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Direct calculation of parton distributions in momentum space from lattice QCD
Authors:
Anthony V. Grebe,
Daniel C. Hackett,
Michael L. Wagman,
Rui Zhang,
Yong Zhao
Abstract:
Coulomb-gauge quasi-parton distributions can be computed directly in momentum space on a finite lattice, enabled by the commutativity of their renormalization and Fourier transform. This approach removes the formal inverse problem in coordinate-space methods. Our momentum-space pion quasi-distributions agree with coordinate-space results Fourier transformed with asymptotic extrapolation, indicatin…
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Coulomb-gauge quasi-parton distributions can be computed directly in momentum space on a finite lattice, enabled by the commutativity of their renormalization and Fourier transform. This approach removes the formal inverse problem in coordinate-space methods. Our momentum-space pion quasi-distributions agree with coordinate-space results Fourier transformed with asymptotic extrapolation, indicating that the formal inverse problem in the latter is not a concern at this volume. We further extend the framework to higher dimensions and obtain the first 3D image of the pion directly from lattice QCD.
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Submitted 15 June, 2026;
originally announced June 2026.
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Excited-state uncertainties in lattice-QCD calculations of hadron masses and scattering phase shifts
Authors:
William Detmold,
Anthony V. Grebe,
Daniel C. Hackett,
Marc Illa,
Robert J. Perry,
Phiala E. Shanahan,
Michael L. Wagman
Abstract:
Lattice QCD has historically produced energy results interpretable as either estimates relying on implicit assumptions about asymptotic behavior or one-sided upper bounds. New Lanczos methods providing two-sided bounds with less-restrictive assumptions are introduced and quantified in a high-statistics calculation with unphysical quark masses. Two-sided bounds without spectral assumptions provide…
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Lattice QCD has historically produced energy results interpretable as either estimates relying on implicit assumptions about asymptotic behavior or one-sided upper bounds. New Lanczos methods providing two-sided bounds with less-restrictive assumptions are introduced and quantified in a high-statistics calculation with unphysical quark masses. Two-sided bounds without spectral assumptions provide sub-percent constraints on the nucleon mass. Other bounds, which assume all states in a given energy window are resolved, provide meaningful two-sided constraints on nucleon-nucleon scattering phase shifts.
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Submitted 29 January, 2026;
originally announced January 2026.
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Excited-state uncertainties in lattice-QCD calculations of multi-hadron systems
Authors:
William Detmold,
Anthony V. Grebe,
Daniel C. Hackett,
Marc Illa,
Robert J. Perry,
Phiala E. Shanahan,
Michael L. Wagman
Abstract:
Excited-state effects lead to hard-to-quantify systematic uncertainties in lattice quantum chromodynamics (LQCD) spectroscopy calculations when computationally accessible imaginary times are smaller than inverse excitation gaps, as often arises for multi-hadron systems with signal-to-noise problems. Lanczos residual bounds address this by providing two-sided constraints on energies that do not req…
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Excited-state effects lead to hard-to-quantify systematic uncertainties in lattice quantum chromodynamics (LQCD) spectroscopy calculations when computationally accessible imaginary times are smaller than inverse excitation gaps, as often arises for multi-hadron systems with signal-to-noise problems. Lanczos residual bounds address this by providing two-sided constraints on energies that do not require assumptions beyond Hermiticity, but often give very conservative systematic uncertainty estimates. Here, a more-constraining set of gap bounds is introduced for hadron spectroscopy. These bounds provide tighter constraints whose validity requires an explicit assumption about an energy gap. Exactly solvable lattice field theory correlators are used to test the utility of residual and gap bounds at finite and infinite statistics. Two-sided bounds and other analysis methods are then applied to a high-statistics LQCD calculation of nucleon-nucleon scattering at $m_π\sim 800$ MeV. Generalized eigenvalue problem (GEVP) and Lanczos energy estimators are compatible when applied to the same correlator data, but analyses including different interpolating operators show statistically significant inconsistencies. However, two-sided bounds from all operators are consistent. Under the assumption that the number of energy levels below $NΔ$ and $ΔΔ$ thresholds is the same as for non-interacting nucleons, gap bounds are sufficient to constrain nucleon-nucleon scattering amplitudes at phenomenologically relevant precision. Lanczos methods further reveal that energy-eigenstate estimates from previously studied asymmetric correlators have not converged over accessible imaginary times. Nevertheless, data-driven examples demonstrate why assumptions are required to draw conclusions about the natures of two-nucleon ground states at these masses.
