arXiv subjects

Michael L. Wagman

Publications and source records attributed to Michael L. Wagman.

At least 55 records · Page 3Linked to original sources

arXiv2021

The axial charge of the triton from lattice QCD

The axial charge of the triton is investigated using lattice quantum chromodynamics (QCD). Extending previous work at heavier quark masses, calculations are performed using three ensembles of gauge field configurations generated with quark masses corresponding to a pion mass of 450 MeV. Finite-volume energy levels for the triton, as well as for the deuteron and diproton systems, are extracted from analysis of correlation functions computed on these ensembles, and the corresponding energies are extrapolated to infinite volume using finite-volume pionless effective field theory (FVEFT). It is found with high likelihood that there is a compact bound state with the quantum numbers of the triton at these quark masses. The axial current matrix elements are computed using background field techniques on one of the ensembles and FVEFT is again used to determine the axial charge of the proton and triton. A simple quark mass extrapolation of these results and earlier calculations at heavier quark masses leads to a value of the ratio of the triton to proton axial charges at the physical quark masses of $g_A^{^{3}{\rm H}}/g_A^p=0.91\substack{+0.07 \\ -0.09}$. This result is consistent with the ratio determined from experiment and prefers values less than unity (in which case the triton axial charge would be unmodified from that of the proton), thereby demonstrating that QCD can explain the modification of the axial charge of the triton.

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arXiv2021

Path integral contour deformations for observables in $SU(N)$ gauge theory

Path integral contour deformations have been shown to mitigate sign and signal-to-noise problems associated with phase fluctuations in lattice field theories. We define a family of contour deformations applicable to $SU(N)$ lattice gauge theory that can reduce sign and signal-to-noise problems associated with complex actions and complex observables. For observables, these contours can be used to define deformed observables with identical expectation value but different variance. As a proof-of-principle, we apply machine learning techniques to optimize the deformed observables associated with Wilson loops in two dimensional $SU(2)$ and $SU(3)$ gauge theory. We study loops consisting of up to 64 plaquettes and achieve variance reduction of up to 4 orders of magnitude.

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arXiv2020

Lattice QCD constraints on the parton distribution functions of ${}^3\text{He}$

The fraction of the longitudinal momentum of ${}^3\text{He}$ that is carried by the isovector combination of $u$ and $d$ quarks is determined using lattice QCD for the first time. The ratio of this combination to that in the constituent nucleons is found to be consistent with unity at the few-percent level from calculations with quark masses corresponding to $m_π\sim 800$ MeV, extrapolated to the physical quark masses. This constraint is consistent with, and significantly more precise than, determinations from global nuclear parton distribution function fits. Including the lattice QCD determination of the momentum fraction in the nNNPDF global fitting framework results in the uncertainty on the isovector momentum fraction ratio being reduced by a factor of 2.5, and thereby enables a more precise extraction of the $u$ and $d$ parton distributions in ${}^3\text{He}$.

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arXiv2020

Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes

Over the last decade, numerical solutions of Quantum Chromodynamics (QCD) using the technique of lattice QCD have developed to a point where they are beginning to connect fundamental aspects of nuclear physics to the underlying degrees of freedom of the Standard Model. In this review, the progress of lattice QCD studies of nuclear matrix elements of electroweak currents and beyond-Standard-Model operators is summarized, and connections with effective field theories and nuclear models are outlined. Lattice QCD calculations of nuclear matrix elements can provide guidance for low-energy nuclear reactions in astrophysics, dark matter direct detection experiments, and experimental searches for violations of the symmetries of the Standard Model, including searches for additional CP violation in the hadronic and leptonic sectors, baryon-number violation, and lepton-number or flavor violation. Similarly, important inputs to neutrino experiments seeking to determine the neutrino-mass hierarchy and oscillation parameters, as well as other electroweak and beyond-Standard-Model processes can be determined. The phenomenological implications of existing studies of electroweak and beyond-Standard-Model matrix elements in light nuclear systems are discussed, and future prospects for the field toward precision studies of these matrix elements are outlined.

