arXiv subjects

M. A. Clark

Publications and source records attributed to M. A. Clark.

At least 19 recordsLinked to original sources

arXiv2026

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 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.

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arXiv2025

Using Exascale Computing to Explain the Delicate Balance of Nuclear Forces in the Universe

The vast majority of visible matter in our universe comes from protons and neutrons (the nucleons). Nucleon interactions are fundamental to how the universe developed after the Big Bang and govern all nuclear phenomena. The subtle balance in how two nucleons interact shapes the universe's hydrogen content that is central to our existence. Our objective is to compute the interaction strength while varying the parameters of nature to understand how delicate this balance is. We developed a new code using sophisticated physics algorithms and a highly optimized library for simulations on CPU-GPU parallel architectures. It has excellent weak scaling and impressive linear scaling for a fixed problem size with increasing number of nodes up to El Capitan's full $\sim$11,000 nodes. On Alps, El Capitan, Frontier, Jupiter, and Perlmutter supercomputers we achieve a maximum disruptive speed-up of $\sim$240 times the previous state-of-the-art, signaling a new era of supercomputing.

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arXiv2025

Signs of Non-Monotonic Finite-Volume Corrections to $g_A$

We study finite-volume (FV) corrections to determinations of $g_A$ via lattice quantum chromodynamics (QCD) using analytic results and numerical analysis. We observe that $SU(2)$ Heavy Baryon Chiral Perturbation Theory does not provide an unambiguous prediction for the sign of the FV correction, which is not surprising when one also considers large-$N_c$ constraints on the axial couplings. We further show that non-monotonic FV corrections are naturally allowed when one considers either including explicit $Δ$-resonance degrees of freedom or one works to higher orders in the chiral expansion. We investigate the potential impact of these FV corrections with a precision study of $g_A$ using models of FV corrections that are monotonic and non-monotonic. Using lattice QCD data that is approximately at the 1% level of precision, we do not see significant evidence of non-monotonic corrections. Looking forward to the next phase of lattice QCD calculations, we estimate that calculations that are between the 0.1%-1%-level of precision may be sensitive to these FV artifacts. Finally, we present an update of the CalLat prediction of $g_A$ in the isospin limit with sub-percent precision, $g_A^{\rm QCD} = 1.2674(96)$.

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arXiv2025

Improving HISQ propagator solves using deflation

Typically, the conjugate gradient (CG) algorithm employs mixed precision and even-odd preconditioning to compute propagators for highly improved staggered quarks (HISQ). This approach suffers from critical slowing down as the light quark mass is decreased to its physical value. Multigrid is one alternative to combat critical slowing down; however, it involves setup costs that are not always easy to amortize. We consider deflation, which can also remove critical slowing down, but incurs its own setup cost to compute eigenvectors. Results using the MILC and QUDA software libraries to generate eigenvectors and to perform deflated solves on lattices up to $144^3 \times 288$ (with lattice spacing 0.04 fm) and with a range of quark masses from the physical strange down to the physical light quark values will be presented. We compare with CG and comment on deflation versus multigrid.

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arXiv2023

Accelerating Dedispersion using Many-Core Architectures

Astrophysical radio signals are excellent probes of extreme physical processes that emit them. However, to reach Earth, electromagnetic radiation passes through the ionised interstellar medium (ISM), introducing a frequency-dependent time delay (dispersion) to the emitted signal. Removing dispersion enables searches for transient signals like Fast Radio Bursts (FRB) or repeating signals from isolated pulsars or those in orbit around other compact objects. The sheer volume and high resolution of data that next generation radio telescopes will produce require High-Performance Computing (HPC) solutions and algorithms to be used in time-domain data processing pipelines to extract scientifically valuable results in real-time. This paper presents a state-of-the-art implementation of brute force incoherent dedispersion on NVIDIA GPUs, and on Intel and AMD CPUs. We show that our implementation is 4x faster (8-bit 8192 channels input) than other available solutions and demonstrate, using 11 existing telescopes, that our implementation is at least 20 faster than real-time. This work is part of the AstroAccelerate package.

astro-ph.IM↗

arXiv2023

Maximizing the Bang Per Bit

Reducing memory traffic is critical to accelerate Lattice QCD computations on modern processors, given that such computations are memory-bandwidth bound. A commonly used strategy is mixed-precision solvers, however, these require careful treatment to ensure stable convergence. We give an overview of the strategies employed in QUDA to stabilize mixed-precision variants of Conjugate Gradient (CG), and its multi-shift brethren. Through the use of customized numerical storage formats we can significantly improve upon the precision achievable compared to IEEE numerical formats, increasing both the solver precision and stability achievable at fixed word size. We give examples using BiCGStab(l) and multi-shift CG solvers using the HISQ operator.

