Lattice QCD Calculations Research Articles

Electroweak three-body decays in the presence of two- and three-body bound states

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

Transverse-momentum-dependent wave functions of the pion from lattice QCD

We present a lattice QCD calculation of the transverse-momentum-dependent wave function (TMDWF) of the pion using large-momentum effective theory. Numerical simulations are based on one ensemble with 2+1+1 flavors of highly improved staggered quarks with lattice spacing a=0.121 fm from the MILC collaboration, and one with 2+1 flavor clover fermions and tree-level Symanzik gauge action generated by the CLS collaboration with a=0.098 fm. As a key ingredient, the soft function is first obtained by incorporating the one-loop perturbative contributions and a proper normalization. Based on this and the equal-time quasi-TMDWF simulated on the lattice, we extract the TMDWF. The results for both lattice ensembles are compatible and a comparison with a phenomenological parametrization is made. Our studies provide a first attempt of calculation of TMDWFs which will eventually lead to crucial theory inputs for making predictions for exclusive processes under QCD factorization. Published by the American Physical Society 2024

Electromagnetic form factors of the nucleon from Nf=2+1 lattice QCD

There is a long-standing discrepancy between different measurements of the electric and magnetic radii of the proton. Lattice QCD calculations are a well-suited tool for theoretical investigations of the structure of the nucleon from first principles. However, all previous lattice studies of the proton’s electromagnetic radii have either neglected quark-disconnected contributions or were not extrapolated to the continuum and infinite-volume limit. Here, we present results for the electromagnetic form factors of the proton and neutron computed on the (2+1)-flavor coordinated lattice simulations (CLS) ensembles including both quark-connected and -disconnected contributions. From simultaneous fits to the Q2-, pion-mass, lattice-spacing, and finite-volume dependence of the form factors, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron. For the proton, we obtain as our final values ⟨rE2⟩p=(0.672±0.014(stat)±0.018(syst)) fm2, ⟨rM2⟩p=(0.658±0.012(stat)±0.008(syst)) fm2, and μMp=(2.739±0.063(stat)±0.018(syst). The magnetic moment is in good agreement with the experimental value, as is the one of the neutron. On the one hand, our result for the electric (charge) radius of the proton clearly points towards a small value, as favored by muonic hydrogen spectroscopy and the recent ep-scattering experiment by PRad. Our estimate for the magnetic radius, on the other hand, is well compatible with that inferred from the A1 ep-scattering experiment. Published by the American Physical Society 2024

Radiative transitions in charmonium from lattice QCD

The coupling of various charmonium mesons to a photon is studied using lattice QCD, giving access to radiative form factors and transitions, and probing the mesons’ structure. Methods are developed which allow the robust determination of amplitudes, including those involving an excited state as well as multiple form factors, for a range of kinematics. These are applied in dynamical lattice QCD calculations using the distillation technique to compute the underlying three-point correlation functions. Form factors and amplitudes involving the low-lying charmonia, ηc, J/ψ, χc0 and ηc′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\eta}_c^{\\prime } $$\\end{document}, are calculated, demonstrating the methods and providing the first dynamical lattice QCD results for some quantities.

Baryon Electric Charge Correlation as a Magnetometer of QCD.

The correlation between net baryon number and electric charge, χ_{11}^{BQ}, can serve as a magnetometer of QCD. This is demonstrated by lattice QCD computations using the highly improved staggered quarks with physical pion mass of M_{π}=135 MeV on N_{τ}=8 and 12 lattices. We find that χ_{11}^{BQ} along the transition line starts to increase rapidly with magnetic field strength eB≳2M_{π}^{2} and by a factor 2 at eB≃8M_{π}^{2}. Furthermore, the ratio of electric charge chemical potential to baryon chemical potential, μ_{Q}/μ_{B}, shows significant dependence on the magnetic field strength and varies from the ratio of electric charge to baryon number in the colliding nuclei in heavy ion collisions. These results can provide baselines for effective theory and model studies, and both χ_{11}^{BQ} and μ_{Q}/μ_{B} could be useful probes for the detection of magnetic fields in relativistic heavy ion collision experiments as compared with corresponding results from the hadron resonance gas model.

