arXiv subjects

David G. Richards

Publications and source records attributed to David G. Richards.

At least 19 recordsLinked to original sources

arXiv2022

Towards the determination of the gluon helicity distribution in the nucleon from lattice quantum chromodynamics

We present the first exploratory lattice quantum chromodynamics (QCD) calculation of the polarized gluon Ioffe-time pseudo-distribution in the nucleon. The Ioffe-time pseudo-distribution provides a frame-independent and gauge-invariant framework to determine the gluon helicity in the nucleon from first principles. We employ a high-statistics computation using a $32^3\times 64$ lattice ensemble characterized by a $358$ MeV pion mass and a $0.094$ fm lattice spacing. We establish the pseudo-distribution approach as a feasible method to address the proton spin puzzle with successive improvements in statistical and systematic uncertainties anticipated in the future. Within the statistical precision of our data, we find a good comparison between the lattice determined polarized gluon Ioffe-time distribution and the corresponding expectations from the state-of-the-art global analyses. We find a hint for a nonzero gluon spin contribution to the proton spin from the model-independent extraction of the gluon helicity pseudo-distribution over a range of Ioffe-time, $ν\lesssim 9$.

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arXiv2022

Lattice QCD and Particle Physics

Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).

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arXiv2021

Unpolarized gluon distribution in the nucleon from lattice quantum chromodynamics

In this study, we present a determination of the unpolarized gluon Ioffe-time distribution in the nucleon from a first principles lattice quantum chromodynamics calculation. We carry out the lattice calculation on a $32^3\times 64$ ensemble with a pion mass of $358$ MeV and lattice spacing of $0.094$ fm. We construct the nucleon interpolating fields using the distillation technique, flow the gauge fields using the gradient flow, and solve the summed generalized eigenvalue problem to determine the glounic matrix elements. Combining these techniques allows us to provide a statistically well-controlled Ioffe-time distribution and unpolarized gluon PDF. We obtain the flow time independent reduced Ioffe-time pseudo-distribution, and calculate the light-cone Ioffe-time distribution and unpolarized gluon distribution function in the $\overline{\rm MS}$ scheme at $μ= 2$ GeV, neglecting the mixing of the gluon operator with the quark singlet sector. Finally, we compare our results to phenomenological determinations.

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arXiv2021

Towards High-Precision Parton Distributions From Lattice QCD via Distillation

We apply the Distillation spatial smearing program to the extraction of the unpolarized isovector valence PDF of the nucleon. The improved volume sampling and control of excited-states afforded by distillation leads to a dramatically improved determination of the requisite Ioffe-time Pseudo-distribution (pITD). The impact of higher-twist effects is subsequently explored by extending the Wilson line length present in our non-local operators to one half the spatial extent of the lattice ensemble considered. The valence PDF is extracted by analyzing both the matched Ioffe-time Distribution (ITD), as well as a direct matching of the pITD to the PDF. Through development of a novel prescription to obtain the PDF from the pITD, we establish a concerning deviation of the pITD from the expected DGLAP evolution of the pseudo-PDF. The presence of DGLAP evolution is observed once more following introduction of a discretization term into the PDF extractions. Observance and correction of this discrepancy further highlights the utility of distillation in such structure studies.

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arXiv2021

Insights into the Emergence of Mass from Studies of Pion and Kaon Structure

There are two mass generating mechanisms in the standard model of particle physics (SM). One is related to the Higgs boson and fairly well understood. The other is embedded in quantum chromodynamics (QCD), the SM's strong interaction piece; and although responsible for emergence of the roughly 1 GeV mass scale that characterises the proton and hence all observable matter, the source and impacts of this emergent hadronic mass (EHM) remain puzzling. As bound states seeded by a valence-quark and -antiquark, pseudoscalar mesons present a simpler problem in quantum field theory than that associated with the nucleon. Consequently, there is a large array of robust predictions for pion and kaon properties whose empirical validation will provide a clear window onto many effects of both mass generating mechanisms and the constructive interference between them. This has now become significant because new-era experimental facilities, in operation, construction, or planning, are capable of conducting such tests and thereby contributing greatly to resolving the puzzles of EHM. These aspects of experiment, phenomenology, and theory, along with contemporary successes and challenges, are sketched herein, simultaneously highlighting the potential gains that can accrue from a coherent effort aimed at finally reaching an understanding of the character and structure of Nature's Nambu-Goldstone modes.

