 GeV2, the dependence of the radii extraction on the shape of the form factors is minimized. As a result, we anticipate the uncertainty of the extracted charge radii difference to be 0.03 fm, a reduction of 70% from the current measurement. Using precise measurements of the 3He charge radius from isotopic shift or μHe measurements [2–4], we can deduce the absolute 3H charge radius. The results will provide a direct comparison to recent calculations of the charge radii.

Myers, Luke S.↗

DOE OSTI2021

B- and D-meson semileptonic decays with highly improved staggered quarks

We present results for $B_{(s)}$- and $D_{(s)}$-meson semileptonic decays from ongoing calculations by the Fermilab Lattice and MILC Collaborations. Our calculation employs the highly improved staggered quark (HISQ) action for both sea and valence quarks and includes several ensembles with physical-mass up, down, strange, and charm quarks and lattice spacings ranging from $a\approx0.15$ fm down to 0.06 fm. At most lattice spacings, an ensemble with physical-mass light quarks is included. The use of the highly improved action, combined with the MILC Collaboration's gauge ensembles with lattice spacings down to $a\approx0.042$ fm, allows heavy valence quarks to be treated with the same discretization as the light and strange quarks. This unified treatment of the valence quarks allows (in some cases) for absolutely normalized currents, bypassing the need for perturbative matching, which has been a leading source of uncertainty in previous calculations of $B$-meson decay form factors by our collaboration. All preliminary form-factor results are blinded.

Jay, William I.↗

DOE OSTI2018

Spectroscopy of a one-dimensional V-shaped quantum well with a point impurity

We consider the one-dimensional Hamiltonian with a V-shaped potential H{sub 0}=(1/2) [−((d{sup 2})/(dx{sup 2}))+|x|], decorated with a point impurity of either δ-type, or local δ{sup ′}-type or even nonlocal δ{sup ′}-type, thus yielding three exactly solvable models. We analyse the behaviour of the change in the energy levels when an interaction of the type −λ δ(x) or −λ δ(x−x{sub 0}) is switched on. In the first case, even energy levels, pertaining to antisymmetric bound states, remain invariant with respect to λ even though odd energy levels, pertaining to symmetric bound states, decrease as λ increases. In the second, all energy levels decrease when the factor λ increases. A similar study has been performed for the so-called nonlocal δ{sup ′} interaction, requiring a coupling constant renormalisation, which implies the replacement of the form factor λ by a renormalised form factor β. In terms of β, odd energy levels are unchanged. However, we show the existence of level crossings: after a fixed value of β the energy of each even level, with the natural exception of the first one, becomes lower than the constant energy of the previous odd level. Finally, we consider an interaction of the type −λδ(x)+μδ{sup ′}(x), and analyse in detail the discrete spectrum of the resulting self-adjoint Hamiltonian.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Twist-three cross-sections in deeply virtual Compton scattering

We study the deeply virtual Compton scattering process with both twist-two and twist-three Compton form factors and present our cross-sections formulas with all polarization configurations. While the twist-three contributions are generally assumed to be negligible in the literature due to the kinematical suppression, we compare them with the twist-two ones at typical JLab 6 GeV and 12 GeV kinematics as well as EIC kinematics and show their kinematical suppression explicitly, justifying the leading-twist approximation made in the literature. In addition, we also estimate the twist-three Compton form factors using Wandzura-Wilczek relations and inputs of twist-two generalized parton distributions based on a reggeized spectator model. With those estimated Compton form factors, we analyze the kinematical behavior of twist-two and twist-three cross-sections in a wide range of kinematics, and discuss the optimal regions for separating the leading-twist effects from the higher-twist ones.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Penguin-like diagrams from the standard model