Non-extensive effects on the QCD equation of state and fluctuations of conserved charges within Polyakov quark meson model

The influence of non-extensive Tsallis statistics on the hadron phase structure has been investigated using the Polyakov-quark-meson (PQM) model. The analysis examines the non-extensive effects on the temperature dependence of PQM order parameters, thermodynamic quantities related to the quantum chromodynamics (QCD) equation of state, and fluctuations of conserved charges at varying chemical potentials. The results show that non-extensive effects have the most significant deviations near the crossover region. The pseudo-critical temperature T χ (μ B ) is not a universal constant and decreases with increasing non-extensive q parameter. The chiral phase diagram of the PQM model indicates a decrease in the behavior of the (T χ − μ B ) plane with increasing non-extensive q parameter. The PQM model exhibits good qualitative agreement with lattice QCD calculations. Moreover, these findings suggest the existence of a Tsallis limit, which serves as an alternative to the Stefan–Boltzmann limit for the massless ideal gas. The critical endpoint exhibits lower temperature but higher chemical potential with increasing non-extensive q parameter. Overall, this study highlights the importance of non-extensive Tsallis statistics in characterizing the quark-hadron phase structure of the PQM model and contributes to a deeper understanding of non-extensive effects in the quark-hadron phase transition.

Lattice QCD Calculation of Electroweak Box Contributions to Superallowed Nuclear and Neutron Beta Decays.

We present the first lattice QCD calculation of the universal axial γW-box contribution □_{γW}^{VA} to both superallowed nuclear and neutron beta decays. This contribution emerges as a significant component within the theoretical uncertainties surrounding the extraction of |V_{ud}| from superallowed decays. Our calculation is conducted using two domain wall fermion ensembles at the physical pion mass. To construct the nucleon four-point correlation functions, we employ the random sparsening field technique. Furthermore, we incorporate long-distance contributions to the hadronic function using the infinite-volume reconstruction method. Upon performing the continuum extrapolation, we arrive at □_{γW}^{VA}=3.65(7)_{lat}(1)_{PT}×10^{-3}. Consequently, this yields a slightly higher value of |V_{ud}|=0.973 86(11)_{exp}(9)_{RC}(27)_{NS}, reducing the previous 2.1σ tension with the CKM unitarity to 1.8σ. Additionally, we calculate the vector γW-box contribution to the axial charge g_{A}, denoted as □_{γW}^{VV}, and explore its potential implications.

Analysis of parton distributions in a pion with Bézier parametrizations

We explore the role of parametrizations for nonperturbative QCD functions in global analyses, with a specific application to extending a phenomenological analysis of the parton distribution functions (PDFs) in the charged pion realized in the xFitter fitting framework. The parametrization dependence of PDFs in our pion fits substantially enlarges the uncertainties from the experimental sources estimated in the previous analyses. We systematically explore the parametrization dependence by employing a novel technique to automate generation of polynomial parametrizations for PDFs that makes use of Bézier curves. This technique is implemented in a ++ module that is included in the xFitter program. Our analysis reveals that the sea and gluon distributions in the pion are not well disentangled, even when considering measurements in leading-neutron deep inelastic scattering. For example, the pion PDF solutions with a vanishing gluon and large quark sea are still experimentally allowed, which elevates the importance of ongoing lattice and nonperturbative QCD calculations, together with the planned pion scattering experiments, for conclusive studies of the pion structure. Published by the American Physical Society 2024

Four-gluon vertex from lattice QCD

A lattice QCD calculation for the four-gluon one-particle irreducible Green function in the Landau gauge is discussed. Results for some of the associated form factors are reported for kinematical configurations with a single momentum scale. Our results show that the computation of this Green function requires large statistical ensembles with 10 K or larger number of gauge configurations. The simulations considered herein have a clear Monte Carlo signal for momenta up to ∼1 GeV. The form factors show an hierarchy, with the form factor associated with the tree level Feynman rule being dominant and essentially constant for the range of momenta accessed. The remaining form factors seem to increase as the momentum decreases, suggesting that a possible log divergence may occur. The computed form factors are, at least, in qualitative agreement with the results obtained with continuum approaches to this vertex, when available. Published by the American Physical Society 2024