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arXiv2020

Nonperturbative renormalization of staple-shaped Wilson line operators in lattice QCD

Quark bilinear operators with staple-shaped Wilson lines are used to study transverse-momentum-dependent parton distribution functions (TMDPDFs) from lattice quantum chromodynamics (QCD). Here, the renormalization factors for the isovector operators, including all mixings between operators with different Dirac structures, are computed nonperturbatively in the regularization-independent momentum subtraction scheme for the first time. This study is undertaken in quenched QCD with three different lattice spacings. With Wilson flow applied to the gauge fields in the calculations, the operator mixing pattern due to chiral symmetry breaking with the lattice regularization is found to be significantly different from that predicted by one-loop lattice perturbation theory calculations. These results constitute a critical step towards the systematic extraction of TMDPDFs from lattice QCD.

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arXiv2020

Path integral contour deformations for noisy observables

Monte Carlo studies of many quantum systems face exponentially severe signal-to-noise problems. We show that noise arising from complex phase fluctuations of observables can be reduced without introducing bias using path integral contour deformation techniques. A numerical study of contour deformations for correlation functions in Abelian gauge theory and complex scalar field theory demonstrates that variance can be reduced by orders of magnitude without modifying Monte Carlo sampling.

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arXiv2019

Lattice Analysis of $SU(2)$ with 1 Adjoint Dirac Flavor

Recently $SU(2)$ Yang-Mills theory with one massless adjoint Dirac quark flavor emerges as a novel critical theory that can describe the evolution between a trivial insulator and a topological insulator in AIII class in $3+1$ dimensions. There are several classes of conjectured infrared dynamics for this theory. One possibility is that the theory undergoes spontaneous chiral symmetry breaking, with two massless Goldstone bosons (the scalar diquark and its antiparticle) in the infrared. Another scenario, which is suggested by previous lattice studies by Athenodorou et al., is that the IR sector of the theory is a strongly interacting conformal field theory as the quark mass vanishes. The most recent theoretical proposals argue for a case that in the infrared a composite fermion composed of two quarks and an antiquark becomes massless and non-interacting as the quark mass goes to zero, while other sectors are decoupled from this low-energy fermion. This work expands upon previous studies by including the composite fermion to investigate which of these three potential scenarios captures the infrared behavior of this theory.

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arXiv2019

Lattice QCD determination of neutron-antineutron matrix elements with physical quark masses

Matrix elements of six-quark operators are needed to extract new physics constraints from experimental searches for neutron-antineutron oscillations. This work presents in detail the first lattice quantum chromodynamics calculations of the necessary neutron-antineutron transition matrix elements including calculation methods and discussions of systematic uncertainties. Implications of isospin and chiral symmetry on the matrix elements, power counting in the isospin limit, and renormalization of a chiral basis of six-quark operators are discussed. Calculations are performed with a chiral-symmetric discretization of the quark action and physical light quark masses in order to avoid the need for chiral extrapolation. Non-perturbative renormalization is performed, including a study of lattice cutoff effects. Excited-state effects are studied using two nucleon operators and multiple values of source-sink separation. Results for the dominant matrix elements are found to be significantly larger compared to previous results from the MIT bag model. Future calculations are needed to fully account for systematic uncertainties associated with discretization and finite-volume effects but are not expected to significantly affect this conclusion.

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arXiv2019

Neutron-antineutron oscillations from lattice QCD

Fundamental symmetry tests of baryon number violation in low-energy experiments can probe beyond the Standard Model (BSM) explanations of the matter-antimatter asymmetry of the universe. Neutron-antineutron oscillations are predicted to be a signature of many baryogenesis mechanisms involving low-scale baryon number violation. This work presents first-principles calculations of neutron-antineutron matrix elements needed to accurately connect measurements of the neutron-antineutron oscillation rate to constraints on $|ΔB|=2$ baryon number violation in BSM theories. Several important systematic uncertainties are controlled by using a state-of-the-art lattice gauge field ensemble with physical quark masses and approximate chiral symmetry, performing nonperturbative renormalization with perturbative matching to the $\overline{\text{MS}}$ scheme, and studying excited state effects in two-state fits. Phenomenological implications are highlighted by comparing expected bounds from proposed neutron-antineutron oscillation experiments to predictions of a specific model of post-sphaleron baryogenesis. Quantum chromodynamics is found to predict at least an order of magnitude more events in neutron-antineutron oscillation experiments than previous estimates based on the "MIT bag model" for fixed BSM parameters. Lattice artifacts and other systematic uncertainties that are not controlled in this pioneering calculation are not expected to significantly change this conclusion.