The Standard Model is highly successful in describing the interactions of leptons and quarks. There are, however, rare processes that involve higher order effects in electroweak interactions. One specific class of processes is the penguin-like diagram. Such class of diagrams involves the neutral change of quark flavours accompanied by the emission of a gluon (gluon penguin), a photon (photon penguin), a gluon and a photon (gluon-photon penguin), a Z-boson (Z penguin), or a Higgs-boson (Higgs penguin). Such diagrams do not arise at the tree level in the Standard Model. They are, however, induced by one-loop effects. In this paper, we present an exact calculation of the penguin diagram vertices in the ‘tHooft-Feynman gauge. Renormalization of the vertex is effected by a prescription by Chia and Chong which gives an expression for the counter term identical to that obtained by employing Ward-Takahashi identity. The on-shell vertex functions for the penguin diagram vertices are obtained. The various penguin diagram vertex functions are related to one another via Ward-Takahashi identity. From these, a set of relations is obtained connecting the vertex form factors of various penguin diagrams. Explicit expressions for the gluon-photon penguin vertex form factors are obtained, and their contributions to the flavor changing processes estimated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

Study of the e + e - → K + K - reaction in the energy range from 2.6 to 8.0 GeV

The e + e - →K + K - cross section and charged-kaon electromagnetic form factor are measured in the e + e - center-of-mass energy range (E) from 2.6 to 8.0 GeV using the initial-state radiation technique with an undetected photon. The study is performed using 469 fb-1 of data collected with the BABAR detector at the PEP-II2 e + e - collider at center-of-mass energies near 10.6 GeV. The form factor is found to decrease with energy faster than 1/E 2 and approaches the asymptotic QCD prediction. Production of the K + K - final state through the J/ψ and ψ(2S) intermediate states is observed. The results for the kaon form factor are used together with data from other experiments to perform a model-independent determination of the relative phases between electromagnetic (single-photon) and strong amplitudes in J/ψ and ψ(2S)→K + K - decays. The values of the branching fractions measured in the reaction e + e - →K + K - are shifted relative to their true values due to interference between resonant and nonresonant amplitudes. The values of these shifts are determined to be about ±5% for the J/ψ meson and ±15% for the ψ(2S) meson.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Variational Calculation of the Ground State of Closed-Shell Nuclei Up to $A$ = 40

Variational calculations of ground-state properties of 4He, 16O and 40Ca are carried out employing realistic phenomenological two- and three-nucleon potentials. The trial wave function includes twoand three-body correlations acting on a product of single-particle determinants. Expectation values are evaluated with a cluster expansion for the spin-isospin dependent correlations considering up to five-body cluster terms. The optimal wave function is obtained by minimizing the energy expectation value over a set of up to 20 parameters by means of a nonlinear optimization library. We present results for the binding energy, charge radius, point density, single-nucleon momentum distribution, charge form factor, and Coulomb sum rule. We find that the employed three-nucleon interaction becomes repulsive for A ≥ 16. In 16O the inclusion of such a force provides a better description of the properties of the nucleus. In 40Ca instead, the repulsive behavior of the three-body interaction fails to reproduce experimental data for the charge radius and the charge form factor. We find that the high-momentum region of the momentum distributions, determined by the short-range terms of nuclear correlations, exhibit a universal behavior independent of the particular nucleus. The comparison of the Coulomb sum rules for 4He, 16O, and 40Ca reported in this work will help elucidate in-medium modifications of the nucleon form factors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2017

Connecting different TMD factorization formalisms in QCD

In the original Collins-Soper-Sterman (CSS) presentation of the results of transverse-momentum-dependent (TMD) factorization for the Drell-Yan process, results for perturbative coefficients can be obtained from calculations for collinear factorization. Here we show how to use these results, plus known results for the quark form factor, to obtain coefficients for TMD factorization in more recent formulations, e.g., that due to Collins, and apply them to known results at order $\alpha_s^2$ and $\alpha_s^3$. We also show that the ``non-perturbative'' functions as obtained from fits to data are equal in the two schemes. We compile the higher-order perturbative inputs needed for the updated CSS scheme by appealing to results obtained in a variety of different formalisms. In addition, we derive the connection between both versions of the CSS formalism and several formalisms based in soft-collinear effective theory (SCET). As a result, our work uses some important new results for factorization for the quark form factor, which we derive.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