Lattice QCD Calculations Research Articles

Quark spin and orbital angular momentum from proton generalized parton distributions

We calculate the leading-twist helicity-dependent generalized parton distributions (GPDs) of the proton at finite skewness in the Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics (QCD). From these (and previously calculated helicity-independent GPDs) we obtain the spin decomposition of the proton, including predictions for quark intrinsic spin and orbital angular momentum. The inclusion of multiple species of diquarks is found to have a significant effect on the flavor decomposition, and resolving the internal structure of these dynamical diquark correlations proves essential for the mechanical stability of the proton. At a scale of $Q^2=4\,$GeV$^2$ we find that the up and down quarks carry an intrinsic spin and orbital angular momentum of $S_u=0.534$, $S_d=-0.214$, $L_u=-0.189$, and $L_d=0.210$, whereas the gluons have a total angular momentum of $J_g=0.151$. The down quark is therefore found to carry almost no total angular momentum due to cancellations between spin and orbital contributions. Comparisons are made between these spin decomposition results and lattice QCD calculations.

Few-nucleon matrix elements in pionless effective field theory in a finite volume

Pionless effective field theory in a finite volume (FVEFT$_{\pi\!/}$) is investigated as a framework for the analysis of multi-nucleon spectra and matrix elements calculated in lattice QCD (LQCD). By combining FVEFT$_{\pi\!/}$ with the stochastic variational method, the spectra of nuclei with atomic number $A\in\{2,3\}$ are matched to existing finite-volume LQCD calculations at heavier-than-physical quark masses corresponding to a pion mass $m_\pi=806$ MeV, thereby enabling infinite-volume binding energies to be determined using infinite-volume variational calculations. Based on the variational wavefunctions that are constructed in this approach, the finite-volume matrix elements of various local operators are computed in FVEFT$_{\pi\!/}$ and matched to LQCD calculations of the corresponding QCD operators in the same volume, thereby determining the relevant one and two-body EFT counterterms and enabling an extrapolation of the LQCD matrix elements to infinite volume. As examples, the scalar, tensor, and axial matrix elements are considered, as well as the magnetic moments and the isovector longitudinal momentum fraction.

Universality driven analytic structure of the QCD crossover: Radius of convergence in the baryon chemical potential

Recent lattice QCD calculations strongly indicate that the chiral crossover of QCD at zero baryon chemical potential \mu_B is a remnant of the second-order chiral phase transition. Universal properties of this second-order phase transition can be mapped to QCD temperature T and \mu_B using non-universal parameters determined by lattice QCD recently. Motivated by these results, first, we discuss the analytic structure of the partition function in the QCD crossover regime - the so-called Yang-Lee edge singularity - solely based on universal properties. Next, utilizing the lattice QCD results for non-universal parameters we map this singularity to the real T and complex \mu_B plane, leading to the determination of the radius of convergence is in \mu_B in the QCD crossover regime. These universality- and QCD-based results provide tight constraints on the range of validity of the lattice QCD calculations at \mu_B. Implication of this result on the location of the conjectured QCD critical point is discussed.

Flavor-diagonal CP violation: the electric dipole moment.

The observed baryon asymmetry in the universe cannot be reconciled with the current form of the Standard Model (SM) of particle physics. The Standard Model breaks charge conjugation parity (CP) symmetry, but not in a sufficient amount to explain the observed matter-antimatter asymmetry. Historically one of the first systems to be studied in the search of symmetry breaking within the Standard Model is the electric dipole moment (EDM) of the neutron. The contribution to the neutron EDM coming from the SM is several order of magnitudes smaller than the current experimental bound, thus providing a unique, background-free window for potential discovery of physics Beyond the Standard Model (BSM). The strong CP-violating theta term can also contribute to the neutron EDM, as can all the CP-violating effective operators describing, at energies below the electro-weak scale, the contributions from BSM. To constrain all these contributions to the neutron EDM we need to precisely determine the hadronic matrix elements of the corresponding renormalized operators. After a brief introduction on baryon asymmetry and baryogenesis, I summarize the current stuatus for experiments in search of a neutron EDM. I then describe in more details the different CP-violating sources, and some results in Chiral Perturbation Theory precede a discussion on the current status of Lattice QCD calculations. I will in particular focus on the 2 main challenges for these type of calculations: the signal-to-noise ratio and the renormalization. I will discuss several improvement techniques trying to improve these two aspects of the calculation and I will conclude with an optimistic view into the future.