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arXiv2022

Optimizing Staggered Multigrid for Exascale performance

Adaptive multi-grid methods have proven very successful in dealing with critical slow down for the Wilson-Dirac solver in lattice gauge theory. Multi-grid algorithms developed for Staggered fermions using the Kähler-Dirac preconditioning~\cite{Brower:2018ymy} have shown remarkable success. In this work, we discuss the performance of this staggered multi-grid algorithm in four dimensions. We also demonstrate that offloading some components of a multi-shift solve to a multi-grid solver leads to a significant performance improvement in an existing MILC spectrum workflow on the Summit and Selene supercomputers.

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arXiv2022

Detailed analysis of excited state systematics in a lattice QCD calculation of $g_A$

Excited state contamination remains one of the most challenging sources of systematic uncertainty to control in lattice QCD calculations of nucleon matrix elements and form factors: early time separations are contaminated by excited states and late times suffer from an exponentially bad signal-to-noise problem. High-statistics calculations at large time separations $\gtrsim1$ fm are commonly used to combat these issues. In this work, focusing on $g_A$, we explore the alternative strategy of utilizing a large number of relatively low-statistics calculations at short to medium time separations (0.2--1 fm), combined with a multi-state analysis. On an ensemble with a pion mass of approximately 310 MeV and a lattice spacing of approximately 0.09 fm, we find this provides a more robust and economical method of quantifying and controlling the excited state systematic uncertainty. A quantitative separation of various types of excited states enables the identification of the transition matrix elements as the dominant contamination. The excited state contamination of the Feynman-Hellmann correlation function is found to reduce to the 1% level at approximately 1 fm while for the more standard three-point functions, this does not occur until after 2 fm. Critical to our findings is the use of a global minimization, rather than fixing the spectrum from the two-point functions and using them as input to the three-point analysis. We find that the ground state parameters determined in such a global analysis are stable against variations in the excited state model, the number of excited states, and the truncation of early-time or late-time numerical data.

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arXiv2022

QED with massive photons for precision physics: zero modes and first result for the hadron spectrum

The current precision reached by lattice QCD calculations of low-energy hadronic observables, requires not only the introduction of electromagnetic corrections, but also control over all the potential systematic uncertainties introduced by the lattice version of QED. Introducing a massive photon as an infrared regulator in lattice QED, provides a well defined theory, dubbed QEDM, amenable to numerical evaluation [arXiv:1507.08916]. The photon mass is removed through extrapolation. In this contribution we scrutinise aspects of QEDM such as the presence and fate of the zero modes contributions and we describe the determination of the photon mass corrections in finite and infinite volume. We demonstrate that the required extrapolations are well controlled using numerical data obtained on two ensembles which only differ in volume.

hep-lat↗

arXiv2022

The hyperon spectrum from lattice QCD

Hyperon decays present a promising alternative for extracting $\vert V_{us} \vert$ from lattice QCD combined with experimental measurements. Currently $\vert V_{us} \vert$ is determined from the kaon decay widths and a lattice calculation of the associated form factor. In this proceeding, I will present preliminary work on a lattice determination of the hyperon mass spectrum. I will additionally summarize future goals in which we will calculate the hyperon transition matrix elements, which will provide an alternative means for accessing $\vert V_{us} \vert$. This work is based on a particular formulation of SU(2) chiral perturbation theory for hyperons; determining the extent to which this effective field theory converges is instrumental in understanding the limits of its predictive power, especially since some hyperonic observables are difficult to calculate near the physical pion mass (e.g., hyperon-to-nucleon form factors), and thus the use of heavier than physical pion masses is likely to yield more precise results when combined with extrapolations to the physical point.}

