arXiv subjects

André Walker-Loud

Publications and source records attributed to André Walker-Loud.

At least 19 recordsLinked to original sources

arXiv2026

Investigating the role of tetraquark operators in lattice QCD studies of the $a_0(980)$ and $κ$ resonances

The role of tetraquark operators in studying the isodoublet strange $κ$ and isovector nonstrange $a_0(980)$ scalar mesons in lattice QCD is examined using an ensemble with $m_π\approx230$ MeV and spatial extent $L$ such that $m_πL\approx4.4$. Hermitian correlation matrices using both single-meson, meson-meson, and tetraquark interpolating operators are used to extract the spectrum of finite-volume stationary states in the appropriate symmetry channels. Hundreds of local and extended tetraquark operators are explored. Determinations of the spectrum in each channel are found to be unreliable without the inclusion of at least one tetraquark operator. For example, the inclusion of tetraquark operators with isospin 1/2 and strangeness 1 quantum numbers reveals the existence of an additional energy level in the $Kη$ sub-system below the $Kη$ threshold. The implications of this on parametrizing the scattering $K$-matrix through a well-known quantization condition to extract properties of the $κ$ and $a_0(980)$ scalar meson resonances are discussed.

hep-lat↗

arXiv2026

$F_K/F_π$ as a precision test of a new four flavor Domain Wall Fermion action

We present a new set of lattice QCD ensembles with four flavors of smeared Möbius Domain Wall Fermions with good chiral symmetry and small fifth-dimensional extent. A modest amount of computing resources was sufficient to generate 30 publicly-available ensembles spanning five lattice spacings and a broad range of pion masses down to physical. To scrutinize our action we determine $F_{K^{\pm}}/F_{π^{\pm}} = 1.1962(34)$, a key quantity for precision CKM unitarity tests, heralding a future of inexpensive high-precision calculations of hadronic observables with chiral fermions.

hep-lat↗

arXiv2026

Preliminary study of the $H$ dibaryon in $N_{\rm f}=2+1$ lattice QCD

We present preliminary results on the $I=0$, $S=-2$ $H$ dibaryon in $N_{\rm f}=2+1$ QCD. The calculation is performed with heavier-than-physical quarks ($m_π\approx 280$ MeV) on a single CLS ensemble. Correlation matrices are constructed using the distillation technique and the three relevant channels, $ΛΛ$, $NΞ$, $ΣΣ$, are investigated to determine the interacting spectrum relevant for $S$-wave across multiple momentum frames. The scattering amplitude is determined by solving the corresponding two-body quantization condition. These preliminary results are part of the ongoing efforts to determine the properties of di-hyperons and to establish whether the $H$ dibaryon exists down to physical quark masses.

hep-lat↗

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.

hep-lat↗

arXiv2025

Moments of parton distributions functions of the pion from lattice QCD using gradient flow

We present a nonperturbative determination of the pion valence parton distribution function (PDF) moment ratios $\left\langle x^{n-1} \right\rangle / \left\langle x \right\rangle$ up to $n=6$, using the gradient flow in lattice QCD. As a testing ground, we employ SU($3$) isosymmetric gauge configurations generated by the OpenLat initiative with a pseudoscalar mass of $m_π\simeq 411~\text{MeV}$. Our analysis uses four lattice spacings and a nonperturbatively improved action, enabling full control over the continuum extrapolation, and the limit of vanishing flow time, $t\to0$. The flowed ratios exhibit O($a^2$) scaling across the ensembles, and the continuum-extrapolated results, matched to the $\overline {\text{MS}}$ scheme at $μ= 2$ GeV using next-to-next-to-leading order matching coefficients, show only mild residual flow-time dependence. The resulting ratios, computed with a relatively small number of configurations, are consistent with phenomenological expectations for the pion's valence distribution, with statistical uncertainties that are competitive with modern global fits. These findings demonstrate that the gradient flow provides an efficient and systematically improvable method to access partonic quantities from first principles. Future extensions of this work will target lighter pion masses toward the physical point, and applications to nucleon structure such as the proton PDFs and the gluon and sea-quark distributions.

hep-lat↗

arXiv2025

Gradient flow for parton distribution functions: first application to the pion

Parton distribution functions (PDFs) are central to precision QCD phenomenology. Their Mellin moments can be computed on the lattice, but direct determinations using local operators, besides $\langle x \rangle$, face severe challenges from reduced hypercubic symmetry, limiting results to the lowest moments. A recently proposed method resolves these issues using gradient flow. We demonstrate the efficacy of this method by computing ratios of flavor non-singlet pion PDF moments up to $\langle x^5 \rangle$, on four lattice spacings at $m_π\simeq 411$ MeV. The moments and reconstructed PDF agree quantitatively with recent phenomenological extractions.

hep-lat↗

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, $g_A^{\rm QCD} = 1.2674(96)$.