Entanglement rearrangement in self-consistent nuclear structure calculations

Background: Entanglement plays a central role in a diverse array of increasingly important research areas, including quantum computation, simulation, measurement, sensing, and communication. Extensive suites of investigations have been performed to better understand entanglement in atomic and molecular quantum many-body systems, while the exploration of entanglement in the structure of nuclei and their reactions is presently in its infancy.Purpose: The goal of this work is to begin investigating the entanglement properties of nuclei from first-principles nuclear many-body calculations. We attempt to identify common features and emergent structures of entanglement that could ultimately lead to new and natural many-body schemes. With an eye toward quantum accelerators in future hybrid-supercomputers, criteria for partitioning nuclear many-body calculations into quantum and classical components may provide advantages in future large-scale computations. Along the way we look for explanations of the relative success of phenomenological models such as the nuclear shell model, and for better ways to match to low-energy nuclear effective field theories and lattice QCD calculations to nuclear many-body techniques that are based upon entanglement.Method: We explore the entanglement between single-particle states in $^{4}\mathrm{He}$ and $^{6}\mathrm{He}$. The patterns of entanglement emerging from different single-particle bases are compared, and possible links with the convergence of observables are explored, in particular, ground-state energies. The nuclear wave functions are obtained by performing active-space no-core configuration-interaction calculations using a two-body nucleon-nucleon interaction derived from chiral effective field theory. Entanglement measures within single-particle bases exhibiting different degrees of complexity are determined, in particular, harmonic oscillator (HO), Hartree-Fock (HF), natural (NAT) and variational natural (VNAT) bases. Specifically, single-orbital entanglement entropy, two-orbital mutual information, and negativity are studied.Results: The entanglement structures in $^{4}\mathrm{He}$ and $^{6}\mathrm{He}$ are found to be more localized within NAT and VNAT bases than within a HO basis for the optimal HO parameters we have worked with. In particular a core-valence structure clearly emerges from the full no-core calculation of $^{6}\mathrm{He}$. The two-nucleon mutual information shows that the VNAT basis, which typically exhibits good convergence properties, effectively decouples the active and inactive spaces.Conclusions: Measures of one- and two-nucleon entanglement are found to be useful in analyzing the structure of nuclear wave functions, in particular the efficacy of basis states, and may provide useful metrics toward developing more efficient schemes for ab initio computations of the structure and reactions of nuclei, and quantum many-body systems more generally.

Electron-ion collider impact study on the tensor charge of the nucleon

In this letter we study the impact of the Electron-Ion Collider (EIC) on the phenomenological extraction of the tensor charge from a QCD global analysis of single transverse-spin asymmetries (SSAs). We generate EIC pseudo-data for the Collins effect in semi-inclusive deep-inelastic scattering for proton and H3e beams across multiple center-of-mass energies. We find a significant reduction in the uncertainties for the up, down, and isovector tensor charges that will make their extraction from EIC data on SSAs as precise as current lattice QCD calculations. We also analyze the constraints placed by future data from the proposed SoLID experiment at Jefferson Lab, discuss its important complementary role to the EIC, and present the combined impact from both facilities.

Magnetic field dependence of the neutral pion mass in the linear sigma model with quarks: The strong field case

We use the linear sigma model with quarks to find the magnetic field-induced modifications to the neutral pion mass at one-loop level. The magnetic field effects are introduced by using charged particle propagators in the presence of a magnetic background in the strong field regime. We show that when accounting for the effects of the magnetic field on the model couplings, the vacuum sigma field and the neutral pion self-energy, the neutral pion mass decreases monotonically as a function of the field strength. We find an excellent qualitative and quantitative agreement with recent lattice QCD calculations, reproducing the monotonically decreasing trend with the field strength as well as the decrease when lattice data approaches the physical vacuum pion mass from larger values.

Heavy Quark Expansion of Λb→Λ*(1520) Form Factors beyond Leading Order

I review the parametrisation of the full set of Λb→Λ*(1520) form factors in the framework of Heavy Quark Expansion, including next-to-leading-order O(αs) and, for the first time, next-to-leading-power O(1/mb) corrections. The unknown hadronic parameters are obtained by performing a fit to recent lattice QCD calculations. I investigate the compatibility of the Heavy Quark Expansion and the current lattice data, finding tension between these two approaches in the case of tensor and pseudo-tensor form factors, whose origin could come from an underestimation of the current lattice QCD uncertainties and higher order terms in the Heavy Quark Expansion.