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arXiv2021

Toward a resolution of the NN controversy

Lattice QCD calculations of two-nucleon interactions have been underway for about a decade, but still haven't reached the pion mass regime necessary for matching onto effective field theories and extrapolating to the physical point. Furthermore, results from different methods, including the use of the Luscher formalism with different types of operators, as well as the HALQCD potential method, do not agree even qualitatively at very heavy pion mass. We investigate the role that different operators employed in the literature may play on the extraction of spectra for use within the Luscher method. We first explore expectations from Effective Field Theory solved within a finite volume, for which the exact spectrum may be computed given different physical scenarios. We then present preliminary lattice QCD results for two-nucleon spectra calculated using different operators on a common lattice ensemble.

hep-lat↗

arXiv2021

Nucleon Axial Form Factor from Domain Wall on HISQ

The Deep Underground Neutrino Experiment (DUNE) is an upcoming neutrino oscillation experiment that is poised to answer key questions about the nature of neutrinos. Lattice QCD has the ability to make significant impact upon DUNE, beginning with computations of nucleon-neutrino interactions with weak currents. Nucleon amplitudes involving the axial form factor are part of the primary signal measurement process for DUNE, and precise calculations from LQCD can significantly reduce the uncertainty for inputs into Monte Carlo generators. Recent calculations of the nucleon axial charge have demonstrated that sub-percent precision is possible on this vital quantity. In these proceedings, we discuss preliminary results for the CalLat collaboration's calculation of the axial form factor of the nucleon. These computations are performed with Möbius domain wall valence quarks on HISQ sea quark ensembles generated by the MILC and CalLat collaborations. The results use a variety of ensembles including several at physical pion mass.

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arXiv2021

Solving DWF Dirac Equation Using Multi-splitting Preconditioned Conjugate Gradient with Tensor Cores on NVIDIA GPUs

We show that using the multi-splitting algorithm as a preconditioner for the domain wall Dirac linear operator, arising in lattice QCD, effectively reduces the inter-node communication cost, at the expense of performing more on-node floating point and memory operations. Correctly including the boundary \textit{snake} terms, the preconditioner is implemented in the QUDA framework, where it is found that utilizing kernel fusion and the tensor cores on NVIDIA GPUs is necessary to achieve a sufficiently performant preconditioner. A reduced-dimension (reduced-$L_s$) strategy is also proposed and tested for the preconditioner. We find the method achieves lower time to solution than regular CG at high node count despite the additional local computational requirements from the preconditioner. This method could be useful for supercomputers with more on-node flops and memory bandwidth than inter-node communication bandwidth.

hep-lat↗

arXiv2021

Scale setting the Möbius Domain Wall Fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales $t_0$ and $w_0$

We report on a sub-percent scale determination using the omega baryon mass and gradient-flow methods. The calculations are performed on 22 ensembles of $N_f=2+1+1$ highly improved, rooted staggered sea-quark configurations generated by the MILC and CalLat Collaborations. The valence quark action used is Möbius Domain-Wall fermions solved on these configurations after a gradient-flow smearing is applied with a flowtime of $t_{\rm gf}=1$ in lattice units. The ensembles span four lattice spacings in the range $0.06 \lesssim a \lesssim 0.15$ fm, six pion masses in the range $130 \lesssim m_π\lesssim 400$ MeV and multiple lattice volumes. On each ensemble, the gradient-flow scales $t_0/a^2$ and $w_0/a$ and the omega baryon mass $a m_Ω$ are computed. The dimensionless product of these quantities is then extrapolated to the continuum and infinite volume limits and interpolated to the physical light, strange and charm quark mass point in the isospin limit, resulting in the determination of $\sqrt{t_0}=0.1422(14)$ fm and $w_0 = 0.1709(11)$ fm with all sources of statistical and systematic uncertainty accounted for. The dominant uncertainty in this result is the stochastic uncertainty, providing a clear path for a few-per-mille uncertainty, as recently obtained by the Budapest-Marseille-Wuppertal Collaboration.