Nonperturbative Collins-Soper kernel from chiral quarks with physical masses

We present a lattice QCD calculation of the rapidity anomalous dimension of quark transverse-momentum-dependent distributions, i.e., the Collins-Soper (CS) kernel, up to transverse separations of about 1 fm. This unitary lattice calculation is conducted, for the first time, employing the chiral-symmetry-preserving domain wall fermion discretization and physical values of light and strange quark masses. The CS kernel is extracted from the ratios of pion quasi-transverse-momentum-dependent wave functions (quasi-TMDWFs) at next-to-leading logarithmic perturbative accuracy. Also for the first time, we utilize the recently proposed Coulomb-gauge-fixed quasi-TMDWF correlator without a Wilson line. We observe significantly slower signal decay with increasing quark separations compared to the established gauge-invariant method with a staple-shaped Wilson line. This enables us to determine the CS kernel at large nonperturbative transverse separations and find its near-linear dependence on the latter. Our result is consistent with the recent lattice calculation using gauge-invariant quasi-TMDWFs, and agrees with various recent phenomenological parametrizations of experimental data.

Low-mode deflation for twisted-mass and RHMC reweighting in lattice QCD

We propose improved estimators to compute the reweighting factors which are needed for lattice QCD calculations that rely on twisted-mass reweighting for the light quark contribution and the Rational Hybrid Monte Carlo (RHMC) algorithm for non-degenerate quark masses. This is the case for a number of modern large-scale simulations based on O(a) improved Wilson fermions. We find a significant reduction of uncertainties for the reweighting factors at similar computational cost compared to the conventional estimation. This leads to a significant increase in precision for phenomenologically relevant observables with high correlation to the low eigenmodes of the Wilson-Dirac operator in the presence of exceptionally small eigenvalues. Supplementary details regarding the spectral gap of the light quark Dirac operator on the 2+1 flavor large-volume ensembles explored in this study can be found in an accompanying appendix.

Transversity PDFs of the proton from lattice QCD with physical quark masses

We present a lattice QCD calculation of the transversity isovector- and isoscalar-quark parton distribution functions (PDFs) of the proton utilizing a perturbative matching at next-to-leading-order (NLO) accuracy. Additionally, we determine the isovector and isoscalar tensor charges for the proton. In both calculations, the disconnected contributions to the isoscalar matrix elements have been ignored. The calculations are performed using a single ensemble of Nf=2+1 highly improved staggered quarks simulated with physical-mass quarks and a lattice spacing of a=0.076 fm. The Wilson-clover action, with physical quark masses and smeared gauge links obtained from one iteration of hypercubic smearing, is used in the valence sector. Using the NLO operator product expansion, we extract the lowest four to six Mellin moments and the PDFs via a neural network from the matrix elements in the pseudo-PDF approach. In addition, we calculate the PDFs in the quasi-PDF approach with hybrid-scheme renormalization and the recently developed leading-renormalon resummation technique, at NLO with the resummation of leading small-x logarithms. Published by the American Physical Society 2024

Structure of the Λ(1670) resonance

We examine the internal structure of the Λ(1670) through an analysis of lattice QCD simulations and experimental data within Hamiltonian effective field theory. Two scenarios are presented. The first describes the Λ(1670) as a bare three-quark basis state, which mixes with the πΣ, K¯N, ηΛ and KΞ meson-baryon channels. In the second scenario, the Λ(1670) is dynamically generated from these isospin-0 coupled channels. The K−p scattering data and the pole structures of the Λ(1405) and the Λ(1670) can be simultaneously described well in both scenarios. However, a comparison of the finite-volume spectra to lattice QCD calculations reveals significant differences between these scenarios, with a clear preference for the first case. Thus the lattice QCD results play a crucial role in allowing us to distinguish between these two scenarios for the internal structure of the Λ(1670). Published by the American Physical Society 2024