Geometric quantum information structure in quantum fields and their lattice simulation

An upper limit to distillable entanglement between two disconnected regions of massless non-interacting scalar field theory has an exponential decay defined by a geometric decay constant. When regulated at short distances with a spatial lattice, this entanglement abruptly vanishes beyond a dimensionless separation, defining a negativity sphere. In two spatial dimensions, we determine this geometric decay constant between a pair of disks and the growth of the negativity sphere toward the continuum through a series of lattice calculations. Making the connection to quantum field theories in three-spatial dimensions, assuming such quantum information scales appear also in quantum chromodynamics (QCD), a new relative scale may be present in effective field theories describing the low-energy dynamics of nucleons and nuclei. We highlight potential impacts of the distillable entanglement structure on effective field theories, lattice QCD calculations and future quantum simulations.

Low-energy scattering and effective interactions of two baryons at mπ∼450 MeV from lattice quantum chromodynamics

The interactions between two octet baryons are studied at low energies using lattice quantum chromodynamics (LQCD) with larger-than-physical quark masses corresponding to a pion mass of ${m}_{\ensuremath{\pi}}\ensuremath{\sim}450\text{ }\text{ }\mathrm{MeV}$ and a kaon mass of ${m}_{K}\ensuremath{\sim}596\text{ }\text{ }\mathrm{MeV}$. The two-baryon systems that are analyzed range from strangeness $S=0$ to $S=\ensuremath{-}4$ and include the spin-singlet and triplet $NN$, $\mathrm{\ensuremath{\Sigma}}N$ ($I=3/2$), and $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Xi}}$ states, the spin-singlet $\mathrm{\ensuremath{\Sigma}}\mathrm{\ensuremath{\Sigma}}$ ($I=2$) and $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Sigma}}$ ($I=3/2$) states, and the spin-triplet $\mathrm{\ensuremath{\Xi}}N$ ($I=0$) state. The corresponding $s$-wave scattering phase shifts, low-energy scattering parameters, and binding energies when applicable are extracted using L\"uscher's formalism. While the results are consistent with most of the systems being bound at this pion mass, the interactions in the spin-triplet $\mathrm{\ensuremath{\Sigma}}N$ and $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Xi}}$ channels are found to be repulsive and do not support bound states. Using results from previous studies of these systems at a larger pion mass, an extrapolation of the binding energies to the physical point is performed and is compared with available experimental values and phenomenological predictions. The low-energy coefficients in pionless effective field theory (EFT) relevant for two-baryon interactions, including those responsible for $SU(3)$ flavor-symmetry breaking, are constrained. The $SU(3)$ flavor 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.

Predicting the [formula omitted] bound states as the partners of [formula omitted

In this work, we investigate the SU(3) flavor symmetry, heavy quark spin symmetry and their breaking effects in the di-meson systems. We prove the existence of the [D‾s∗Ds∗]0++, [D‾s∗Ds/D‾sDs∗]1+-, and [D‾s∗Ds∗]1+- bound states as the consequence of two prerequisites in the SU(3) flavor symmetry and heavy quark spin symmetry. The first prerequisite, the X(3872) as the weakly D‾∗D/D‾D∗ bound state is supported by its mass and decay branching ratios. The second prerequisite, the existence of the [D‾sDs]0++ bound state is supported by the lattice QCD calculation and the observation of χc0(3930) by the LHCb Collaboration. We hope the future experimental analyses can search for these bound states in the B→D(s)(*)D‾(s)(*)h processes (h denotes the light hadrons). The [D‾s∗Ds∗]0++ bound state is also expected to be reconstructed in the J/ψϕ final state in the B→J/ψϕK decay.

Two-Loop Analysis of the Pion Mass Dependence of the ρ Meson.

Analyzing the pion mass dependence of ππ scattering phase shifts beyond the low-energy region requires the unitarization of the amplitudes from chiral perturbation theory. In the two-flavor theory, unitarization via the inverse-amplitude method (IAM) can be justified from dispersion relations, which is therefore expected to provide reliable predictions for the pion mass dependence of results from lattice QCD calculations. In this work, we provide compact analytic expression for the two-loop partial-wave amplitudes for J=0, 1, 2 required for the IAM at subleading order. To analyze the pion mass dependence of recent lattice QCD results for the P wave, we develop a fit strategy that for the first time allows us to perform stable two-loop IAM fits and assess the chiral convergence of the IAM approach. While the comparison of subsequent orders suggests a breakdown scale not much below the ρ mass, a detailed understanding of the systematic uncertainties of lattice QCD data is critical to obtain acceptable fits, especially at larger pion masses.