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Submitted 29 January, 2026;
originally announced January 2026.
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Improving Neutrino Oscillation Measurements through Event Classification
Authors:
Sebastian A. R. Ellis,
Daniel C. Hackett,
Shirley Weishi Li,
Pedro A. N. Machado,
Karla Tame-Narvaez
Abstract:
Precise neutrino energy reconstruction is essential for next-generation long-baseline oscillation experiments, yet current methods remain limited by large uncertainties in neutrino-nucleus interaction modeling. Even so, it is well established that different interaction channels produce systematically varying amounts of missing energy and therefore yield different reconstruction performance--inform…
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Precise neutrino energy reconstruction is essential for next-generation long-baseline oscillation experiments, yet current methods remain limited by large uncertainties in neutrino-nucleus interaction modeling. Even so, it is well established that different interaction channels produce systematically varying amounts of missing energy and therefore yield different reconstruction performance--information that standard calorimetric approaches do not exploit. We introduce a strategy that incorporates this structure by classifying events according to their underlying interaction type prior to energy reconstruction. Using supervised machine-learning techniques trained on labeled generator events, we leverage intrinsic kinematic differences among quasi-elastic scattering, meson-exchange current, resonance production, and deep-inelastic scattering processes. A cross-generator testing framework demonstrates that this classification approach is robust to microphysics mismodeling and, when applied to a simulated DUNE $ν_μ$ disappearance analysis, yields improved accuracy and sensitivity at the 10-20% level. These results highlight a practical path toward reducing reconstruction-driven systematics in future oscillation measurements.
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Submitted 12 April, 2026; v1 submitted 14 November, 2025;
originally announced November 2025.
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Lattice evidence that scalar glueballs are small
Authors:
Ryan Abbott,
Daniel C. Hackett,
Dimitra A. Pefkou,
Fernando Romero-López,
Phiala E. Shanahan
Abstract:
This work reports the first calculation of the gravitational form factors (GFFs) of the scalar glueball, performed via lattice field theory in Yang-Mills theory at a single lattice spacing. The glueball GFFs are compared with those of other hadrons as determined in previous lattice calculations, providing strong indications that glueballs have a different gluonic structure than typical hadronic st…
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This work reports the first calculation of the gravitational form factors (GFFs) of the scalar glueball, performed via lattice field theory in Yang-Mills theory at a single lattice spacing. The glueball GFFs are compared with those of other hadrons as determined in previous lattice calculations, providing strong indications that glueballs have a different gluonic structure than typical hadronic states. A mass radius of 0.263(31) fm is predicted, supporting previous suggestions that the scalar glueball is significantly smaller than other hadrons. These results point towards a potential smoking-gun characteristic to target by experimental glueball searches.
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Submitted 29 August, 2025;
originally announced August 2025.
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Kinematically-enhanced interpolating operators for boosted hadrons
Authors:
Rui Zhang,
Anthony V. Grebe,
Daniel C. Hackett,
Michael L. Wagman,
Yong Zhao
Abstract:
We propose to use interpolating operators for lattice quantum chromodyanmics (QCD) calculations of highly-boosted pions and nucleons with kinematically-enhanced ground-state overlap factors at large momentum. Because this kinematic enhancement applies to the signal but not the variance of the correlation function, these interpolating operators can achieve better signal-to-noise ratios at large mom…
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We propose to use interpolating operators for lattice quantum chromodyanmics (QCD) calculations of highly-boosted pions and nucleons with kinematically-enhanced ground-state overlap factors at large momentum. Because this kinematic enhancement applies to the signal but not the variance of the correlation function, these interpolating operators can achieve better signal-to-noise ratios at large momentum. We perform proof-of-principle calculations with boosted pions and nucleons using close-to-physical and larger quark masses to explore the utility of our proposal. Results for effective energies and matrix elements, as well as Lanczos ground-state energy estimators, are consistent with theoretical expectations for signal-to-noise improvement at large momenta.
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Submitted 26 September, 2025; v1 submitted 1 January, 2025;
originally announced January 2025.