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arXiv2020

Parton Distribution Functions from Ioffe Time Pseudodistributions from Lattice Calculations: Approaching the Physical Point

We present results for the unpolarized parton distribution function of the nucleon computed in lattice QCD at the physical pion mass. This is the first study of its kind employing the method of Ioffe time pseudo-distributions. Beyond the reconstruction of the Bjorken-$x$ dependence we also extract the lowest moments of the distribution function using the small Ioffe time expansion of the Ioffe time pseudo-distribution. We compare our findings with the pertinent phenomenological determinations.

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arXiv2020

Distillation at High-Momentum

Extraction of hadronic observables at finite-momenta from Lattice QCD (LQCD) is constrained by the well-known signal-to-noise problems afflicting all such LQCD calculations. Traditional quark smearing algorithms are commonly used tools to improve the statistical quality of hadronic $n$-point functions, provided operator momenta are small. The momentum smearing algorithm of Bali et al. extends the range of momenta that are cleanly accessible, and has facilitated countless novel lattice calculations. Momentum smearing has, however, not been explicitly demonstrated within the framework of distillation. In this work we extend the momentum-smearing idea, by exploring a few modifications to the distillation framework. Together with enhanced time slice sampling and expanded operator bases engendered by distillation, we find ground-state nucleon energies can be extracted reliably for $\left|\vec{p}\right|\lesssim3\text{ GeV}$ and matrix elements featuring a large momentum dependence can be resolved.

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arXiv2020

Pion valence quark distribution from current-current correlation in lattice QCD

We extract the pion valence quark distribution $q^π_{\rm v}(x)$ from lattice QCD (LQCD) calculated matrix elements of spacelike correlations of one vector and one axial vector current analyzed in terms of QCD collinear factorization, using a new short-distance matching coefficient calculated to one-loop accuracy. We derive the Ioffe time distribution of the two-current correlations in the physical limit by investigating the finite lattice spacing, volume, quark mass, and higher-twist dependencies in a simultaneous fit of matrix elements computed on four gauge ensembles. We find remarkable consistency between our extracted $q^π_{\rm v}(x)$ and that obtained from experimental data across the entire $x$-range. Further, we demonstrate that the one-loop matching coefficient relating the LQCD matrix computed in position space to the $q_{\rm v}^π(x)$ in momentum space has well-controlled behavior with Ioffe time. This justifies that LQCD calculated current-current correlations are good observables for extracting partonic structures by using QCD factorization, which complements to the global effort to extract partonic structure from experimental data.

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arXiv2020

Weak Neutral Current Axial Form Factor Using $(\barν)ν$-Nucleon Scattering and Lattice QCD Inputs

We present a determination of the neutral current weak axial charge $G^Z_A(0)=-0.654(3)_{\rm stat}(5)_{\rm sys}$ using the strange quark axial charge $G^s_A(0)$ calculated with lattice QCD. We then perform a phenomenological analysis, where we combine the strange quark electromagnetic form factor from lattice QCD with (anti)neutrino-nucleon scattering differential cross section from MiniBooNE experiments in a momentum transfer region $0.24\lesssim Q^2 \lesssim 0.71$ GeV$^2$ to determine the neutral current weak axial form factor $G^Z_A(Q^2)$ in the range of $0\lesssim Q^2\leq 1$ GeV$^2$. This yields a phenomenological value of $G^Z_A(0)=-0.687(89)_{\rm stat}(40)_{\rm sys}$. The value of $G^Z_A(0)$ constrained by the lattice QCD calculation of $G^s_A(0)$, when compared to its phenomenological determination, provides a significant improvement in precision and accuracy and can be used to provide a constraint on the fit to $G^Z_A(Q^2)$ for $Q^2>0$. This constrained fit leads to an unambiguous determination of (anti)neutrino-nucleon neutral current elastic scattering differential cross section near $Q^2=0$ and can play an important role in numerically isolating nuclear effects in this region. We show a consistent description of $G^Z_A(Q^2)$ obtained from the (anti)neutrino-nucleon scattering cross section data requires a nonzero contribution of the strange quark electromagnetic form factor. We demonstrate the robustness of our analysis by providing a post-diction of the BNL E734 experimental data.