Deep inelastic scattering on the quark-gluon plasma

We provide an interpretation of the structure functions of a thermal medium such as the quark-gluon plasma in terms of the scattering of an incoming electron on the medium via the exchange of a spacelike photon. We then focus on the deep-inelastic scattering (DIS) regime, and formulate the corresponding moment sum rules obeyed by the structure functions. Accordingly, these moments are given by the thermal expectation value of twist-two operators, which is computable from first principles in lattice QCD for the first few moments. We also show how lattice QCD calculations can be used to probe how large the photon virtuality needs to be in order for the Bjorken scaling of structure functions to set in. Finally, we provide the parton-model interpretation of the structure functions in the Bjorken limit and test its consistency. As in DIS on the proton, the kinematic variable x is proportional to the longitudinal momentum carried by the partons, however x ranges from zero to infinity. Choosing the parton momentum parametrization to be xT u where u is the fluid four-velocity and T its temperature in the rest frame, the parton distribution function for a plasma of non-interacting quarks is proportional to x log(1 + e−x/2).

The D\u2217D\u03c0 and B\u2217B\u03c0 couplings from light-cone sum rules

We revisit the calculation of the strong couplings D∗Dπ and B∗Bπ from the QCD light-cone sum rules using the pion light-cone distribution amplitudes. The accuracy of the correlation function, calculated from the operator product expansion near the light-cone, is upgraded by taking into account the gluon radiative corrections to the twist-3 terms. The double spectral density of the correlation function, including the twist-2, 3 terms at mathcal{O}left({alpha}_sright) and the twist-4 LO terms, is presented in an analytical form for the first time. This form allows us to use various versions of the quark-hadron duality regions in the double dispersion relation underlying the sum rules. We predict {g}_{D^{ast } Dpi}={14.1}_{-1.2}^{+1.3} and {g}_{B^{ast } Bpi}={30.0}_{-2.4}^{+2.6} when the decay constants of heavy mesons entering the light-cone sum rule are taken from lattice QCD results. We compare our results with the experimental value for the charmed meson coupling and with the lattice QCD calculations.

Extraction of Next-to-Next-to-Leading-Order Parton Distribution Functions from Lattice QCD Calculations.

We present for the first time complete next-to-next-to-leading-order coefficient functions to match flavor nonsinglet quark correlation functions in position space, which are calculable in lattice QCD, to parton distribution functions (PDFs). Using PDFs extracted from experimental data and our calculated matching coefficients, we predict valence-quark correlation functions that can be confronted by lattice QCD calculations. The uncertainty of our predictions is greatly reduced with higher order matching coefficients. By performing Fourier transformation, we also obtain matching coefficients for corresponding quasi-PDFs and pseudo-PDFs. Our method of calculations can be readily generalized to evaluate the matching coefficients for sea-quark and gluon correlation functions, making the program to extract partonic structure of hadrons from lattice QCD calculations comparable with and complementary to that from experimental measurements.

Three-Bosons in a Finite 4D Euclidean Volume

The formulation of the Minkowskian and Euclidean homogeneous Faddeev-Bethe-Salpeter (FBS) equations for a three-boson system with a contact interaction in an infinite four-dimensional (4D) volume are reviewed, and the Euclidean one in a finite 4D volume is derived and discussed. In an Euclidean 4D box the periodic boundary conditions leading to quantized momentum turns the continuum homogeneous FBS equation into a discretized form, with solutions determining the spectrum running above the scattering threshold. A truncated set of the discretized FBS equation is solved for three-pions in the maximum isospin state, with scattering length, pion mass and 4D volume from recent lattice QCD calculations, and the results of the approximate FBS equation for the ground state mass are in qualitative agreement with the lattice result. The approximate dependence of the ground state mass on the pion-pion scattering length, pion mass and 4D volume is also suggested.