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Machine Learning Neutrino-Nucleus Cross Sections
Authors:
Daniel C. Hackett,
Joshua Isaacson,
Shirley Weishi Li,
Karla Tame-Narvaez,
Michael L. Wagman
Abstract:
Neutrino-nucleus scattering cross sections are critical theoretical inputs for long-baseline neutrino oscillation experiments. However, robust modeling of these cross sections remains challenging. For a simple but physically motivated toy model of the DUNE experiment, we demonstrate that an accurate neural-network model of the cross section -- leveraging only Standard-Model symmetries -- can be le…
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Neutrino-nucleus scattering cross sections are critical theoretical inputs for long-baseline neutrino oscillation experiments. However, robust modeling of these cross sections remains challenging. For a simple but physically motivated toy model of the DUNE experiment, we demonstrate that an accurate neural-network model of the cross section -- leveraging only Standard-Model symmetries -- can be learned from near-detector data. We perform a neutrino oscillation analysis with simulated far-detector events, finding that oscillation analysis results enabled by our data-driven cross-section model approach the theoretical limit achievable with perfect prior knowledge of the cross section. We further quantify the effects of flux shape and detector resolution uncertainties as well as systematics from cross-section mismodeling. This proof-of-principle study highlights the potential of future neutrino near-detector datasets and data-driven cross-section models.
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Submitted 7 December, 2025; v1 submitted 20 December, 2024;
originally announced December 2024.
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Block Lanczos algorithm for lattice QCD spectroscopy and matrix elements
Authors:
Daniel C. Hackett,
Michael L. Wagman
Abstract:
Recent work introduced a new framework for analyzing correlation functions with improved convergence and signal-to-noise properties, as well as rigorous quantification of excited-state effects, based on the Lanczos algorithm and spurious eigenvalue filtering with the Cullum-Willoughby test. Here, we extend this framework to the analysis of correlation-function matrices built from multiple interpol…
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Recent work introduced a new framework for analyzing correlation functions with improved convergence and signal-to-noise properties, as well as rigorous quantification of excited-state effects, based on the Lanczos algorithm and spurious eigenvalue filtering with the Cullum-Willoughby test. Here, we extend this framework to the analysis of correlation-function matrices built from multiple interpolating operators in lattice quantum chromodynamics (QCD) by constructing an oblique generalization of the block Lanczos algorithm, as well as a new physically motivated reformulation of the Cullum-Willoughby test that generalizes to block Lanczos straightforwardly. The resulting block Lanczos method directly extends generalized eigenvalue problem (GEVP) methods, which can be viewed as applying a single iteration of block Lanczos. Block Lanczos provides qualitative and quantitative advantages over GEVP methods analogous to the benefits of Lanczos over the standard effective mass, including faster convergence to ground- and excited-state energies, explicitly computable two-sided error bounds, straightforward extraction of matrix elements of external currents, and asymptotically constant signal-to-noise. No fits or statistical inference are required. Proof-of-principle calculations are performed for noiseless mock-data examples as well as two-by-two proton correlation-function matrices in lattice QCD.
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Submitted 21 August, 2025; v1 submitted 5 December, 2024;
originally announced December 2024.
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Gravitational form factors of glueballs in Yang-Mills theory
Authors:
Ryan Abbott,
Daniel C. Hackett,
Dimitra A. Pefkou,
Fernando Romero-López,
Phiala Shanahan
Abstract:
This work presents preliminary results of the first determination of the energy-momentum tensor form factors of the scalar glueball, referred to as gravitational form factors (GFFs). The calculation has been carried out in lattice Yang-Mills theory at a single lattice spacing. Using variationally optimized operators, the matrix elements are extracted from ratios of three-point functions to two-poi…
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This work presents preliminary results of the first determination of the energy-momentum tensor form factors of the scalar glueball, referred to as gravitational form factors (GFFs). The calculation has been carried out in lattice Yang-Mills theory at a single lattice spacing. Using variationally optimized operators, the matrix elements are extracted from ratios of three-point functions to two-point functions. The glueball GFFs and their kinematic dependence are compared to those of other hadrons from previous calculations.
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Submitted 31 January, 2025; v1 submitted 3 October, 2024;
originally announced October 2024.
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Gravitational form factors of the proton from lattice QCD
Authors:
Daniel C. Hackett,
Dimitra A. Pefkou,
Phiala E. Shanahan
Abstract:
The gravitational form factors (GFFs) of a hadron encode fundamental aspects of its structure, including its shape and size as defined from e.g., its energy density. This work presents a determination of the flavor decomposition of the GFFs of the proton from lattice QCD, in the kinematic region $0\leq -t\leq 2~\text{GeV}^2$. The decomposition into up-, down-, strange-quark, and gluon contribution…
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The gravitational form factors (GFFs) of a hadron encode fundamental aspects of its structure, including its shape and size as defined from e.g., its energy density. This work presents a determination of the flavor decomposition of the GFFs of the proton from lattice QCD, in the kinematic region $0\leq -t\leq 2~\text{GeV}^2$. The decomposition into up-, down-, strange-quark, and gluon contributions provides first-principles constraints on the role of each constituent in generating key proton structure observables, such as its mechanical radius, mass radius, and $D$-term.