hep-lat↗

arXiv2024

Probing higher moments of pion parton distribution functions

We present the first numerical investigation of the method proposed in Ref. [1] to utilize gradient flow to obtain precise determinations of higher moments of PDFs from lattice QCD, circumventing power divergent mixing with lower dimensional operators. We apply this method to obtain moments of the isovector PDF of the pion using four Stabilized Wilson Fermion ensembles with $m_π\simeq 411$ MeV and lattice spacings $a \simeq 0.064, 0.077, 0.094$, and $0.12$ fm. We present preliminary results of ratios of three-point functions as a function of flow time, which can be used to extract the ratios $\left\langle x^2 \right\rangle/\left\langle x \right\rangle$ and $\left\langle x^3 \right\rangle/\left\langle x \right\rangle$. We find that a significantly higher precision can be achieved with this method compared to the canonical approach, which requires boosting and cannot reach higher than the $\left\langle x^3 \right\rangle$ moment.

hep-lat↗

arXiv2024

Lattice QCD study of $πΣ-\bar{K}N$ scattering and the $Λ(1405)$ resonance

A lattice QCD computation of the coupled channel $πΣ-\bar{K}N$ scattering amplitudes in the $Λ(1405)$ region is detailed. Results are obtained using a single ensemble of gauge field configurations with $N_{\rm f} = 2+1$ dynamical quark flavors and $m_π \approx 200$ MeV and $m_K\approx487$ MeV. Hermitian correlation matrices using both single baryon and meson-baryon interpolating operators for a variety of different total momenta and irreducible representations are used. Several parametrizations of the two-channel scattering $K$-matrix are utilized to obtain the scattering amplitudes from the finite-volume spectrum. The amplitudes, continued to the complex energy plane, exhibit a virtual bound state below the $πΣ$ threshold and a resonance pole just below the $\bar{K}N$ threshold.

hep-lat↗

arXiv2024

Two-pole nature of the $Λ(1405)$ from lattice QCD

This letter presents the first lattice QCD computation of the coupled channel $πΣ-\bar{K}N$ scattering amplitudes at energies near $1405\,{\rm MeV}$. These amplitudes contain the resonance $Λ(1405)$ with strangeness $S=-1$ and isospin, spin, and parity quantum numbers $I(J^P)=0(1/2^-)$. However, whether there is a single resonance or two nearby resonance poles in this region is controversial theoretically and experimentally. Using single-baryon and meson-baryon operators to extract the finite-volume stationary-state energies to obtain the scattering amplitudes at slightly unphysical quark masses corresponding to $m_π\approx200$ MeV and $m_K\approx487$ MeV, this study finds the amplitudes exhibit a virtual bound state below the $πΣ$ threshold in addition to the established resonance pole just below the $\bar{K}N$ threshold. Several parametrizations of the two-channel $K$-matrix are employed to fit the lattice QCD results, all of which support the two-pole picture suggested by $SU(3)$ chiral symmetry and unitarity.

hep-lat↗

arXiv2023

The $Λ(1405)$ from Lattice QCD: Determining the Finite-volume Spectra

This work presents technical details of determining the finite-volume energy spectra for the scattering amplitude of the coupled-channel $πΣ- \bar{K}N$ from lattice QCD data. The importance of reliably extracting such spectra lies in the crucial dependence of the hadronic scattering amplitudes analysis on the energy spectrum when using Lüscher's formalism. Results of the methods used are presented and the final finite-volume spectra are shown. The analysis of the scattering amplitude based on these results, exhibits a two-pole structure for the $Λ(1405)$, a virtual bound state below the $πΣ$ threshold and a resonance pole right below the $\bar{K}N$ threshold.

hep-lat↗

arXiv2023

Lattice QCD studies of the $Δ$ baryon resonance and the $K_0^\ast(700)$ and $a_0(980)$ meson resonances: the role of exotic operators in determining the finite-volume spectrum

Studies of the $Δ$ baryon resonance and the $K_0^\ast(700)$ and $a_0(980)$ meson resonances using $N_f=2+1$ lattice QCD for pion masses near 200 MeV are presented. The $s$-wave scattering lengths for both the $I=1/2$ $N π$ and $I=3/2$ $N π$ channels and properties of the $Δ$ resonance are identified from the finite-volume energy levels of the lattice simulation. The importance of a three-quark $Δ$-operator in the $Nπ$ system and tetraquark operators in the mesonic systems is investigated.

hep-lat↗

arXiv2023

Elastic nucleon-pion scattering at $m_π = 200~{\rm MeV}$ from lattice QCD

Elastic nucleon-pion scattering amplitudes are computed using lattice QCD on a single ensemble of gauge field configurations with $N_{\rm f} = 2+1$ dynamical quark flavors and $m_π = 200~{\rm MeV}$. The $s$-wave scattering lengths with both total isospins $I=1/2$ and $I=3/2$ are inferred from the finite-volume spectrum below the inelastic threshold together with the $I=3/2$ $p$-wave containing the $Δ(1232)$ resonance. The amplitudes are well-described by the effective range expansion with parameters constrained by fits to the finite-volume energy levels enabling a determination of the $I=3/2$ scattering length with statistical errors below $5\%$, while the $I = 1/2$ is somewhat less precise. Systematic errors due to excited states and the influence of higher partial waves are controlled, providing a pathway for future computations down to the physical light quark masses with multiple lattice spacings and physical volumes.