Isovector Axial Charge and Form Factors of Nucleons from Lattice QCD

A survey of the calculations of the isovector axial vector form factor of the nucleon using lattice QCD is presented. Attention is paid to statistical and systematic uncertainties, in particular those due to excited state contributions. Based on a comparison of results from various collaborations, a case is made that lattice results are consistent within 10%. A similar level of uncertainty is in the axial charge gAu−d, the mean squared axial charge radius ⟨rA2⟩, the induced pseudoscalar charge gP∗, and the pion–nucleon coupling gπNN. Even with the current methodology, a significant reduction in errors is expected over the next few years with higher statistics data on more ensembles closer to the physical point. Lattice QCD results for the form factor GA(Q2) are compatible with those obtained from the recent MINERνA experiment but lie 2–3σ higher than the phenomenological extraction from the old ν–deuterium bubble chamber scattering data for Q2>0.3 GeV2. Current data show that the dipole ansatz does not have enough parameters to fit the form factor over the range 0≤Q2≤1 GeV2, whereas even a z2 truncation of the z expansion or a low order Padé are sufficient. Looking ahead, lattice QCD calculations will provide increasingly precise results over the range 0≤Q2≤1 GeV2, and MINERνA-like experiments will extend the range to Q2∼2 GeV2 or higher. Nevertheless, improvements in lattice methods to (i) further control excited state contributions and (ii) extend the range of Q2 are needed.

Masses of magnetized pseudoscalar and vector mesons in an extended NJL model: The role of axial vector mesons

We study the mass spectrum of light pseudoscalar and vector mesons in the presence of an external uniform magnetic field B→, considering the effects of the mixing with the axial-vector meson sector. The analysis is performed within a two-flavor NJL-like model which includes isoscalar and isovector couplings together with a flavor mixing ’t Hooft-like term. The effect of the magnetic field on charged particles is taken into account by retaining the Schwinger phases carried by quark propagators, and expanding the corresponding meson fields in proper Ritus-like bases. The spin-isospin and spin-flavor decomposition of meson mass states is also analyzed. For neutral pion masses it is shown that the mixing with axial vector mesons improves previous theoretical results, leading to a monotonic decreasing behavior with B that is in good qualitative agreement with lattice QCD (LQCD) calculations, both for the case of constant or B-dependent couplings. Regarding charged pions, it is seen that the mixing softens the enhancement of their mass with B. As a consequence, the energy becomes lower than the one corresponding to a pointlike pion, improving the agreement with LQCD results. The agreement is also improved for the magnetic behavior of the lowest ρ+ energy state, which does not vanish for the considered range of values of B—a fact that can be relevant in connection with the occurrence of meson condensation for strong magnetic fields. Published by the American Physical Society 2024

SIMULATeQCD: A simple multi-GPU lattice code for QCD calculations

The rise of exascale supercomputers has fueled competition among GPU vendors, driving lattice QCD developers to write code that supports multiple APIs. Moreover, new developments in algorithms and physics research require frequent updates to existing software. These challenges have to be balanced against constantly changing personnel. At the same time, there is a wide range of applications for HISQ fermions in QCD studies. This situation encourages the development of software featuring a HISQ action that is flexible, high-performing, open source, easy to use, and easy to adapt. In this technical paper, we explain the design strategy, provide implementation details, list available algorithms and modules, and show key performance indicators for SIMULATeQCD, a simple multi-GPU lattice code for large-scale QCD calculations, mainly developed and used by the HotQCD collaboration. The code is publicly available on GitHub. Program summaryProgram Title: SIMULATeQCDCPC Library link to program files:https://doi.org/10.17632/ytgycy9nc3.1Developer's repository link:https://github.com/LatticeQCD/SIMULATeQCDLicensing provisions: MITProgramming language: C++, CUDA, HIPNature of problem: Quantum chromodynamics (QCD) is the fundamental theory behind the strong force, one of the four fundamental forces in nature. It describes interactions, mediated by gluons, between quarks, the elementary particles that build up protons, neutrons and other hadrons. One of its unique features is asymptotic freedom: with increasing energy, the interaction strength or coupling between quarks and gluons weakens, which enables studying QCD with peturbation theory. At lower energy scales, however, the strong coupling between quarks and gluons causes perturbation theory to break down, and other tools, such as lattice QCD, need to be employed to obtain QCD predictions.Solution method: Lattice QCD is a technique to solve QCD non-perturbatively by discretizing space and time onto a four-dimensional grid. The QCD path integral is thereby rendered finite dimensional and can be evaluated numerically via Monte Carlo methods. In this paper, we present SIMULATeQCD, a C++ code to perform lattice QCD calculations on multiple GPUs, supporting multiple APIs. SIMULATeQCD implements various Monte Carlo sampling methods ranging from sampling of purely gluonic configurations to fully dynamical quark simulations with the Highly Improved Staggered Quark (HISQ) discretization. Modules for measuring various physical observables on these samples are also available.

