arXiv subjects

Frank Winter

Publications and source records attributed to Frank Winter.

At least 19 recordsLinked to original sources

arXiv2026

The Momentum Fraction, Helicity and Transversity Isovector Moments of Nucleons from \texorpdfstring{$2+1$}{2+1}-flavor Lattice QCD

Results for the isovector momentum fraction, $\langle x \rangle_{u-d}$, helicity moment, $\langle x \rangle_{\Delta u-\Delta d}$, and the transversity moment, $\langle x\rangle_{\delta u-\delta d}$, of the nucleon are presented using high-statistics data on thirteen NME ensembles of gauge configurations generated by the JLab/W\&M/LANL/MIT/Marseille collaborations using $2+1$-flavors of dynamical Wilson-clover quarks. The much higher statistics facilitated better control over all systematics compared to our previous lattice calculation. The least controlled systematic---excited-state contamination---is quantified by studying the variation of the results as a function of three estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions. The final results are obtained using a simultaneous fit to extrapolate in the lattice spacing, $a$, pion and kaon masses, $M_\pi$ and $M_K$, and the finite volume parameter, $M_\pi L$. The data show no significant finite-volume correction, and some dependence on the lattice spacing and the renormalization factors. The largest systematic uncertainty is due to possible remaining excited states contributions. Our final results, in the $\overline{\rm MS}$ scheme at 2~GeV, are $\langle x \rangle_{u-d} = 0.154(10)(9)$, $\langle x \rangle_{\Delta u-\Delta d} = 0.177(10)(15)$ and $\langle x \rangle_{\delta u-\delta d} = 0.197(12)(18)$, where the first error is the overall statistical uncertainty and the second represents the various systematic uncertainties added in quadrature. Results for the momentum fraction and helicity moment are consistent with phenomenological global fit values, while the transversity moment is a prediction.

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arXiv2026

The Spectrum and Scale Setting on 2+1-flavor NME Lattices

This paper describes the thirteen ensembles, named NME, generated with 2+1-flavor Wilson-clover fermions by the JLab/W\&M/LANL/MIT/Marseille collaborations, and presents an analysis of the meson and baryon spectrum, decay constants $f_\pi$ and $f_K$, flow scales $t_0$ and $w_0$, and time histories of the $\Theta$ and Weinberg operators under gradient flow. Using these quantities, the physical point values of the two flow scales, ${t_0^{\rm Phy}}$ and ${w_0^{\rm Phy}}$, and the ratio $\mathop{f_K / f_\pi}^{\rm Phy}$ are determined. The masses of the octet and decuplet baryons are analyzed using both the next-to-leading order (NLO) and the next-next-to-leading order (NNLO) ansatz from heavy baryon chiral perturbation theory (HB$\chi$PT). The NNLO fit to the octet baryons, $M_N$, $M_\Sigma$, $M_\Lambda$ and $M_\Xi$, is preferred while the corresponding fits to the decuplet Omega mass, $M_\Omega$, are not distinguished. We also present a study of the autocorrelations in the data and show that there is no evidence, even at large flow time, of the freezing of the topological charge or the Weinberg three-gluon operator.

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arXiv2023

Nucleon form factors and the pion-nucleon sigma term

This talk summarizes the progress made since Lattice 2021 in understanding and controlling the contributions of towers of multihadron excited states with mass gaps starting lower than of radial excitations, and in increasing our confidence in the extraction of ground state nucleon matrix elements. The most clear evidence for multihadron excited state contributions (ESC) is in axial/pseudoscalar form factors that are required to satisfy the PCAC relation between them. The talk examines the broader question--which and how many of the theoretically allowed positive parity states $N(\textbf p)π(-\textbf p)$, $N(\textbf 0)π(\textbf 0)π(\textbf 0)$, $N(\textbf p)π(\textbf 0)$, $N(\textbf 0)π(\textbf p),\ \ldots$ make significant contributions to a given nucleon matrix element? New data for the axial, electric and magnetic form factors are presented. They continue to show trends observed in Ref[1]. The N${}^2$LO $χ$PT analysis of the ESC to the pion-nucleon sigma term, $σ_{πN}$, has been extended to include the $Δ$ as an explicit degree of freedom [2]. The conclusion reached in Ref [3] that $N π$ and $N ππ$ states each contribute about 10 MeV to $σ_{πN}$, and the consistency between the lattice result with $N π$ state included and the phenomenological estimate is not changed by this improvement.