hep-lat↗

arXiv2022

Gate Based Implementation of the Laplacian with BRGC Code for Universal Quantum Computers

We study the gate-based implementation of the binary reflected Gray code (BRGC) and binary code of the unitary time evolution operator due to the Laplacian discretized on a lattice with periodic boundary conditions. We find that the resulting Trotter error is independent of system size for a fixed lattice spacing through the Baker-Campbell-Hausdorff formula. We then present our algorithm for building the BRGC quantum circuit. For an adiabatic evolution time $t$ with this circuit, and spectral norm error $ε$, we find the circuit cost (number of gates) and depth required are $\mc{O}(t^2 n A D /ε)$ with $n-3$ auxiliary qubits for a system with $2^n$ lattice points per dimension $D$ and particle number $A$; an improvement over binary position encoding which requires an exponential number of $n$-local operators. Further, under the reasonable assumption that $[T,V]$ bounds $Δt$, with $T$ the kinetic energy and $V$ a non-trivial potential, the cost of QFT (Quantum Fourier Transform ) implementation of the Laplacian scales as $\mc{O}\left(n^2\right)$ with depth $\mc{O}\left(n\right)$ while BRGC scales as $\mc{O}\left(n\right)$, giving an advantage to the BRGC implementation.

quant-ph↗

arXiv2022

Status of Lattice QCD Determination of Nucleon Form Factors and their Relevance for the Few-GeV Neutrino Program

Calculations of neutrino-nucleus cross sections begin with the neutrino-nucleon interaction, making the latter critically important to flagship neutrino oscillation experiments, despite limited measurements with poor statistics. Alternatively, lattice QCD (LQCD) can be used to determine these interactions from the Standard Model with quantifiable theoretical uncertainties. Recent LQCD results of $g_{\mathrm{A}}$ are in excellent agreement with data, and results for the (quasi-)elastic nucleon form factors with full uncertainty budgets are expected within a few years. We review the status of the field and LQCD results for the nucleon axial form factor, $F_{\mathrm{A}}(Q^2)$, a major source of uncertainty in modeling sub-GeV neutrino-nucleon interactions. Results from different LQCD calculations are consistent, but collectively disagree with existing models, with potential implications for current and future neutrino oscillation experiments. We describe a road map to solidify confidence in the LQCD results and discuss future calculations of more complicated processes, important to few-GeV neutrino oscillation experiments.

hep-lat↗

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.

hep-lat↗

arXiv2022

Neutrinoless Double-Beta Decay: A Roadmap for Matching Theory to Experiment

The observation of neutrino oscillations and hence non-zero neutrino masses provided a milestone in the search for physics beyond the Standard Model. But even though we now know that neutrinos are massive, the nature of neutrino masses, i.e., whether they are Dirac or Majorana, remains an open question. A smoking-gun signature of Majorana neutrinos is the observation of neutrinoless double-beta decay, a process that violates the lepton-number conservation of the Standard Model. This white paper focuses on the theoretical aspects of the neutrinoless double-beta decay program and lays out a roadmap for future developments. The roadmap is a multi-scale path starting from high-energy models of neutrinoless double-beta decay all the way to the low-energy nuclear many-body problem that needs to be solved to supplement measurements of the decay rate. The path goes through a systematic effective-field-theory description of the underlying processes at various scales and needs to be supplemented by lattice quantum chromodynamics input. The white paper also discusses the interplay between neutrinoless double-beta decay, experiments at the Large Hadron Collider and results from astrophysics and cosmology in probing simplified models of lepton-number violation at the TeV scale, and the generation of the matter-antimatter asymmetry via leptogenesis. This white paper is prepared for the topical groups TF11 (Theory of Neutrino Physics), TF05 (Lattice Gauge Theory), RF04 (Baryon and Lepton Number Violating Processes), NF03 (Beyond the Standard Model) and NF05 (Neutrino Properties) within the Theory Frontier, Rare Processes and Precision Frontier, and Neutrino Physics Frontier of the U.S. Community Study on the Future of Particle Physics (Snowmass 2021).

hep-ph↗

arXiv2022

Pion-induced radiative corrections to neutron beta-decay

We compute the electromagnetic corrections to neutron beta decay using a low-energy hadronic effective field theory. We identify and compute new radiative corrections arising from virtual pions that were missed in previous studies. The largest correction is a percent-level shift in the axial charge of the nucleon proportional to the electromagnetic part of the pion-mass splitting. Smaller corrections, comparable to anticipated experimental precision, impact the $β$-$ν$ angular correlations and the $β$-asymmetry. We comment on implications of our results for the comparison of the experimentally measured axial charge with first-principle computations using lattice QCD and on the potential of $β$-decay experiments to constrain beyond-the-Standard-Model interactions.

nucl-th↗