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Submitted 23 June, 2024; v1 submitted 12 October, 2023;
originally announced October 2023.
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Gravitational form factors of the pion from lattice QCD
Authors:
Daniel C. Hackett,
Patrick R. Oare,
Dimitra A. Pefkou,
Phiala E. Shanahan
Abstract:
The two gravitational form factors of the pion, $A^π(t)$ and $D^π(t)$, are computed as functions of the momentum transfer squared $t$ in the kinematic region $0\leq -t< 2~\text{GeV}^2$ on a lattice QCD ensemble with quark masses corresponding to a close-to-physical pion mass $m_π\approx 170~\text{MeV}$ and $N_f=2+1$ quark flavors. The flavor decomposition of these form factors into gluon, up/down…
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The two gravitational form factors of the pion, $A^π(t)$ and $D^π(t)$, are computed as functions of the momentum transfer squared $t$ in the kinematic region $0\leq -t< 2~\text{GeV}^2$ on a lattice QCD ensemble with quark masses corresponding to a close-to-physical pion mass $m_π\approx 170~\text{MeV}$ and $N_f=2+1$ quark flavors. The flavor decomposition of these form factors into gluon, up/down light-quark, and strange-quark contributions is presented in the $\overline{\text{MS}}$ scheme at energy scale $μ=2~\text{GeV}$, with renormalization factors computed nonperturbatively via the RI-MOM scheme. Using monopole and $z$-expansion fits to the gravitational form factors, we obtain estimates for the pion momentum fraction and $D$-term that are consistent with the momentum fraction sum rule and the next-to-leading order chiral perturbation theory prediction for $D^π(0)$.
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Submitted 11 December, 2023; v1 submitted 21 July, 2023;
originally announced July 2023.
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The Present and Future of QCD
Authors:
P. Achenbach,
D. Adhikari,
A. Afanasev,
F. Afzal,
C. A. Aidala,
A. Al-bataineh,
D. K. Almaalol,
M. Amaryan,
D. Androić,
W. R. Armstrong,
M. Arratia,
J. Arrington,
A. Asaturyan,
E. C. Aschenauer,
H. Atac,
H. Avakian,
T. Averett,
C. Ayerbe Gayoso,
X. Bai,
K. N. Barish,
N. Barnea,
G. Basar,
M. Battaglieri,
A. A. Baty,
I. Bautista
, et al. (378 additional authors not shown)
Abstract:
This White Paper presents the community inputs and scientific conclusions from the Hot and Cold QCD Town Meeting that took place September 23-25, 2022 at MIT, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 424 physicists registered for the meeting. The meeting highlighted progress in Quantum Chromodynamics (QCD) nuclear physics since the 2015…
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This White Paper presents the community inputs and scientific conclusions from the Hot and Cold QCD Town Meeting that took place September 23-25, 2022 at MIT, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 424 physicists registered for the meeting. The meeting highlighted progress in Quantum Chromodynamics (QCD) nuclear physics since the 2015 LRP (LRP15) and identified key questions and plausible paths to obtaining answers to those questions, defining priorities for our research over the coming decade. In defining the priority of outstanding physics opportunities for the future, both prospects for the short (~ 5 years) and longer term (5-10 years and beyond) are identified together with the facilities, personnel and other resources needed to maximize the discovery potential and maintain United States leadership in QCD physics worldwide. This White Paper is organized as follows: In the Executive Summary, we detail the Recommendations and Initiatives that were presented and discussed at the Town Meeting, and their supporting rationales. Section 2 highlights major progress and accomplishments of the past seven years. It is followed, in Section 3, by an overview of the physics opportunities for the immediate future, and in relation with the next QCD frontier: the EIC. Section 4 provides an overview of the physics motivations and goals associated with the EIC. Section 5 is devoted to the workforce development and support of diversity, equity and inclusion. This is followed by a dedicated section on computing in Section 6. Section 7 describes the national need for nuclear data science and the relevance to QCD research.
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Submitted 4 March, 2023;
originally announced March 2023.