Energy loss of heavy quarks in the presence of magnetic field

We study the heavy quark energy loss in the presence of a background magnetic field. The analysis considers the high magnetic field generated by spectators from initial hard collisions that were incorporated using the medium-modified Debye mass, determined from quark condensates at finite temperature and magnetic field via recent lattice quantum chromodynamics calculations. We analyse the impact of medium polarization on the heavy quark propagation in a quark–gluon plasma formed in relativistic heavy-ion colliders like relativistic heavy ion collider and large hadron collider. For simplification, we considered the static medium with constant temperature and magnetic field values. Then, we explore the nuclear modification factor (R AA) at different magnitudes of magnetic field strengths at fixed temperatures. The energy loss of heavy quarks significantly increases, leading to R AA suppression at higher magnetic field values.

Unitary model analysis of f0(500) pole positions by continuously varying mπ : Comparison with discrete lattice predictions

Resonance, bound-state, and virtual-state pole positions of the f0(500) scalar meson are computed as a continuous function of pion mass in the framework of a unitarized and analytic coupled-channel model for scalar mesons, described as dynamical quark-antiquark states. The f0(500) is modeled with both light and strange qq¯ seeds, mixing with each other through the common S-wave ππ, KK¯, and ηη meson-meson decay channels. The few model parameters are fitted to experimental S-wave ππ phase shifts up to 1 GeV. In the case of the physical π± mass of 139.57 MeV, resonance poles at (460−i222) MeV and (978−i37.2) MeV are found for the f0(500) and f0(980), respectively. Resonance, bound-state, and virtual-state pole trajectories are computed and plotted as a function of pion masses up to 500 MeV, both in the complex-energy and complex-momentum planes. The results are discussed and compared to the most advanced lattice QCD computations employing interpolators that correspond to the qq¯ and meson-meson channels in the present model, that is, for a few discrete values of the unphysical pion mass in those lattice calculations. Published by the American Physical Society 2024

Improved method to determine the Ξc−Ξc′ mixing

We develop an improved method to explore the Ξc−Ξc′ mixing, which arises from the flavor SU(3) and heavy quark symmetry breaking. In this method, the flavor eigenstates under the SU(3) symmetry are at first constructed, and the corresponding masses can be nonperturbatively determined. Matrix elements of the mass operators, which break the flavor SU(3) symmetry sandwiched by the flavor eigenstates, are then calculated. Diagonalizing the corresponding matrix of Hamiltonian gives the mass eigenstates of the full Hamiltonian and determines the mixing. Following the previous lattice QCD calculation of Ξc and Ξc′, and estimating an off diagonal matrix element, we extract the mixing angle between the Ξc and Ξc′. Preliminary numerical results for the mixing angle confirm the previous observation that such mixing is incapable to explain the large SU(3) symmetry breaking in semileptonic decays of charmed baryons. Published by the American Physical Society 2024

Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Axial-vector case

Recently, we made significant advancements in improving the computational efficiency of lattice QCD calculations for generalized parton distributions (GPDs). This progress was achieved by adopting calculations of matrix elements in asymmetric frames, deviating from the computationally-expensive symmetric frame typically used, and allowing freedom in the choice for the distribution of the momentum transfer between the initial and final states. A crucial aspect of this approach involves the adoption of a Lorentz covariant parametrization for the matrix elements, introducing Lorentz-invariant amplitudes. This approach also allows us to propose an alternative definition of quasi-GPDs, ensuring frame independence and potentially reduce power corrections in matching to light cone GPDs. In our previous work, we presented lattice QCD results for twist-2 unpolarized GPDs (H and E) of quarks obtained from calculations performed in asymmetric frames at zero skewness. Building upon this work, we now introduce a novel Lorentz covariant parametrization for the axial-vector matrix elements. We employ this parametrization to compute the axial-vector GPD H˜ at zero skewness, using an Nf=2+1+1 ensemble of twisted mass fermions with clover improvement. The light-quark masses employed in our calculations correspond to a pion mass of approximately 260 MeV. Published by the American Physical Society 2024