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arXiv2019

Pion Valence Structure from Ioffe Time Pseudo-Distributions

We present a calculation of the pion valence quark distribution extracted using the formalism of reduced Ioffe time pseudo-distributions or more commonly known as pseudo-PDFs. Our calculation is carried out on two different 2+1 flavor QCD ensembles using the isotropic-clover fermion action, with lattice dimensions $24^3\times 64$ and $32^3\times 96$ at the lattice spacing of $a=0.127$ fm, and with the quark mass equivalent to a pion mass of $m_π\simeq 415$ MeV. We incorporate several combinations of smeared-point and smeared-smeared pion source-sink interpolation fields in obtaining the lattice QCD matrix elements using the summation method. After one-loop perturbative matching and combining the pseudo-distributions from these two ensembles, we extract the pion valence quark distribution using a phenomenological functional form motivated by the global fits of parton distribution functions. We also calculate the lowest four moments of the pion quark distribution through the "OPE without OPE". We present a qualitative comparison between our lattice QCD extraction of the pion valence quark distribution with that obtained from global fits and previous lattice QCD calculations.

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arXiv2019

Pion and Kaon Structure at the Electron-Ion Collider

Understanding the origin and dynamics of hadron structure and in turn that of atomic nuclei is a central goal of nuclear physics. This challenge entails the questions of how does the roughly 1 GeV mass-scale that characterizes atomic nuclei appear; why does it have the observed value; and, enigmatically, why are the composite Nambu-Goldstone (NG) bosons in quantum chromodynamics (QCD) abnormally light in comparison? In this perspective, we provide an analysis of the mass budget of the pion and proton in QCD; discuss the special role of the kaon, which lies near the boundary between dominance of strong and Higgs mass-generation mechanisms; and explain the need for a coherent effort in QCD phenomenology and continuum calculations, in exa-scale computing as provided by lattice QCD, and in experiments to make progress in understanding the origins of hadron masses and the distribution of that mass within them. We compare the unique capabilities foreseen at the electron-ion collider (EIC) with those at the hadron-electron ring accelerator (HERA), the only previous electron-proton collider; and describe five key experimental measurements, enabled by the EIC and aimed at delivering fundamental insights that will generate concrete answers to the questions of how mass and structure arise in the pion and kaon, the Standard Model's NG modes, whose surprisingly low mass is critical to the evolution of our Universe.

nucl-ex↗

arXiv2019

Lattice QCD and Neutrino-Nucleus Scattering

This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD in neutrino-oscillation physics, which inevitably entails nucleon and nuclear structure. In addition to discussing pertinent lattice-QCD calculations of nucleon and nuclear matrix elements, the interplay with models of nuclei is discussed. This program of lattice- QCD calculations is relevant to current and upcoming neutrino experiments, becoming increasingly important on the timescale of LBNF/DUNE and HyperK.

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arXiv2019

Pion Valence Quark Distribution from Matrix Element Calculated in Lattice QCD

We present the first exploratory lattice QCD calculation of the pion valence quark distribution extracted from spatially separated current-current correlations in coordinate space. We show that an antisymmetric combination of vector and axial-vector currents provides direct information on the pion valence quark distribution. Using the collinear factorization approach, we calculate the perturbative tree-level kernel for this current combination and extract the pion valence distribution. The main goal of this article is to demonstrate the efficacy of this general lattice QCD approach in the reliable extraction of parton distributions. With controllable power corrections and a good understanding of the lattice systematics, this method has the potential to serve as a complementary to the many efforts to extract parton distributions in global analyses from experimentally measured cross sections. We perform our calculation on an ensemble of 2+1 flavor QCD using the isotropic-clover fermion action, with lattice dimensions $32^3\times 96$ at a lattice spacing \mbox{$a=0.127$ fm} and the quark mass equivalent to a pion mass $m_π\simeq 416$ MeV.