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Report of the Snowmass 2021 Topical Group on Lattice Gauge Theory
Authors:
Zohreh Davoudi,
Ethan T. Neil,
Christian W. Bauer,
Tanmoy Bhattacharya,
Thomas Blum,
Peter Boyle,
Richard C. Brower,
Simon Catterall,
Norman H. Christ,
Vincenzo Cirigliano,
Gilberto Colangelo,
Carleton DeTar,
William Detmold,
Robert G. Edwards,
Aida X. El-Khadra,
Steven Gottlieb,
Rajan Gupta,
Daniel C. Hackett,
Anna Hasenfratz,
Taku Izubuchi,
William I. Jay,
Luchang Jin,
Christopher Kelly,
Andreas S. Kronfeld,
Christoph Lehner
, et al. (13 additional authors not shown)
Abstract:
Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure…
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Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure and spectrum, to serve as a numerical laboratory to reach beyond the Standard Model, or to invent and improve state-of-the-art computational paradigms, the lattice-gauge-theory program is in a prime position to impact the course of developments and enhance discovery potential of a vibrant experimental program in High-Energy Physics over the coming decade. This projection is based on abundant successful results that have emerged using lattice gauge theory over the years: on continued improvement in theoretical frameworks and algorithmic suits; on the forthcoming transition into the exascale era of high-performance computing; and on a skillful, dedicated, and organized community of lattice gauge theorists in the U.S. and worldwide. The prospects of this effort in pushing the frontiers of research in High-Energy Physics have recently been studied within the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021), and the conclusions are summarized in this Topical Report.
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Submitted 21 September, 2022;
originally announced September 2022.
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Applications of Machine Learning to Lattice Quantum Field Theory
Authors:
Denis Boyda,
Salvatore Calì,
Sam Foreman,
Lena Funcke,
Daniel C. Hackett,
Yin Lin,
Gert Aarts,
Andrei Alexandru,
Xiao-Yong Jin,
Biagio Lucini,
Phiala E. Shanahan
Abstract:
There is great potential to apply machine learning in the area of numerical lattice quantum field theory, but full exploitation of that potential will require new strategies. In this white paper for the Snowmass community planning process, we discuss the unique requirements of machine learning for lattice quantum field theory research and outline what is needed to enable exploration and deployment…
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There is great potential to apply machine learning in the area of numerical lattice quantum field theory, but full exploitation of that potential will require new strategies. In this white paper for the Snowmass community planning process, we discuss the unique requirements of machine learning for lattice quantum field theory research and outline what is needed to enable exploration and deployment of this approach in the future.
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Submitted 10 February, 2022;
originally announced February 2022.
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Soft pion scattering in infrared-conformal gauge-fermion theories
Authors:
Daniel C. Hackett,
Ethan T. Neil
Abstract:
We consider the problem of soft scattering for the analogue of pion states in gauge-fermion theories which approach a conformal fixed point in the infrared limit. Introducing a fermion mass into such a theory will explicitly break both scale invariance and chiral symmetry, leading to confinement and a spectrum of bound states. We argue that in such a theory, the pion scattering length diverges in…
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We consider the problem of soft scattering for the analogue of pion states in gauge-fermion theories which approach a conformal fixed point in the infrared limit. Introducing a fermion mass into such a theory will explicitly break both scale invariance and chiral symmetry, leading to confinement and a spectrum of bound states. We argue that in such a theory, the pion scattering length diverges in the limit of zero fermion mass, in sharp contrast to QCD-like theories where the chiral Lagrangian predicts a vanishing scattering length. We demonstrate this effect both with a simple dimensional argument, and in a generalized linear sigma model which we argue can be used to describe the interactions of light scalar and pseudoscalar bound states in the soft limit of a mass-deformed infrared-conformal theory. As a result, lattice calculations of pion scattering lengths could be a sensitive probe for infrared scale invariance in gauge-fermion theories.
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Submitted 7 August, 2023; v1 submitted 1 July, 2021;
originally announced July 2021.
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Towards a composite Higgs and a partially composite top quark
Authors:
B. Svetitsky,
V. Ayyar,
T. DeGrand,
M. Golterman,
D. C. Hackett,
W. I. Jay,
E. T. Neil,
Y. Shamir
Abstract:
We have calculated quantities of interest to a theory of compositeness. The lattice model, approximating the candidate theory, is the SU(4) gauge theory coupled to fermions in two color representations. For the composite Higgs, a current correlator gives one of the ingredients of the effective Higgs potential. For the partially composite top quark, we have hyperbaryon matrix elements that govern m…
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We have calculated quantities of interest to a theory of compositeness. The lattice model, approximating the candidate theory, is the SU(4) gauge theory coupled to fermions in two color representations. For the composite Higgs, a current correlator gives one of the ingredients of the effective Higgs potential. For the partially composite top quark, we have hyperbaryon matrix elements that govern mixing of the fundamental quark with its heavy composite partner. The matrix elements turn out to be so small that the theory is disfavored as a source of a realistic top mass.