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arXiv2022

Excited states and precision results for nucleon charges and form factors

The exponentially falling signal-to-noise ratio in all nucleon correlation functions, and the presence of towers of multihadron excited states with relatively small mass gaps makes extraction of matrix elements of various operators within the ground state nucleon challenging. Theoretically, the allowed positive parity states with the smallest mass gaps are the $N(\bm p)π(-\bm p)$, $N(\bm 0)π(\bm 0)π(\bm 0)$, $N(\bm p)π(\bm 0)$, $N(\bm 0)π(\bm p),\ \ldots$, states. A priori, the contribution of these states arises at one loop in chiral perturbation theory ($χ$PT), however, in many cases the contributions are enhanced. In this talk, I will review four such cases: the correlation functions from which the axial form factors, electric and magnetic form factors, the $Θ$-term contribution to neutron electric dipole moment (nEDM), and the pion-nucleon sigma term are extracted. Including appropriate multihadron states in the analysis can lead to significantly different results compared to standard analyses with the mass gaps taken from fits to 2-point functions. The $χ$PT case for $N π$ states is the most clear in the axial/pseudoscalar form factors which need to satisfy the PCAC relation between them. Our analyses, supported by $χ$PT, suggests similarly large effects in the calculations of the $Θ$-term and the pion-nucleon sigma term that have significant phenomenological implications.

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arXiv2022

Precision Nucleon Charges and Form Factors Using 2+1-flavor Lattice QCD

We present high statistics results for the isovector nucleon charges and form factors using seven ensembles of 2+1-flavor Wilson-clover fermions. The axial and pseudoscalar form factors obtained on each ensemble satisfy the PCAC relation once the lowest energy $Nπ$ excited state is included in the spectral decomposition of the correlation functions used for extracting the ground state matrix elements. Similarly, we find evidence that the $Nππ$ excited state contributes to the correlation functions with the vector current, consistent with the vector meson dominance model. The resulting form factors are consistent with the Kelly parameterization of the experimental electric and magnetic data. Our final estimates for the isovector charges are $g_{A}^{u-d} = 1.31(06)(05)_{sys}$, $g_{S}^{u-d} = 1.06(10)(06)_{sys}$, and $g_{T}^{u-d} = 0.95(05)(02)_{sys}$, where the first error is the overall analysis uncertainty and the second is an additional combined systematic uncertainty. The form factors yield: (i) the axial charge radius squared, ${\langle r_A^2 \rangle}^{u-d}=0.428(53)(30)_{sys}\ {\rm fm}^2$, (ii) the induced pseudoscalar charge, $g_P^\ast=7.9(7)(9)_{sys}$, (iii) the pion-nucleon coupling $g_{π{\rm NN}} = 12.4(1.2)$, (iv) the electric charge radius squared, ${\langle r_E^2 \rangle}^{u-d} = 0.85(12)(19)_{sys} \ {\rm fm}^2$, (v) the magnetic charge radius squared, ${\langle r_M^2 \rangle}^{u-d} = 0.71(19)(23)_{\rm sys} \ {\rm fm}^2$, and (vi) the magnetic moment $μ^{u-d} = 4.15(22)(10)_{\rm sys}$. All our results are consistent with phenomenological/experimental values but with larger errors. Lastly, we present a Padé parameterization of the axial, electric and magnetic form factors over the range $0.04< Q^2 <1$ GeV${}^2$ for phenomenological studies.