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arXiv2015

QCD and Hadron Physics

This document presents the recommendations and scientific conclusions from the Town Meeting on QCD and Hadronic Physics that took place in the period 13-15 September 2014 at Temple University as part of the NSAC 2014 Long Range Planning process. It highlights progress in hadron physics in the seven years since the 2007 Long Range Plan (LRP07), and presents a vision for the future by identifying key questions and plausible paths to solutions which should define our next decade. In defining the priority of outstanding physics opportunities for the future, both prospects for the short (roughly 5 years) and longer term (beyond 10 years) are identified together with the facilities, personnel and other resources needed to maximize the discovery potential in hadronic physics worldwide. In this connection, the potential of an electron ion collider is highlighted.

hep-ph↗

arXiv2014

Decay constants of the pion and its excitations on the lattice

We present a calculation using lattice QCD of the ratios of decay constants of the excited states of the pion, to that of the pion ground state, at three values of the pion mass between 400 and 700 MeV, using an anisotropic clover fermion action with three flavors of quarks. We find that the decay constant of the first excitation, and more notably of the second, is suppressed with respect to that of the ground-state pion, but that the suppression shows little dependence on the quark mass. The strong suppression of the decay constant of the second excited state is consistent with its interpretation as a predominantly hybrid state.

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arXiv2013

Lattice study of the leptonic decay constant of the pion and its excitations

We present a calculation of the decay constant of the pion, and its lowest-lying three excitations, at three values of the pion mass between around 400 and 700 MeV, using anisotropic clover lattices. We use the variational method to determine an optimal interpolating operator for each of the states. We find that the decay constant of the first excitation, and more notably of the second, is suppressed with respect to that of the ground-state pion, but that the suppression shows little dependence on the quark mass.

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arXiv2013

The Flavor Structure of the Excited Baryon Spectra from Lattice QCD

Excited state spectra are calculated using lattice QCD for baryons that can be formed from $u$, $d$ and $s$ quarks, namely the $N$, $Δ$, $Λ$, $Σ$, $Ξ$ and $Ω$ families of baryons. Baryonic operators are constructed from continuum operators that transform as irreducible representations of SU(3)$_F$ symmetry for flavor, SU(4) symmetry for Dirac spins of quarks and O(3) symmetry for orbital angular momenta. Covariant derivatives are used to realize orbital angular momenta. Using the operators, we calculate matrices of correlation functions in order to extract excited states. The resulting lattice spectra have bands of baryonic states with well-defined total spins up to $J=7/2$. Each state can be assigned a dominant flavor symmetry and the counting of states of each flavor and spin reflects $SU(6) \times O(3)$ symmetry for the lowest negative-parity and positive-parity bands. States with strong hybrid content are identified through the dominance of chromo-magnetic operators.

hep-ph↗

arXiv2012

Excited and exotic charmonium spectroscopy from lattice QCD

We present a spectrum of highly excited charmonium mesons up to around 4.5 GeV calculated using dynamical lattice QCD. Employing novel computational techniques and the variational method with a large basis of carefully constructed operators, we extract and reliably identify the continuum spin of an extensive set of excited states, states with exotic quantum numbers (0+-, 1-+, 2+-) and states with high spin. Calculations are performed on two lattice volumes with pion mass approximately 400 MeV and the mass determinations have high statistical precision even for excited states. We discuss the results in light of experimental observations, identify the lightest 'supermultiplet' of hybrid mesons and comment on the phenomenological implications of the spectrum of exotic mesons.

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