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Submitted 25 November, 2019;
originally announced November 2019.
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Radiative contribution to the composite-Higgs potential in a two-representation lattice model
Authors:
Venkitesh Ayyar,
Maarten Golterman,
Daniel C. Hackett,
William I. Jay,
Ethan T. Neil,
Yigal Shamir,
and Benjamin Svetitsky
Abstract:
Working in a two-representation lattice gauge theory that is close to a composite Higgs model, we calculate the low-energy constant CLR which controls the contribution of the electroweak gauge bosons to the Higgs potential. In QCD, the corresponding low-energy constant governs the mass splitting of the pion multiplet. Taking the continuum and chiral limits, we find that CLR, in units of the pseudo…
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Working in a two-representation lattice gauge theory that is close to a composite Higgs model, we calculate the low-energy constant CLR which controls the contribution of the electroweak gauge bosons to the Higgs potential. In QCD, the corresponding low-energy constant governs the mass splitting of the pion multiplet. Taking the continuum and chiral limits, we find that CLR, in units of the pseudoscalar decay constant, is roughly of the same size as its QCD counterpart.
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Submitted 4 March, 2019;
originally announced March 2019.
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Partial compositeness and baryon matrix elements on the lattice
Authors:
Venkitesh Ayyar,
Thomas DeGrand,
Daniel C. Hackett,
William I. Jay,
Ethan T. Neil,
Yigal Shamir,
Benjamin Svetitsky
Abstract:
Partial compositeness is a mechanism for the generation of fermion masses which replaces a direct Higgs coupling to the fermions by a linear mixing with heavy composite partners. We present the first calculation of the relevant matrix element in a lattice model which is very close to a candidate theory containing a composite Higgs boson and a partially composite top quark. Specifically, our model…
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Partial compositeness is a mechanism for the generation of fermion masses which replaces a direct Higgs coupling to the fermions by a linear mixing with heavy composite partners. We present the first calculation of the relevant matrix element in a lattice model which is very close to a candidate theory containing a composite Higgs boson and a partially composite top quark. Specifically, our model is an SU(4) gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations. The matrix element we obtain is small and hence our result disfavors the scenario of obtaining a realistic top mass in this model.
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Submitted 17 May, 2019; v1 submitted 6 December, 2018;
originally announced December 2018.
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Digitizing Gauge Fields: Lattice Monte Carlo Results for Future Quantum Computers
Authors:
Daniel C. Hackett,
Kiel Howe,
Ciaran Hughes,
William Jay,
Ethan T. Neil,
James N. Simone
Abstract:
In the near-future noisy intermediate-scale quantum (NISQ) era of quantum computing technology, applications of quantum computing will be limited to calculations of very modest scales in terms of the number of qubits used. The need to represent numeric quantities using limited resources leads to digitization errors which must be taken into account. As a first step towards quantum simulations of re…
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In the near-future noisy intermediate-scale quantum (NISQ) era of quantum computing technology, applications of quantum computing will be limited to calculations of very modest scales in terms of the number of qubits used. The need to represent numeric quantities using limited resources leads to digitization errors which must be taken into account. As a first step towards quantum simulations of realistic high-energy physics problems, we explore classically the effects of digitizing elements of the $\mathrm{SU}(2)$ gauge group to a finite set. We consider several methods for digitizing the group, finding the best performance from an action-preserving projection onto a mesh. Working in (3+1) dimensions, we find that using $\sim 7$ (qu)bits to represent each $\mathrm{SU}(2)$ gauge link induces a digitization error on the order of $10\%$ in short-distance observables and $2\%$ in long-distance observables. Promisingly, our results indicate that each $\mathrm{SU}(2)$ gauge link can be represented by $\mathcal{O}(10)$ (qu)bits, from which we estimate that a $16^3$ $\mathrm{SU}(2)$ lattice could be simulated with no more than $\mathcal{O}(10^5)$ (qu)bits. Our results on digitization are also of interest as a form of lossy compression that could be used in high-performance classical computing to alleviate communications bottlenecks.