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arXiv2021

Nucleon isovector momentum fraction, helicity and transversity moment using Lattice QCD

We present our recent high precision calculations (Phys. Rev. D102 (2020) no.5, 054512 and JHEP 04 (2021) 044, JHEP 21 (2020) 004) of the first moment of nucleon isovector polarized, unpolarized and transversity distributions, i.e., momentum fraction, helicity and transversity moment, respectively. We use the standard method for the calculation of these moments (via matrix elements of twist two operators), and carry out a detailed analysis of the sources of systematic uncertainty, in particular of excited state contributions. Our calculations have been performed using two different lattice setups (Clover-on-HISQ and Clover-on-Clover), each with several ensembles. They give consistent results that are in agreement with global fit analyses.

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arXiv2021

The Positive-Parity Baryon Spectrum and the Role of Hybrid Baryons

We calculate the low-lying spectra for the positive-parity $Δ$ and $N$ at two pion masses of 358 and 278 MeV using an isotropic clover action with two degenerate light-quaark and one strange-quark flavors through the application of the generalized variational method within the distillation framework. The spectrum exhibits the general features observed in previous calculations using an anisotropic clover lattice, with a counting of states at least as rich as the quark model. Furthermore, we identify states that are hybrid in nature, where gluonic degrees of freedom play a structural role, indicatinng that such states appear a feature of the excited baryon spectrum, irrespective of the lattice action, or the precise details of the smearing of the lattice interpolating operators used to identify such states.

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arXiv2021

Low-energy Scattering and Effective Interactions of Two Baryons at $m_π\sim 450$ MeV from Lattice Quantum Chromodynamics

The interactions between two octet baryons are studied at low energies using lattice QCD (LQCD) with larger-than-physical quark masses corresponding to a pion mass of $m_π\sim 450$ MeV and a kaon mass of $m_{K}\sim 596$ MeV. The two-baryon systems that are analyzed range from strangeness $S=0$ to $S=-4$ and include the spin-singlet and triplet $NN$, $ΣN$ ($I=3/2$), and $ΞΞ$ states, the spin-singlet $ΣΣ$ ($I=2$) and $ΞΣ$ ($I=3/2$) states, and the spin-triplet $ΞN$ ($I=0$) state. The $s$-wave scattering phase shifts, low-energy scattering parameters, and binding energies when applicable, are extracted using Lüscher's formalism. While the results are consistent with most of the systems being bound at this pion mass, the interactions in the spin-triplet $ΣN$ and $ΞΞ$ channels are found to be repulsive and do not support bound states. Using results from previous studies at a larger pion mass, an extrapolation of the binding energies to the physical point is performed and is compared with experimental values and phenomenological predictions. The low-energy coefficients in pionless EFT relevant for two-baryon interactions, including those responsible for $SU(3)$ flavor-symmetry breaking, are constrained. The $SU(3)$ symmetry is observed to hold approximately at the chosen values of the quark masses, as well as the $SU(6)$ spin-flavor symmetry, predicted at large $N_c$. A remnant of an accidental $SU(16)$ symmetry found previously at a larger pion mass is further observed. The $SU(6)$-symmetric EFT constrained by these LQCD calculations is used to make predictions for two-baryon systems for which the low-energy scattering parameters could not be determined with LQCD directly in this study, and to constrain the coefficients of all leading $SU(3)$ flavor-symmetric interactions, demonstrating the predictive power of two-baryon EFTs matched to LQCD.

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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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arXiv2020

Nucleon Momentum Fraction, Helicity and Transversity from 2+1-flavor Lattice QCD

High statistics results for the isovector momentum fraction, $\langle x \rangle_{u-d}$, helicity moment, $\langle x \rangle_{Δu-Δd}$, and the transversity moment, $\langle x\rangle_{δu-δd}$, of the nucleon are presented using seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using $2+1$-flavors of dynamical Wilson-clover quarks. Attention is given to understanding and controlling the contributions of excited states. The final results are obtained using a simultaneous fit in the lattice spacing $a$, pion mass $M_π$ and the finite volume parameter $M_πL$ keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. The main variation is with $M_π$, whose magnitude depends on the mass gap of the first excited state used in the analysis. Our final results, in the $\overline{\rm MS}$ scheme at 2 GeV, are $\langle x \rangle_{u-d} = 0.160(16)(20)$, $\langle x \rangle_{Δu-Δd} = 0.192(13)(20)$ and $\langle x \rangle_{δu-δd} = 0.215(17)(20)$, where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with other recent lattice calculations and phenomenological global fit values.