Lattice QCD study of static quark and antiquark correlations at finite T via entanglement entropies

With the aim of clarification of color correlations among quarks, we investigate the color correlation between a static quark and an antiquark (static $q\bar q$) below and above the phase transition temperature $T_c$ through the entanglement entropy(EE). By a quenched lattice QCD calculation on an anisotropic lattice adopting the standard Wilson gauge action in the Coulomb gauge, we compute a reduced density matrix $\rho$ defined in the color space, and the entanglement entropy $S_{\rm EE}$ constructed from $\rho$. The spatial volume is $L^3 = 24^3$ and the temporal extents are $N_T = 12,13,14,15,16,18,20$ and $24$, with a gauge coupling $\beta = 5.75$ and a renormalized anisotropy $\xi = 4.0$, which corresponds to temperatures between 180 and 370 MeV. From an analysis of $\rho$ and $S_{\rm EE}$, the color correlation between $q\bar q$ pairs is obtained as a function of the interquark distance $R$ and the temperature $T$. Below $T_c$, the $R$-dependence of the color correlation resembles that at $T=0$: the quark's color correlation gradually decreases as $R$ increases due to the color screening by in-between gluons. Above $T_c$, due to the deconfinement phase transition, the color correlation among quarks is found to quickly dissappear. Further, we investigate the color screening effect via the screening mass defined by $\rho$, and discuss the differences in the screening properties between the small and large R regions.

Gluon distributions and their applications to Ioffe-time distributions

We investigate unpolarized and polarized gluon distributions and their applications to the Ioffe-time distributions, which are related to lattice QCD calculations of parton distribution functions. Guided by the counting rules based on the perturbative QCD at large momentum fraction $x$ and the color coherence of gluon couplings at small $x$, we parametrize gluon distributions in the helicity basis. By fitting the unpolarized gluon distribution, the inferred polarized gluon distribution from our parametrization agrees with the one from global analysis. A simultaneous fit to both unpolarized and polarized gluon distributions is also performed to explore the model uncertainty. The agreement with the global analysis supports the $(1-x)$ power suppression of the helicity-antialigned distribution relative to the helicity-aligned distribution. The corresponding Ioffe-time distributions and their asymptotic expansions are calculated from the gluon distributions. Our results of the Ioffe-time distributions can provide guidance to the extrapolation of lattice QCD data to the region lacking precise gluonic matrix elements. Therefore, they can help regulate the ill-posed inverse problem associated with extracting the gluon distributions from discrete data from first-principle calculations, which are available in a limited range of the nucleon momentum and the spatial separation between the gluonic currents. Given various limitations in obtaining lattice QCD data at large Ioffe time, phenomenological approaches can provide important complementary information to extract the gluon distributions in the entire $x$ region. The possibility of investigating higher-twist effects and other systematic uncertainties in the contemporary first-principle calculations of parton distributions from phenomenologically well-determined Ioffe-time distributions in the large Ioffe-time region is also discussed.

Momentum dependent mean-fields of (anti)hyperons

We investigate the in-medium properties of hyperons and anti-hyperons in the framework of the Non-Linear Derivative (NLD) model. We focus on the momentum dependence of in-medium strangeness optical potentials. The NLD model is based on the simplicity of the well-established Relativistic Mean-Field (RMF) approximation, but it incorporates an explicit momentum dependence on a field-theoretical level. The extension of the NLD model to the (anti)baryon-octet is formulated in the spirit of SU(6) and G-parity arguments. It is shown that with an appropriate choice of momentum cut-offs the Λ, Σ and Ξ optical potentials are consistent with recent studies of the chiral effective field theory and Lattice-QCD calculations over a wide momentum region. In addition, we present NLD predictions for the in-medium momentum dependence of Λ‾-, Σ‾- and Ξ‾-hyperons. This work is important for future experimental studies such as CBM, PANDA at the Facility for Antiproton and Ion Research (FAIR). It is relevant for nuclear astrophysics too.

Distillation at high momentum

Extraction of hadronic observables at finite-momenta from Lattice QCD (LQCD) is constrained by the well-known signal-to-noise problems afflicting all such LQCD calculations. Traditional quark smearing algorithms are commonly used tools to improve the statistical quality of hadronic $n$-point functions, provided operator momenta are small. The momentum smearing algorithm of Bali et al. extends the range of momenta that are cleanly accessible, and has facilitated countless novel lattice calculations. Momentum smearing has, however, not been explicitly demonstrated within the framework of distillation. In this work we extend the momentum-smearing idea, by exploring a few modifications to the distillation framework. Together with enhanced time slice sampling and expanded operator bases engendered by distillation, we find ground-state nucleon energies can be extracted reliably for $\left|\vec{p}\right|\lesssim3\text{ GeV}$ and matrix elements featuring a large momentum dependence can be resolved.