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Submitted 8 November, 2018;
originally announced November 2018.
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Large $N_c$ Thermodynamics with Dynamical Fermions
Authors:
Thomas DeGrand,
Daniel C. Hackett,
Ethan T. Neil
Abstract:
We present a progress report on our investigation of the thermodynamics of QCD with $N_f=2$ flavors of dynamical Wilson fermions in the limit of a large number of colors $N_c$. To date, studies of the thermodynamics of QCD at large $N_c$ have been limited to the quenched approximation, i.e., to the behavior of pure $\mathrm{SU}(N_c)$ gauge theory at large $N_c$. This is the first study of thermody…
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We present a progress report on our investigation of the thermodynamics of QCD with $N_f=2$ flavors of dynamical Wilson fermions in the limit of a large number of colors $N_c$. To date, studies of the thermodynamics of QCD at large $N_c$ have been limited to the quenched approximation, i.e., to the behavior of pure $\mathrm{SU}(N_c)$ gauge theory at large $N_c$. This is the first study of thermodynamics at large $N_c$ using dynamical fermions, and thus the first study able to test whether the quenched approximation is a valid way to investigate large $N_c$ thermodynamics. After reviewing 't Hooft's large $N_c$ limit, we discuss the automation we use to make this study feasible, and finally compare our preliminary physics results for $\mathrm{SU}(3-5)$ with large $N_c$ expectations.
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Submitted 26 September, 2018; v1 submitted 31 August, 2018;
originally announced September 2018.
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Finite-temperature phase structure of SU(4) gauge theory with multiple fermion representations
Authors:
Venkitesh Ayyar,
Thomas DeGrand,
Daniel C. Hackett,
William I. Jay,
Ethan T. Neil,
Yigal Shamir,
Benjamin Svetitsky
Abstract:
We investigate the phase structure of SU(4) gauge theory with the gauge field simultaneously coupled to two flavors of fermion in the fundamental representation and two flavors of fermion in the two-index antisymmetric representation. We find that the theory has only two phases, a low-temperature phase with both species of fermion confined and chirally broken, and a high-temperature phase with bot…
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We investigate the phase structure of SU(4) gauge theory with the gauge field simultaneously coupled to two flavors of fermion in the fundamental representation and two flavors of fermion in the two-index antisymmetric representation. We find that the theory has only two phases, a low-temperature phase with both species of fermion confined and chirally broken, and a high-temperature phase with both species of fermion deconfined and chirally restored. The single phase transition in the theory appears to be first order, in agreement with theoretical predictions.
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Submitted 26 February, 2018;
originally announced February 2018.
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Baryon spectrum of SU(4) composite Higgs theory with two distinct fermion representations
Authors:
Venkitesh Ayyar,
Thomas DeGrand,
Daniel C. Hackett,
William I. Jay,
Ethan T. Neil,
Yigal Shamir,
Benjamin Svetitsky
Abstract:
We use lattice simulations to compute the baryon spectrum of SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. This model is closely related to a composite Higgs model in which the chimera baryon made up of fermions from both representations plays the role of a composite top-quark partner. The dependence…
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We use lattice simulations to compute the baryon spectrum of SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. This model is closely related to a composite Higgs model in which the chimera baryon made up of fermions from both representations plays the role of a composite top-quark partner. The dependence of the baryon masses on each underlying fermion mass is found to be generally consistent with a quark-model description and large-Nc scaling. We combine our numerical results with experimental bounds on the scale of the new strong sector to derive a lower bound on the mass of the top partner.
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Submitted 17 January, 2018;
originally announced January 2018.
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Stability Analysis of the Chiral Transition in SU(4) Gauge Theory with Fermions in Multiple Representations
Authors:
Daniel C. Hackett
Abstract:
We present a Pisarski-Wilczek stability analysis of SU(4) gauge theory coupled simultaneously to fermions charged under the fundamental and two-index antisymmetric representations of the gauge group. We carry out the calculation to one loop in the $ε$ expansion, assuming that the two species of fermion undergo a simultaneous chiral transition. The results indicate that the chiral transition is fir…
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We present a Pisarski-Wilczek stability analysis of SU(4) gauge theory coupled simultaneously to fermions charged under the fundamental and two-index antisymmetric representations of the gauge group. We carry out the calculation to one loop in the $ε$ expansion, assuming that the two species of fermion undergo a simultaneous chiral transition. The results indicate that the chiral transition is first order.
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Submitted 5 December, 2017;
originally announced December 2017.