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arXiv2019

The Role of Lattice QCD in Searches for Violations of Fundamental Symmetries and Signals for New Physics

This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for Lattice Quantum Chromodynamics (LQCD) in the research frontier in fundamental symmetries and signals for new physics. LQCD, in synergy with effective field theories and nuclear many-body studies, provides theoretical support to ongoing and planned experimental programs in searches for electric dipole moments of the nucleon, nuclei and atoms, decay of the proton, $n$-$\overline{n}$ oscillations, neutrinoless double-$β$ decay of a nucleus, conversion of muon to electron, precision measurements of weak decays of the nucleon and of nuclei, precision isotope-shift spectroscopy, as well as direct dark matter detection experiments using nuclear targets. This whitepaper details the objectives of the LQCD program in the area of Fundamental Symmetries within the USQCD collaboration, identifies priorities that can be addressed within the next five years, and elaborates on the areas that will likely demand a high degree of innovation in both numerical and analytical frontiers of the LQCD research.

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arXiv2018

Unwrapping phase fluctuations in one dimension

Correlation functions in one-dimensional complex scalar field theory provide a toy model for phase fluctuations, sign problems, and signal-to-noise problems in lattice field theory. Phase unwrapping techniques from signal processing are applied to lattice field theory in order to map compact random phases to noncompact random variables that can be numerically sampled without sign or signal-to-noise problems. A cumulant expansion can be used to reconstruct average correlation functions from moments of unwrapped phases, but points where the field magnitude fluctuates close to zero lead to ambiguities in the definition of the unwrapped phase and significant noise at higher orders in the cumulant expansion. Phase unwrapping algorithms that average fluctuations over physical length scales improve, but do not completely resolve, these issues in one dimension. Similar issues are seen in other applications of phase unwrapping, where they are found to be more tractable in higher dimensions.

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arXiv2018

Phase Unwrapping and One-Dimensional Sign Problems

Sign problems in path integrals arise when different field configurations contribute with different signs or phases. Phase unwrapping describes a family of signal processing techniques in which phase differences between elements of a time series are integrated to construct non-compact unwrapped phase differences. By combining phase unwrapping with a cumulant expansion, path integrals with sign problems arising from phase fluctuations can be systematically approximated as linear combinations of path integrals without sign problems. This work explores phase unwrapping in zero-plus-one-dimensional complex scalar field theory. Results with improved signal-to-noise ratios for the spectrum of scalar field theory can be obtained from unwrapped phases, but the size of cumulant expansion truncation errors is found to be undesirably sensitive to the parameters of the phase unwrapping algorithm employed. It is argued that this numerical sensitivity arises from discretization artifacts that become large when phases fluctuate close to singularities of a complex logarithm in the definition of the unwrapped phase.

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arXiv2018

Nuclear modification of scalar, axial and tensor charges from lattice QCD

Complete flavour decompositions of the scalar, axial and tensor charges of the proton, deuteron, diproton and $^3$He at SU(3)-symmetric values of the quark masses corresponding to a pion mass $m_π\sim806$ MeV are determined using lattice QCD. At the physical quark masses, the scalar charges constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor charges of nuclei constrain their spin content, integrated transversity and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elements of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. Significant nuclear modifications are found, with particularly large, O(10%), effects in the scalar charges. Typically, these nuclear effects reduce the effective charge of the nucleon (quenching), although in some cases an enhancement is not excluded. Given the size of the nuclear modifications of the scalar charges resolved here, contributions from correlated multi-nucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.

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arXiv2018

Comment on "Are two nucleons bound in lattice QCD for heavy quark masses? - Sanity check with Lüscher's finite volume formula -"

In this comment, we address a number of erroneous discussions and conclusions presented in a recent preprint by the HALQCD collaboration, arXiv:1703.07210. In particular, we demonstrate that lattice QCD determinations of bound states at quark masses corresponding to a pion mass of $m_π= 806$ MeV are robust, and that the phases shifts extracted by the NPLQCD collaboration for these systems pass all of the 'sanity checks' introduced in arXiv:1703.07210.