hep-lat↗

arXiv2021

Two-nucleon S-wave interactions at the $SU(3)$ flavor-symmetric point with $m_{ud}\simeq m_s^{\rm phys}$: a first lattice QCD calculation with the stochastic Laplacian Heaviside method

We report on the first application of the stochastic Laplacian Heaviside method for computing multi-particle interactions with lattice QCD to the two-nucleon system. Like the Laplacian Heaviside method, this method allows for the construction of interpolating operators which can be used to construct a positive definite set of two-nucleon correlation functions, unlike nearly all other applications of lattice QCD to two nucleons in the literature. It also allows for a variational analysis in which optimal linear combinations of the interpolating operators are formed that couple predominantly to the eigenstates of the system. Utilizing such methods has become of paramount importance in order to help resolve the discrepancy in the literature on whether two nucleons in either isospin channel form a bound state at pion masses heavier than physical, with the discrepancy persisting even in the $SU(3)$-flavor symmetric point with all quark masses near the physical strange quark mass. This is the first in a series of papers aimed at resolving this discrepancy. In the present work, we employ the stochastic Laplacian Heaviside method without a hexaquark operator in the basis at a lattice spacing of $a\sim0.086$~fm, lattice volume of $L=48a\simeq4.1$~fm and pion mass $m_π\simeq714$ MeV. With this setup, the observed spectrum of two-nucleon energy levels strongly disfavors the presence of a bound state in either the deuteron or dineutron channel.

hep-lat↗

arXiv2020

$F_K / F_π$ 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 $130 \lesssim m_π\lesssim 400$ MeV, four lattice spacings of $a\sim 0.15, 0.12, 0.09$ 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 $a\sim0.06$ 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 $F_{K^\pm}/F_{π^\pm} = 1.1942(45)$ 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 $|V_{us}|/|V_{ud}| = 0.2311(10)$.

hep-lat↗

arXiv2020

Multigrid for Chiral Lattice Fermions: Domain Wall

Critical slowing down for the Krylov Dirac solver presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. We propose a new multi-grid approach for chiral fermions, applicable to both the 5-d domain wall or 4-d Overlap operator. The central idea is to directly coarsen the 4-d Wilson kernel, giving an effective domain wall or overlap operator on each level. We provide here an explicit construction for the Shamir domain wall formulation with numerical tests for the 2-d Schwinger prototype, demonstrating near ideal multi-grid scaling. The framework is designed for a natural extension to 4-d lattice QCD chiral fermions, such as the Möbius, Zolotarev or Borici domain wall discretizations or directly to a rational expansion of the 4-d Overlap operator. For the Shamir operator, the effective overlap operator is isolated by the use of a Pauli-Villars preconditioner in the spirit of the Kähler-Dirac spectral map used in a recent staggered MG algorithm [1].

hep-lat↗

arXiv2019

Lattice QCD Determination of $g_A$

The nucleon axial coupling, $g_A$, is a fundamental property of protons and neutrons, dictating the strength with which the weak axial current of the Standard Model couples to nucleons, and hence, the lifetime of a free neutron. The prominence of $g_A$ in nuclear physics has made it a benchmark quantity with which to calibrate lattice QCD calculations of nucleon structure and more complex calculations of electroweak matrix elements in one and few nucleon systems. There were a number of significant challenges in determining $g_A$, notably the notorious exponentially-bad signal-to-noise problem and the requirement for hundreds of thousands of stochastic samples, that rendered this goal more difficult to obtain than originally thought. I will describe the use of an unconventional computation method, coupled with "ludicrously'" fast GPU code, access to publicly available lattice QCD configurations from MILC and access to leadership computing that have allowed these challenges to be overcome resulting in a determination of $g_A$ with 1% precision and all sources of systematic uncertainty controlled. I will discuss the implications of these results for the convergence of $SU(2)$ Chiral Perturbation theory for nucleons, as well as prospects for further improvements to $g_A$ (sub-percent precision, for which we have preliminary results) which is part of a more comprehensive application of lattice QCD to nuclear physics. This is particularly exciting in light of the new CORAL supercomputers coming online, Sierra and Summit, for which our lattice QCD codes achieve a machine-to-machine speed up over Titan of an order of magnitude.

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