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Confinement study of an SU(4) gauge theory with fermions in multiple representations
Authors:
Venkitesh Ayyar,
Daniel Hackett,
William Jay,
Ethan Neil
Abstract:
We discuss the phase diagnostics used in our finite-temperature study of an SU(4) gauge theory with dynamical fermions in both the fundamental and two-index antisymmetric representations. Beyond the usual Polyakov loop diagnostics of confinement, we employ several Wilson flow phase diagnostics. The first, what we call the "flow anisotropy", is known in the literature: the deconfinement transition…
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We discuss the phase diagnostics used in our finite-temperature study of an SU(4) gauge theory with dynamical fermions in both the fundamental and two-index antisymmetric representations. Beyond the usual Polyakov loop diagnostics of confinement, we employ several Wilson flow phase diagnostics. The first, what we call the "flow anisotropy", is known in the literature: the deconfinement transition introduces anisotropy between the spatial and temporal directions, to which the flow is extremely sensitive. The second, the "long flow time Polyakov loop," is related but novel. While we do not claim to fully understand this diagnostic, we have empirically found it to be useful as an unusually sharp diagnostic of phase.
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Submitted 9 October, 2017;
originally announced October 2017.
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Spectroscopy of SU(4) composite Higgs theory with two distinct fermion representations
Authors:
Venkitesh Ayyar,
Thomas DeGrand,
Maarten Golterman,
Daniel C. Hackett,
William I. Jay,
Ethan T. Neil,
Yigal Shamir,
Benjamin Svetitsky
Abstract:
We have simulated the SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. Such theories arise naturally in the context of composite Higgs models that include a partially composite top quark. We describe the low-lying meson spectrum of the theory and fit the pseudoscalar masses and decay constants to chiral…
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We have simulated the SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. Such theories arise naturally in the context of composite Higgs models that include a partially composite top quark. We describe the low-lying meson spectrum of the theory and fit the pseudoscalar masses and decay constants to chiral perturbation theory. We infer as well the mass and decay constant of the Goldstone boson corresponding to the non-anomalous U(1) symmetry of the model. Our results are broadly consistent with large-Nc scaling and vector-meson dominance.
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Submitted 7 May, 2018; v1 submitted 2 October, 2017;
originally announced October 2017.
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Chiral Transition of SU(4) Gauge Theory with Fermions in Multiple Representations
Authors:
Venkitesh Ayyar,
Thomas DeGrand,
Daniel C. Hackett,
William I. Jay,
Ethan T. Neil,
Yigal Shamir,
Benjamin Svetitsky
Abstract:
We report preliminary results on the finite temperature behavior of SU(4) gauge theory with dynamical quarks in both the fundamental and two-index antisymmetric representations. This system is a candidate to present scale separation behavior, where fermions in different representations condense at different temperature or coupling scales. Our simulations, however, reveal a single finite-temperatur…
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We report preliminary results on the finite temperature behavior of SU(4) gauge theory with dynamical quarks in both the fundamental and two-index antisymmetric representations. This system is a candidate to present scale separation behavior, where fermions in different representations condense at different temperature or coupling scales. Our simulations, however, reveal a single finite-temperature phase transition at which both representations deconfine and exhibit chiral restoration. It appears to be strongly first order. We compare our results to previous single-representation simulations. We also describe a Pisarski-Wilczek stability analysis, which suggests that the transition should be first order.
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Submitted 18 September, 2017;
originally announced September 2017.
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Towards Partial Compositeness on the Lattice: Baryons with Fermions in Multiple Representations
Authors:
Thomas A. DeGrand,
Daniel Hackett,
William I. Jay,
Ethan T. Neil,
Yigal Shamir,
Benjamin Svetitsky
Abstract:
We describe our recent lattice study of SU(4) gauge theory with fermions in the fundamental and sextet representations. In this theory, a new type of baryon consists of quarks in both representations. The spectrum of these "chimera baryons" has a straightforward interpretation in terms of a non-relativistic quark model based on SU(4). Our results are particularly relevant to composite Higgs models…
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We describe our recent lattice study of SU(4) gauge theory with fermions in the fundamental and sextet representations. In this theory, a new type of baryon consists of quarks in both representations. The spectrum of these "chimera baryons" has a straightforward interpretation in terms of a non-relativistic quark model based on SU(4). Our results are particularly relevant to composite Higgs models in which the top quark is partially composite.
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Submitted 20 October, 2016;
originally announced October 2016.