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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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arXiv2018

Controlling Excited-State Contributions with Distillation in Lattice QCD Calculations of Nucleon Isovector Charges $g_S^{u-d}$, $g_A^{u-d}$, $g_T^{u-d}$

We investigate the application of the distillation smearing approach, and the use of the variational method with an extended basis of operators facilitated by this approach, on the calculation of the nucleon isovector charges $g_S^{u-d}$, $g_A^{u-d}$, and $g_T^{u-d}$. We find that the better sampling of the lattice enabled through the use of distillation yields a substantial reduction in the statistical uncertainty in comparison with the use of alternative smearing methods, and furthermore, appears to offer better control over the contribution of excited-states compared to use of a single, local interpolating operator. The additional benefit arising through the use of the variational method in the distillation approach is less dramatic, but nevertheless significant given that it requires no additional Dirac inversions.

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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

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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arXiv2017

Proton-proton fusion and tritium $β$-decay from lattice quantum chromodynamics

The nuclear matrix element determining the $pp\to d e^+ ν$ fusion cross section and the Gamow-Teller matrix element contributing to tritium $β$-decay are calculated with lattice Quantum Chromodynamics (QCD) for the first time. Using a new implementation of the background field method, these quantities are calculated at the SU(3)-flavor-symmetric value of the quark masses, corresponding to a pion mass of $m_π$ ~ 806 MeV. The Gamow-Teller matrix element in tritium is found to be 0.979(03)(10) at these quark masses, which is within $2σ$ of the experimental value. Assuming that the short-distance correlated two-nucleon contributions to the matrix element (meson-exchange currents) depend only mildly on the quark masses, as seen for the analogous magnetic interactions, the calculated $pp\to d e^+ ν$ transition matrix element leads to a fusion cross section at the physical quark masses that is consistent with its currently accepted value. Moreover, the leading two-nucleon axial counterterm of pionless effective field theory is determined to be $L_{1,A}=3.9(0.1)(1.0)(0.3)(0.9)\ {\rm fm}^3$ at a renormalization scale set by the physical pion mass, also in agreement with the accepted phenomenological range. This work concretely demonstrates that weak transition amplitudes in few-nucleon systems can be studied directly from the fundamental quark and gluon degrees of freedom and opens the way for subsequent investigations of many important quantities in nuclear physics.

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arXiv2017

Baryon-Baryon Interactions and Spin-Flavor Symmetry from Lattice Quantum Chromodynamics

Lattice quantum chromodynamics is used to constrain the interactions of two octet baryons at the SU(3) flavor-symmetric point, with quark masses that are heavier than those in nature (equal to that of the physical strange quark mass and corresponding to a pion mass of $\approx 806~\tt{MeV}$). Specifically, the S-wave scattering phase shifts of two-baryon systems at low energies are obtained with the application of Lüscher's formalism, mapping the energy eigenvalues of two interacting baryons in a finite volume to the two-particle scattering amplitudes below the relevant inelastic thresholds. The values of the leading-order low-energy scattering parameters in the irreducible representations of SU(3) are consistent with an approximate SU(6) spin-flavor symmetry in the nuclear and hypernuclear forces that is predicted in the large-$N_c$ limit of QCD. The two distinct SU(6)-invariant interactions between two baryons are constrained at this value of the quark masses, and their values indicate an approximate accidental SU(16) symmetry. The SU(3) irreducible representations containing the $NN~({^1}S_0)$, $NN~({^3}S_1)$ and $\frac{1}{\sqrt{2}}(Ξ^0n+Ξ^-p)~({^3}S_1)$ channels unambiguously exhibit a single bound state, while the irreducible representation containing the $Σ^+ p~({^3}S_1)$ channel exhibits a state that is consistent with either a bound state or a scattering state close to threshold. These results are in agreement with the previous conclusions of the NPLQCD collaboration regarding the existence of two-nucleon bound states at this value of the quark masses.

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