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arXiv2017

First lattice QCD study of the gluonic structure of light nuclei

The role of gluons in the structure of the nucleon and light nuclei is investigated using lattice quantum chromodynamics (QCD) calculations. The first moment of the unpolarised gluon distribution is studied in nuclei up to atomic number $A=3$ at quark masses corresponding to pion masses of $m_π\sim 450$ and $806$ MeV. Nuclear modification of this quantity defines a gluonic analogue of the EMC effect and is constrained to be less than $\sim 10$% in these nuclei. This is consistent with expectations from phenomenological quark distributions and the momentum sum rule. In the deuteron, the combination of gluon distributions corresponding to the $b_1$ structure function is found to have a small first moment compared with the corresponding momentum fraction. The first moment of the gluon transversity structure function is also investigated in the spin-1 deuteron, where a non-zero signal is observed at $m_π\sim 806$ MeV. This is the first indication of gluon contributions to nuclear structure that can not be associated with an individual nucleon.

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arXiv2017

Statistical Angles on the Lattice QCD Signal-to-Noise Problem

The theory of quantum chromodynamics (QCD) encodes the strong interactions that bind quarks and gluons into nucleons and that bind nucleons into nuclei. Predictive control of QCD would allow nuclear structure and reactions as well as properties of supernovae and neutron stars to be theoretically studied from first principles. Lattice QCD can represent generic QCD predictions in terms of well-defined path integrals, but the sign and signal-to-noise problems have obstructed lattice QCD calculations of large nuclei and nuclear matter in practice. This thesis presents a statistical study of lattice QCD correlation functions, with a particular focus on characterizing the structure of the noise associated with quantum fluctuations. The signal-to-noise problem in baryon correlation functions is demonstrated to arise from a sign problem associated with Monte Carlo sampling of complex correlation functions. The phases of complex correlation functions are analyzed in the framework of circular statistics, and the time evolution of the phase is shown to resemble a heavy-tailed random walk on the unit circle. Building on these observations, a new technique called phase reweighting is investigated that involves calculations of phase differences over fixed-length time intervals. Phase reweighting allows results for hadronic observables to be extracted from large-time correlation functions with constant signal-to-noise ratios. The signal-to-noise problem re-emerges as the length of the phase-difference interval is increased. Applications of phase reweighting to meson, baryon, and two-baryon systems are discussed.

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arXiv2017

Life Outside the Golden Window: Statistical Angles on the Signal-to-Noise Problem

Lattice QCD simulations of multi-baryon correlation functions can predict the structure and reactions of nuclei without encountering the baryon chemical potential sign problem. However, they suffer from a signal-to-noise problem where Monte Carlo estimates of observables have quantum fluctuations that are exponentially larger than their average values. Recent lattice QCD results demonstrate that the complex phase of baryon correlations functions relates the baryon signal-to-noise problem to a sign problem and exhibits unexpected statistical behavior resembling a heavy-tailed random walk on the unit circle. Estimators based on differences of correlation function phases evaluated at different Euclidean times are discussed that avoid the usual signal-to-noise problem, instead facing a signal-to-noise problem as the time interval associated with the phase difference is increased, and allow hadronic observables to be determined from arbitrarily large-time correlation functions.

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arXiv2017

The isotensor axial polarisability and lattice QCD input for nuclear double-$β$ decay phenomenology

The potential importance of short-distance nuclear effects in double-$β$ decay is assessed using a lattice QCD calculation of the $nn\rightarrow pp$ transition and effective field theory methods. At the unphysical quark masses used in the numerical computation, these effects, encoded in the isotensor axial polarisability, are found to be of similar magnitude to the nuclear modification of the single axial current, which phenomenologically is the quenching of the axial charge used in nuclear many-body calculations. This finding suggests that nuclear models for neutrinoful and neutrinoless double-$β$ decays should incorporate this previously neglected contribution if they are to provide reliable guidance for next-generation neutrinoless double-$β$ decay searches. The prospects of constraining the isotensor axial polarisabilities of nuclei using lattice QCD input into nuclear many-body calculations are discussed.

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